AI Avatar Tools

AI Avatar Tools — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

• 

  Supertoroid

  In geometry and computer graphics, a supertoroid or supertorus is usually understood to be a family of doughnut-like surfaces (technically, a topological torus) whose shape is defined by mathematical formulas similar to those that define the superellipsoids. The plural of "supertorus" is either supertori or supertoruses. The family was described and named by Alan Barr in 1994. Barr's supertoroids have been fairly popular in computer graphics as a convenient model for many objects, such as smooth frames for rectangular things. One quarter of a supertoroid can provide a smooth and seamless 90-degree joint between two superquadric cylinders. However, they are not algebraic surfaces (except in special cases). == Formulas == Alan Barr's supertoroids are defined by parametric equations similar to the trigonometric equations of the torus, except that the sine and cosine terms are raised to arbitrary powers. Namely, the generic point P(u, v) of the surface is given by P ( u , v ) = ( X ( u , v ) Y ( u , v ) Z ( u , v ) ) = ( ( a + C u s ) C v t ( b + C u s ) S v t S u s ) {\displaystyle P(u,v)=\left({\begin{array}{c}X(u,v)\\Y(u,v)\\Z(u,v)\end{array}}\right)=\left({\begin{array}{c}(a+C_{u}^{s})C_{v}^{t}\\(b+C_{u}^{s})S_{v}^{t}\\S_{u}^{s}\end{array}}\right)} where C θ ε = sgn ⁡ ( cos ⁡ θ ) | cos ⁡ θ | ε , S θ ε = sgn ⁡ ( sin ⁡ θ ) | sin ⁡ θ | ε , {\displaystyle {\begin{aligned}C_{\theta }^{\varepsilon }&=\operatorname {sgn} (\cos \theta )\,\left|\,\cos \theta \,\right|^{\varepsilon },\\S_{\theta }^{\varepsilon }&=\operatorname {sgn} (\sin \theta )\ \left|\,\sin \theta \ \right|^{\varepsilon },\end{aligned}}} sgn is the sign function, and the parameters u, v range from 0 to 360 degrees (0 to 2π radians). In these formulas, the parameter s > 0 controls the "squareness" of the vertical sections, t > 0 controls the squareness of the horizontal sections, and a, b ≥ 1 are the major radii in the x and y directions. With s = t = 1 and a = b = R one obtains the ordinary torus with major radius R and minor radius 1, with the center at the origin and rotational symmetry about the z-axis. In general, the supertorus defined as above spans the intervals: − ( a + 1 ) ≤ x ≤ + ( a + 1 ) − ( b + 1 ) ≤ y ≤ + ( b + 1 ) − 1 ≤ z ≤ + 1 {\displaystyle {\begin{array}{rcccl}-(a+1)&\leq &x&\leq &+(a+1)\\[4pt]-(b+1)&\leq &y&\leq &+(b+1)\\[4pt]-1&\leq &z&\leq &+1\end{array}}} The whole shape is symmetric about the planes x = 0, y = 0, and z = 0. The hole runs in the z direction and spans the intervals − ( a − 1 ) ≤ x ≤ + ( a − 1 ) − ( b − 1 ) ≤ y ≤ + ( b − 1 ) − ∞ ≤ z ≤ + ∞ {\displaystyle {\begin{array}{rcccl}-(a-1)&\leq &x&\leq &+(a-1)\\[4pt]-(b-1)&\leq &y&\leq &+(b-1)\\[4pt]-\infty &\leq &z&\leq &+\infty \end{array}}} A curve of constant u on this surface is a horizontal Lamé curve with exponent ⁠ 2 t , {\displaystyle {\tfrac {2}{t}},} ⁠ scaled in x and y and displaced in z. A curve of constant v, projected on the plane x = 0 or y = 0, is a Lamé curve with exponent ⁠ 2 s , {\displaystyle {\tfrac {2}{s}},} ⁠ scaled and horizontally shifted. If v = 0, the curve is planar and spans the intervals: a − 1 ≤ x ≤ a + 1 − 1 ≤ z ≤ + 1 {\displaystyle {\begin{array}{rcccl}a-1&\leq &x&\leq &a+1\\[4pt]-1&\leq &z&\leq &+1\end{array}}} and similarly if v = 90°, 180°, 270°. The curve is also planar if a = b. In general, if a ≠ b and v is not a multiple of 90 degrees, the curve of constant v will not be planar; and, conversely, a vertical plane section of the supertorus will not be a Lamé curve. The basic supertoroid shape defined above is often modified by non-uniform scaling to yield supertoroids of specific width, length, and vertical thickness. == Plotting code == The following GNU Octave code generates plots of a supertorus:

  Read more →
• 

  Document mosaicing

  Document mosaicing is a process that stitches multiple, overlapping snapshot images of a document together to produce one large, high resolution composite. The document is slid under a stationary, over-the-desk camera by hand until all parts of the document are snapshotted by the camera's field of view. As the document slid under the camera, all motion of the document is coarsely tracked by the vision system. The document is periodically snapshotted such that the successive snapshots are overlap by about 50%. The system then finds the overlapped pairs and stitches them together repeatedly until all pairs are stitched together as one piece of document. The document mosaicing can be divided into four main processes. Tracking Feature detecting Correspondences establishing Images mosaicing. == Tracking (simple correlation process) == In this process, the motion of the document slid under the camera is coarsely tracked by the system. Tracking is performed by a process called simple correlation process. In the first frame of snapshots, a small patch is extracted from the center of the image as a correlation template. The correlation process is performed in the four times size of the patch area of the next frame. The motion of the paper is indicated by the peak in the correlation function. The peak in the correlation function indicates the motion of the paper. The template is resampled from this frame and the tracking continues until the template reaches the edge of the document. After the template reaches the edge of the document, another snapshot is taken and the tracking process performs repeatedly until the whole document is imaged. The snapshots are stored in an ordered list to facilitate pairing the overlapped images in later processes. == Feature detecting for efficient matching == Feature detection is the process of finding the transformation that aligns one image with another. There are two main approaches for feature detection. Feature-based approach : Motion parameters are estimated from point correspondences. This approach is suitable for the case that there is plenty supply of stable and detectable features. Featureless approach : When the motion between the two images is small, the motion parameters are estimated using optical flow. On the other hand, when the motion between the two images is large, the motion parameters are estimated using generalised cross-correlation. However, this approach requires a computationally expensive resources. Each image is segmented into a hierarchy of columns, lines, and words to match the organised sets of features across images. Skew angle estimation and columns, lines and words finding are the examples of feature detection operations. === Skew angle estimation === Firstly, the angle that the rows of text make with the image raster lines (skew angle) is estimated. It is assumed to lie in the range of ±20°. A small patch of text in the image is selected randomly and then rotated in the range of ±20° until the variance of the pixel intensities of the patch summed along the raster lines is maximised. To ensure that the found skew angle is accurate, the document mosaic system performs calculation at many image patches and derive the final estimation by finding the average of the individual angles weighted by the variance of the pixel intensities of each patch. === Columns, lines and words finding === In this operation, the de-skewed document is intuitively segmented into a hierarchy of columns, lines and words. The sensitivity to illumination and page coloration of the de-skewed document can be removed by applying a Sobel operator to the de-skewed image and thresholding the output to obtain the binary gradient, de-skewed image. The operation can be roughly separated into 3 steps: column segmentation, line segmentation and word segmentation. Columns are easily segmented from the binary gradient, de-skewed images by summing pixels vertically. Baselines of each row are segmented in the same way as the column segmentation process but horizontally. Finally, individual words are segmented by applying the vertical process at each segmented row. These segmentations are important because the document mosaic is created by matching the lower right corners of words in overlapping images pair. Moreover, the segmentation operation can organize the list of images in the context of a hierarchy of rows and column reliably. The segmentation operation involves a considerable amount of summing in the binary gradient, de-skewed images, which done by construct a matrix of partial sums whose elements are given by p i y = ∑ u = 1 i ∑ v = 1 j b u v {\displaystyle p_{iy}=\sum _{u=1}^{i}\sum _{v=1}^{j}b_{uv}} The matrix of partial sums is calculated in one pass through the binary gradient, de-skewed image. ∑ u = u 1 u 2 ∑ v = v 1 v 2 b u v = p u 2 v 2 + p u 1 v 1 − p u 1 v 2 − p u 2 v 1 {\displaystyle \sum _{u=u_{1}}^{u_{2}}\sum _{v=v_{1}}^{v_{2}}b_{uv}=p_{u_{2}v_{2}}+p_{u_{1}v_{1}}-p_{u_{1}v_{2}}-p_{u_{2}v_{1}}} == Correspondences establishing == The two images are now organized in hierarchy of linked lists in following structure : image=list of columns row=list of words column=list of row word=length (in pixels) At the bottom of the structure, the length of each word is recorded for establishing correspondence between two images to reduce to search only the corresponding structures for the groups of words with the matching lengths. === Seed match finding === A seed match finding is done by comparing each row in image1 with each row in image2. The two rows are then compared to each other by every word. If the length (in pixel) of the two words (one from image1 and one from image2) and their immediate neighbours agree with each other within a predefined tolerance threshold (5 pixels, for example), then they are assumed to match. The row of each image is assumed a match if there are three or more word matches between the two rows. The seed match finding operation is terminated when two pairs of consecutive row match are found. === Match list building === After finishing a seed match finding operation, the next process is to build the match list to generate the correspondences points of the two images. The process is done by searching the matching pairs of rows away from the seed row. == Images mosaicing == Given the list of corresponding points of the two images, finding the transformation of the overlapping portion of the images is the next process. Assuming a pinhole camera model, the transformation between pixels (u,v) of image 1 and pixels (u0, v0) of image 2 is demonstrated by a plane-to-plane projectivity. [ s u ′ s v ′ s ] = [ p 11 p 12 p 13 p 21 p 22 p 23 p 31 p 32 1 ] [ u v 1 ] E q .1 {\displaystyle \left[{\begin{array}{c}su'\\sv'\\s\end{array}}\right]=\left[{\begin{array}{ccc}p_{11}&p_{12}&p_{13}\\p_{21}&p_{22}&p_{23}\\p_{31}&p_{32}&1\end{array}}\right]\left[{\begin{array}{c}u\\v\\1\end{array}}\right]\qquad Eq.1} The parameters of the projectivity is found from four pairs of matching points. RANSAC regression technique is used to reject outlying matches and estimate the projectivity from the remaining good matches. The projectivity is fine-tuned using correlation at the corners of the overlapping portion to obtain four correspondences to sub-pixel accuracy. Therefore, image1 is then transformed into image2's coordinate system using Eq.1. The typical result of the process is shown in Figure 5. === Many images coping === Finally, the whole page composition is built up by mapping all the images into the coordinate system of an "anchor" image, which is normally the one nearest the page center. The transformations to the anchor frame are calculated by concatenating the pair-wise transformations found earlier. The raw document mosaic is shown in Figure 6. However, there might be a problem of non-consecutive images that are overlap. This problem can be solved by performing Hierarchical sub-mosaics. As shown in Figure 7, image1 and image2 are registered, as are image3 and image4, creating two sub-mosaics. These two sub-mosaics are later stitched together in another mosaicing process. == Applied areas == There are various areas that the technique of document mosaicing can be applied to such as : Text segmentation of images of documents Document Recognition Interaction with paper on the digital desk Video mosaics for virtual environments Image registration techniques == Relevant research papers == Huang, T.S.; Netravali, A.N. (1994). "Motion and structure from feature correspondences: A review". Proceedings of the IEEE. 82 (2): 252–268. doi:10.1109/5.265351. D.G. Lowe. [1] Perceptual Organization and Visual Recognition. Kluwer Academic Publishers, Boston, 1985. Irani, M.; Peleg, S. (1991). "Improving resolution by image registration". CVGIP: Graphical Models and Image Processing. 53 (3): 231–239. doi:10.1016/1049-9652(91)90045-L. S2CID 4834546. Shivakumara, P.; Kumar, G. Hemantha; Guru, D. S.; Nagabhushan, P. (2006). "

  Read more →
• 

  Scale-space axioms

  In image processing and computer vision, a scale space framework can be used to represent an image as a family of gradually smoothed images. This framework is very general and a variety of scale space representations exist. A typical approach for choosing a particular type of scale space representation is to establish a set of scale-space axioms, describing basic properties of the desired scale-space representation and often chosen so as to make the representation useful in practical applications. Once established, the axioms narrow the possible scale-space representations to a smaller class, typically with only a few free parameters. A set of standard scale space axioms, discussed below, leads to the linear Gaussian scale-space, which is the most common type of scale space used in image processing and computer vision. == Scale space axioms for the linear scale-space representation == The linear scale space representation L ( x , y , t ) = ( T t f ) ( x , y ) = g ( x , y , t ) ∗ f ( x , y ) {\displaystyle L(x,y,t)=(T_{t}f)(x,y)=g(x,y,t)f(x,y)} of signal f ( x , y ) {\displaystyle f(x,y)} obtained by smoothing with the Gaussian kernel g ( x , y , t ) {\displaystyle g(x,y,t)} satisfies a number of properties 'scale-space axioms' that make it a special form of multi-scale representation: linearity T t ( a f + b h ) = a T t f + b T t h {\displaystyle T_{t}(af+bh)=aT_{t}f+bT_{t}h} where f {\displaystyle f} and h {\displaystyle h} are signals while a {\displaystyle a} and b {\displaystyle b} are constants, shift invariance T t S ( Δ x , Δ y ) f = S ( Δ x , Δ y ) T t f {\displaystyle T_{t}S_{(\Delta x,\Delta _{y})}f=S_{(\Delta x,\Delta _{y})}T_{t}f} where S ( Δ x , Δ y ) {\displaystyle S_{(\Delta x,\Delta _{y})}} denotes the shift (translation) operator ( S ( Δ x , Δ y ) f ) ( x , y ) = f ( x − Δ x , y − Δ y ) {\displaystyle (S_{(\Delta x,\Delta _{y})}f)(x,y)=f(x-\Delta x,y-\Delta y)} semi-group structure g ( x , y , t 1 ) ∗ g ( x , y , t 2 ) = g ( x , y , t 1 + t 2 ) {\displaystyle g(x,y,t_{1})g(x,y,t_{2})=g(x,y,t_{1}+t_{2})} with the associated cascade smoothing property L ( x , y , t 2 ) = g ( x , y , t 2 − t 1 ) ∗ L ( x , y , t 1 ) {\displaystyle L(x,y,t_{2})=g(x,y,t_{2}-t_{1})L(x,y,t_{1})} existence of an infinitesimal generator A {\displaystyle A} ∂ t L ( x , y , t ) = ( A L ) ( x , y , t ) {\displaystyle \partial _{t}L(x,y,t)=(AL)(x,y,t)} non-creation of local extrema (zero-crossings) in one dimension, non-enhancement of local extrema in any number of dimensions ∂ t L ( x , y , t ) ≤ 0 {\displaystyle \partial _{t}L(x,y,t)\leq 0} at spatial maxima and ∂ t L ( x , y , t ) ≥ 0 {\displaystyle \partial _{t}L(x,y,t)\geq 0} at spatial minima, rotational symmetry g ( x , y , t ) = h ( x 2 + y 2 , t ) {\displaystyle g(x,y,t)=h(x^{2}+y^{2},t)} for some function h {\displaystyle h} , scale invariance g ^ ( ω x , ω y , t ) = h ^ ( ω x φ ( t ) , ω x φ ( t ) ) {\displaystyle {\hat {g}}(\omega _{x},\omega _{y},t)={\hat {h}}({\frac {\omega _{x}}{\varphi (t)}},{\frac {\omega _{x}}{\varphi (t)}})} for some functions φ {\displaystyle \varphi } and h ^ {\displaystyle {\hat {h}}} where g ^ {\displaystyle {\hat {g}}} denotes the Fourier transform of g {\displaystyle g} , positivity g ( x , y , t ) ≥ 0 {\displaystyle g(x,y,t)\geq 0} , normalization ∫ x = − ∞ ∞ ∫ y = − ∞ ∞ g ( x , y , t ) d x d y = 1 {\displaystyle \int _{x=-\infty }^{\infty }\int _{y=-\infty }^{\infty }g(x,y,t)\,dx\,dy=1} . In fact, it can be shown that the Gaussian kernel is a unique choice given several different combinations of subsets of these scale-space axioms: most of the axioms (linearity, shift-invariance, semigroup) correspond to scaling being a semigroup of shift-invariant linear operator, which is satisfied by a number of families integral transforms, while "non-creation of local extrema" for one-dimensional signals or "non-enhancement of local extrema" for higher-dimensional signals are the crucial axioms which relate scale-spaces to smoothing (formally, parabolic partial differential equations), and hence select for the Gaussian. The Gaussian kernel is also separable in Cartesian coordinates, i.e. g ( x , y , t ) = g ( x , t ) g ( y , t ) {\displaystyle g(x,y,t)=g(x,t)\,g(y,t)} . Separability is, however, not counted as a scale-space axiom, since it is a coordinate dependent property related to issues of implementation. In addition, the requirement of separability in combination with rotational symmetry per se fixates the smoothing kernel to be a Gaussian. There exists a generalization of the Gaussian scale-space theory to more general affine and spatio-temporal scale-spaces. In addition to variabilities over scale, which original scale-space theory was designed to handle, this generalized scale-space theory also comprises other types of variabilities, including image deformations caused by viewing variations, approximated by local affine transformations, and relative motions between objects in the world and the observer, approximated by local Galilean transformations. In this theory, rotational symmetry is not imposed as a necessary scale-space axiom and is instead replaced by requirements of affine and/or Galilean covariance. The generalized scale-space theory leads to predictions about receptive field profiles in good qualitative agreement with receptive field profiles measured by cell recordings in biological vision. In the computer vision, image processing and signal processing literature there are many other multi-scale approaches, using wavelets and a variety of other kernels, that do not exploit or require the same requirements as scale space descriptions do; please see the article on related multi-scale approaches. There has also been work on discrete scale-space concepts that carry the scale-space properties over to the discrete domain; see the article on scale space implementation for examples and references.

  Read more →
• 

  Gorn address

  A Gorn address (Gorn, 1967) is a method of identifying and addressing any node within a tree data structure. This notation is often used for identifying nodes in a parse tree defined by phrase structure rules. The Gorn address is a sequence of zero or more integers conventionally separated by dots, e.g., 0 or 1.0.1. The root which Gorn calls can be regarded as the empty sequence. And the j {\displaystyle j} -th child of the i {\displaystyle i} -th child has an address i . j {\displaystyle i.j} , counting from 0. It is named after American computer scientist Saul Gorn.

  Read more →
• 

  Intelligent automation

  Intelligent automation (IA), or intelligent process automation, is a software term that refers to a combination of artificial intelligence (AI) and robotic process automation (RPA). Companies use intelligent automation to cut costs and streamline tasks by using artificial-intelligence-powered robotic software to mitigate repetitive tasks. As it accumulates data, the system learns in an effort to improve its efficiency. Intelligent automation applications consist of, but are not limited to, pattern analysis, data assembly, and classification. The term is similar to hyperautomation, a concept identified by research group Gartner as being one of the top technology trends of 2020. == Technology == Intelligent automation applies the assembly line concept of breaking tasks into repetitive steps to improve business processes. Rather than having humans perform each step, intelligent automation can replace steps with an intelligent software robot, improving efficiency. Intelligent automation integrates robotic process automation (RPA) with artificial intelligence techniques (such as machine learning, natural-language processing, and computer vision) enabling systems to interpret data, make decisions, and adapt to changing inputs. Modern platforms use a layered architecture combining workflow orchestration, low-code tools, integration middleware, and AI services to coordinate bots and data pipelines across organisational systems. == Applications == Intelligent automation is used to process unstructured content. Common real-world applications include self-driving cars, self-checkouts at grocery stores, smart home assistants, and appliances. Businesses can apply data and machine learning to build predictive analytics that react to consumer behavior changes, or to implement RPA to improve manufacturing floor operations. For example, the technology has also been used to automate the workflow behind distributing COVID-19 vaccines. Data provided by hospital systems’ electronic health records can be processed to identify and educate patients, and schedule vaccinations. Intelligent automation can provide real-time insights on profitability and efficiency. However, in an April 2022 survey by Alchemmy, despite three quarters of businesses acknowledging the importance of Artificial Intelligence to their future development, just a quarter of business leaders (25%) considered Intelligent Automation a “game changer” in understanding current performance. 42% of CTOs see “shortage of talent” as the main obstacle to implementing Intelligent Automation in their business, while 36% of CEOs see ‘upskilling and professional development of existing workforce’ as the most significant adoption barrier. IA is becoming increasingly accessible for firms of all sizes. With this in mind, it is expected to continue to grow rapidly in all industries. This technology has the potential to change the workforce. As it advances, it will be able to perform increasingly complex and difficult tasks. In addition, this may expose certain workforce issues as well as change how tasks are allocated. Tools such as Semrush's AI Visibility Toolkit and Enterprise AIO reflect these developments by analysing how entities are referenced and represented within responses produced by large-language-model-based systems. == Benefits == Streamline processes: Repetitive manual tasks can put a strain on the workforce. However, with AI agents, these tasks can be automated to allow teams to focus on more important matters that require human cognition. Intelligent automation can also be used to mitigate tasks with human error which in turn increases proficiency. This allows the opportunity for firms to scale production without the traditional negative consequences such as reduced quality or increased risk. Customer service improvement: Customer service can be significantly improved, providing the firm with a competitive advantage. IA utilizing chat features allows for instant curated responses to customers. In addition, it can give updates to customers, make appointments, manage calls, and personalize campaigns. Flexibility: Due to the wide range of applications, IA is useful across a variety of fields, technologies, projects and industries. In addition, IA can be integrated with current automated systems in place. This allows for optimized systems unique to each firm to best fit their individual needs. == Capabilities == Cognitive automation: Employs AI techniques to assist humans in decision-making and task completion Natural language processing: Allows computers to automate knowledge work Business process management: Enhances the consistency and agility of corporate operations Process mining: Applies data mining methods to discover, analyze, and improve business processes Intelligent document processing: Utilizes OCR and other advanced technologies to extract data from documents and convert it into structured, usable data Computer vision: Allows computers to extract information from digital images, videos, and other visual inputs Integration automation: Establishes a unified platform with automated workflows that integrate data, applications, and devices.

  Read more →
• 

  Document mosaicing

  Document mosaicing is a process that stitches multiple, overlapping snapshot images of a document together to produce one large, high resolution composite. The document is slid under a stationary, over-the-desk camera by hand until all parts of the document are snapshotted by the camera's field of view. As the document slid under the camera, all motion of the document is coarsely tracked by the vision system. The document is periodically snapshotted such that the successive snapshots are overlap by about 50%. The system then finds the overlapped pairs and stitches them together repeatedly until all pairs are stitched together as one piece of document. The document mosaicing can be divided into four main processes. Tracking Feature detecting Correspondences establishing Images mosaicing. == Tracking (simple correlation process) == In this process, the motion of the document slid under the camera is coarsely tracked by the system. Tracking is performed by a process called simple correlation process. In the first frame of snapshots, a small patch is extracted from the center of the image as a correlation template. The correlation process is performed in the four times size of the patch area of the next frame. The motion of the paper is indicated by the peak in the correlation function. The peak in the correlation function indicates the motion of the paper. The template is resampled from this frame and the tracking continues until the template reaches the edge of the document. After the template reaches the edge of the document, another snapshot is taken and the tracking process performs repeatedly until the whole document is imaged. The snapshots are stored in an ordered list to facilitate pairing the overlapped images in later processes. == Feature detecting for efficient matching == Feature detection is the process of finding the transformation that aligns one image with another. There are two main approaches for feature detection. Feature-based approach : Motion parameters are estimated from point correspondences. This approach is suitable for the case that there is plenty supply of stable and detectable features. Featureless approach : When the motion between the two images is small, the motion parameters are estimated using optical flow. On the other hand, when the motion between the two images is large, the motion parameters are estimated using generalised cross-correlation. However, this approach requires a computationally expensive resources. Each image is segmented into a hierarchy of columns, lines, and words to match the organised sets of features across images. Skew angle estimation and columns, lines and words finding are the examples of feature detection operations. === Skew angle estimation === Firstly, the angle that the rows of text make with the image raster lines (skew angle) is estimated. It is assumed to lie in the range of ±20°. A small patch of text in the image is selected randomly and then rotated in the range of ±20° until the variance of the pixel intensities of the patch summed along the raster lines is maximised. To ensure that the found skew angle is accurate, the document mosaic system performs calculation at many image patches and derive the final estimation by finding the average of the individual angles weighted by the variance of the pixel intensities of each patch. === Columns, lines and words finding === In this operation, the de-skewed document is intuitively segmented into a hierarchy of columns, lines and words. The sensitivity to illumination and page coloration of the de-skewed document can be removed by applying a Sobel operator to the de-skewed image and thresholding the output to obtain the binary gradient, de-skewed image. The operation can be roughly separated into 3 steps: column segmentation, line segmentation and word segmentation. Columns are easily segmented from the binary gradient, de-skewed images by summing pixels vertically. Baselines of each row are segmented in the same way as the column segmentation process but horizontally. Finally, individual words are segmented by applying the vertical process at each segmented row. These segmentations are important because the document mosaic is created by matching the lower right corners of words in overlapping images pair. Moreover, the segmentation operation can organize the list of images in the context of a hierarchy of rows and column reliably. The segmentation operation involves a considerable amount of summing in the binary gradient, de-skewed images, which done by construct a matrix of partial sums whose elements are given by p i y = ∑ u = 1 i ∑ v = 1 j b u v {\displaystyle p_{iy}=\sum _{u=1}^{i}\sum _{v=1}^{j}b_{uv}} The matrix of partial sums is calculated in one pass through the binary gradient, de-skewed image. ∑ u = u 1 u 2 ∑ v = v 1 v 2 b u v = p u 2 v 2 + p u 1 v 1 − p u 1 v 2 − p u 2 v 1 {\displaystyle \sum _{u=u_{1}}^{u_{2}}\sum _{v=v_{1}}^{v_{2}}b_{uv}=p_{u_{2}v_{2}}+p_{u_{1}v_{1}}-p_{u_{1}v_{2}}-p_{u_{2}v_{1}}} == Correspondences establishing == The two images are now organized in hierarchy of linked lists in following structure : image=list of columns row=list of words column=list of row word=length (in pixels) At the bottom of the structure, the length of each word is recorded for establishing correspondence between two images to reduce to search only the corresponding structures for the groups of words with the matching lengths. === Seed match finding === A seed match finding is done by comparing each row in image1 with each row in image2. The two rows are then compared to each other by every word. If the length (in pixel) of the two words (one from image1 and one from image2) and their immediate neighbours agree with each other within a predefined tolerance threshold (5 pixels, for example), then they are assumed to match. The row of each image is assumed a match if there are three or more word matches between the two rows. The seed match finding operation is terminated when two pairs of consecutive row match are found. === Match list building === After finishing a seed match finding operation, the next process is to build the match list to generate the correspondences points of the two images. The process is done by searching the matching pairs of rows away from the seed row. == Images mosaicing == Given the list of corresponding points of the two images, finding the transformation of the overlapping portion of the images is the next process. Assuming a pinhole camera model, the transformation between pixels (u,v) of image 1 and pixels (u0, v0) of image 2 is demonstrated by a plane-to-plane projectivity. [ s u ′ s v ′ s ] = [ p 11 p 12 p 13 p 21 p 22 p 23 p 31 p 32 1 ] [ u v 1 ] E q .1 {\displaystyle \left[{\begin{array}{c}su'\\sv'\\s\end{array}}\right]=\left[{\begin{array}{ccc}p_{11}&p_{12}&p_{13}\\p_{21}&p_{22}&p_{23}\\p_{31}&p_{32}&1\end{array}}\right]\left[{\begin{array}{c}u\\v\\1\end{array}}\right]\qquad Eq.1} The parameters of the projectivity is found from four pairs of matching points. RANSAC regression technique is used to reject outlying matches and estimate the projectivity from the remaining good matches. The projectivity is fine-tuned using correlation at the corners of the overlapping portion to obtain four correspondences to sub-pixel accuracy. Therefore, image1 is then transformed into image2's coordinate system using Eq.1. The typical result of the process is shown in Figure 5. === Many images coping === Finally, the whole page composition is built up by mapping all the images into the coordinate system of an "anchor" image, which is normally the one nearest the page center. The transformations to the anchor frame are calculated by concatenating the pair-wise transformations found earlier. The raw document mosaic is shown in Figure 6. However, there might be a problem of non-consecutive images that are overlap. This problem can be solved by performing Hierarchical sub-mosaics. As shown in Figure 7, image1 and image2 are registered, as are image3 and image4, creating two sub-mosaics. These two sub-mosaics are later stitched together in another mosaicing process. == Applied areas == There are various areas that the technique of document mosaicing can be applied to such as : Text segmentation of images of documents Document Recognition Interaction with paper on the digital desk Video mosaics for virtual environments Image registration techniques == Relevant research papers == Huang, T.S.; Netravali, A.N. (1994). "Motion and structure from feature correspondences: A review". Proceedings of the IEEE. 82 (2): 252–268. doi:10.1109/5.265351. D.G. Lowe. [1] Perceptual Organization and Visual Recognition. Kluwer Academic Publishers, Boston, 1985. Irani, M.; Peleg, S. (1991). "Improving resolution by image registration". CVGIP: Graphical Models and Image Processing. 53 (3): 231–239. doi:10.1016/1049-9652(91)90045-L. S2CID 4834546. Shivakumara, P.; Kumar, G. Hemantha; Guru, D. S.; Nagabhushan, P. (2006). "

  Read more →
• 

  Netomi

  Netomi, formerly msg.ai, is an American artificial intelligence company and developer of chatbot technologies. == History == msg.ai was founded in May 2015 by Puneet Mehta. msg.ai worked with Sony Pictures to launch a chat bot on Facebook Messenger for a $100M film, Goosebumps and subsequently joined Y Combinator as a member of the Winter 2016 class. Later that year and in 2017, msg.ai completed two rounds of seed funding, led by Y Combinator and Index Ventures. In 2018, the company changed its name to Netomi. In 2019, the company raised $14.7 million in a Series A funding round also led by Index Ventures. In 2021, the company raised $30 million in a Series B funding round led by WndrCo LLC.

  Read more →
• 

  Neural network Gaussian process

  A Neural Network Gaussian Process (NNGP) is a Gaussian process (GP) obtained as the limit of a certain type of sequence of neural networks. Specifically, a wide variety of network architectures converges to a GP in the infinitely wide limit, in the sense of distribution. The concept constitutes an intensional definition, i.e., a NNGP is just a GP, but distinguished by how it is obtained. == Motivation == Bayesian networks are a modeling tool for assigning probabilities to events, and thereby characterizing the uncertainty in a model's predictions. Deep learning and artificial neural networks are approaches used in machine learning to build computational models which learn from training examples. Bayesian neural networks merge these fields. They are a type of neural network whose parameters and predictions are both probabilistic. While standard neural networks often assign high confidence even to incorrect predictions, Bayesian neural networks can more accurately evaluate how likely their predictions are to be correct. Computation in artificial neural networks is usually organized into sequential layers of artificial neurons. The number of neurons in a layer is called the layer width. When we consider a sequence of Bayesian neural networks with increasingly wide layers (see figure), they converge in distribution to a NNGP. This large width limit is of practical interest, since the networks often improve as layers get wider. And the process may give a closed form way to evaluate networks. NNGPs also appears in several other contexts: It describes the distribution over predictions made by wide non-Bayesian artificial neural networks after random initialization of their parameters, but before training; it appears as a term in neural tangent kernel prediction equations; it is used in deep information propagation to characterize whether hyperparameters and architectures will be trainable. It is related to other large width limits of neural networks. === Scope === The first correspondence result had been established in the 1995 PhD thesis of Radford M. Neal, then supervised by Geoffrey Hinton at University of Toronto. Neal cites David J. C. MacKay as inspiration, who worked in Bayesian learning. Today the correspondence is proven for: Single hidden layer Bayesian neural networks; deep fully connected networks as the number of units per layer is taken to infinity; convolutional neural networks as the number of channels is taken to infinity; transformer networks as the number of attention heads is taken to infinity; recurrent networks as the number of units is taken to infinity. In fact, this NNGP correspondence holds for almost any architecture: Generally, if an architecture can be expressed solely via matrix multiplication and coordinatewise nonlinearities (i.e., a tensor program), then it has an infinite-width GP. This in particular includes all feedforward or recurrent neural networks composed of multilayer perceptron, recurrent neural networks (e.g., LSTMs, GRUs), (nD or graph) convolution, pooling, skip connection, attention, batch normalization, and/or layer normalization. === Illustration === Every setting of a neural network's parameters θ {\displaystyle \theta } corresponds to a specific function computed by the neural network. A prior distribution p ( θ ) {\displaystyle p(\theta )} over neural network parameters therefore corresponds to a prior distribution over functions computed by the network. As neural networks are made infinitely wide, this distribution over functions converges to a Gaussian process for many architectures. The notation used in this section is the same as the notation used below to derive the correspondence between NNGPs and fully connected networks, and more details can be found there. The figure to the right plots the one-dimensional outputs z L ( ⋅ ; θ ) {\displaystyle z^{L}(\cdot ;\theta )} of a neural network for two inputs x {\displaystyle x} and x ∗ {\displaystyle x^{}} against each other. The black dots show the function computed by the neural network on these inputs for random draws of the parameters from p ( θ ) {\displaystyle p(\theta )} . The red lines are iso-probability contours for the joint distribution over network outputs z L ( x ; θ ) {\displaystyle z^{L}(x;\theta )} and z L ( x ∗ ; θ ) {\displaystyle z^{L}(x^{};\theta )} induced by p ( θ ) {\displaystyle p(\theta )} . This is the distribution in function space corresponding to the distribution p ( θ ) {\displaystyle p(\theta )} in parameter space, and the black dots are samples from this distribution. For infinitely wide neural networks, since the distribution over functions computed by the neural network is a Gaussian process, the joint distribution over network outputs is a multivariate Gaussian for any finite set of network inputs. == Discussion == === Infinitely wide fully connected network === This section expands on the correspondence between infinitely wide neural networks and Gaussian processes for the specific case of a fully connected architecture. It provides a proof sketch outlining why the correspondence holds, and introduces the specific functional form of the NNGP for fully connected networks. The proof sketch closely follows the approach by Novak and coauthors. ==== Network architecture specification ==== Consider a fully connected artificial neural network with inputs x {\displaystyle x} , parameters θ {\displaystyle \theta } consisting of weights W l {\displaystyle W^{l}} and biases b l {\displaystyle b^{l}} for each layer l {\displaystyle l} in the network, pre-activations (pre-nonlinearity) z l {\displaystyle z^{l}} , activations (post-nonlinearity) y l {\displaystyle y^{l}} , pointwise nonlinearity ϕ ( ⋅ ) {\displaystyle \phi (\cdot )} , and layer widths n l {\displaystyle n^{l}} . For simplicity, the width n L + 1 {\displaystyle n^{L+1}} of the readout vector z L {\displaystyle z^{L}} is taken to be 1. The parameters of this network have a prior distribution p ( θ ) {\displaystyle p(\theta )} , which consists of an isotropic Gaussian for each weight and bias, with the variance of the weights scaled inversely with layer width. This network is illustrated in the figure to the right, and described by the following set of equations: x ≡ input y l ( x ) = { x l = 0 ϕ ( z l − 1 ( x ) ) l > 0 z i l ( x ) = ∑ j W i j l y j l ( x ) + b i l W i j l ∼ N ( 0 , σ w 2 n l ) b i l ∼ N ( 0 , σ b 2 ) ϕ ( ⋅ ) ≡ nonlinearity y l ( x ) , z l − 1 ( x ) ∈ R n l × 1 n L + 1 = 1 θ = { W 0 , b 0 , … , W L , b L } {\displaystyle {\begin{aligned}x&\equiv {\text{input}}\\y^{l}(x)&=\left\{{\begin{array}{lcl}x&&l=0\\\phi \left(z^{l-1}(x)\right)&&l>0\end{array}}\right.\\z_{i}^{l}(x)&=\sum _{j}W_{ij}^{l}y_{j}^{l}(x)+b_{i}^{l}\\W_{ij}^{l}&\sim {\mathcal {N}}\left(0,{\frac {\sigma _{w}^{2}}{n^{l}}}\right)\\b_{i}^{l}&\sim {\mathcal {N}}\left(0,\sigma _{b}^{2}\right)\\\phi (\cdot )&\equiv {\text{nonlinearity}}\\y^{l}(x),z^{l-1}(x)&\in \mathbb {R} ^{n^{l}\times 1}\\n^{L+1}&=1\\\theta &=\left\{W^{0},b^{0},\dots ,W^{L},b^{L}\right\}\end{aligned}}} ==== ==== z l | y l {\displaystyle z^{l}|y^{l}} is a Gaussian process We first observe that the pre-activations z l {\displaystyle z^{l}} are described by a Gaussian process conditioned on the preceding activations y l {\displaystyle y^{l}} . This result holds even at finite width. Each pre-activation z i l {\displaystyle z_{i}^{l}} is a weighted sum of Gaussian random variables, corresponding to the weights W i j l {\displaystyle W_{ij}^{l}} and biases b i l {\displaystyle b_{i}^{l}} , where the coefficients for each of those Gaussian variables are the preceding activations y j l {\displaystyle y_{j}^{l}} . Because they are a weighted sum of zero-mean Gaussians, the z i l {\displaystyle z_{i}^{l}} are themselves zero-mean Gaussians (conditioned on the coefficients y j l {\displaystyle y_{j}^{l}} ). Since the z l {\displaystyle z^{l}} are jointly Gaussian for any set of y l {\displaystyle y^{l}} , they are described by a Gaussian process conditioned on the preceding activations y l {\displaystyle y^{l}} . The covariance or kernel of this Gaussian process depends on the weight and bias variances σ w 2 {\displaystyle \sigma _{w}^{2}} and σ b 2 {\displaystyle \sigma _{b}^{2}} , as well as the second moment matrix K l {\displaystyle K^{l}} of the preceding activations y l {\displaystyle y^{l}} , z i l ∣ y l ∼ G P ( 0 , σ w 2 K l + σ b 2 ) K l ( x , x ′ ) = 1 n l ∑ i y i l ( x ) y i l ( x ′ ) {\displaystyle {\begin{aligned}z_{i}^{l}\mid y^{l}&\sim {\mathcal {GP}}\left(0,\sigma _{w}^{2}K^{l}+\sigma _{b}^{2}\right)\\K^{l}(x,x')&={\frac {1}{n^{l}}}\sum _{i}y_{i}^{l}(x)y_{i}^{l}(x')\end{aligned}}} The effect of the weight scale σ w 2 {\displaystyle \sigma _{w}^{2}} is to rescale the contribution to the covariance matrix from K l {\displaystyle K^{l}} , while the bias is shared for all inputs, and so σ b 2 {\displaystyle \sigma _{b}^{2}} makes the z i l {\displaystyle z_{i}^{l}} for different datapoints more similar and

  Read more →
• 

  Exercism

  Exercism is an online, open-source, free coding platform that offers code practice and mentorship on 77 different programming languages. == History == Software developer Katrina Owen created Exercism while she was teaching programming at Jumpstart Labs. The platform was developed as an internal tool to solve the problem of her own students not receiving feedback on the coding problems they were practicing. Katrina put the site publicly online and found that people were sharing it with their friends, practicing together and giving each other feedback. Within 12 months, the site had organically grown to see over 6,000 users had submitted code or feedback, and hundreds of volunteers contribute to the languages or tooling on the platform. In 2016, Jeremy Walker joined as co-founder and CEO. In July 2018, the site was relaunched with a new design and centered around a formal mentoring mode, at which point Katrina stepped back from day-to-day involvement. == Product == In the past, the website differed from other coding platforms by requiring students to download exercises through a command line client, solve the code on their own computers then submit the solution for feedback, at which point they can also view other's solutions to the same problem. Since its second relaunch in 2021, solutions can be edited and submitted through a web editor, though the command line client remains available. Exercism has tracks for 74 programming languages. Among the notable languages taught: ABAP, C, C#, C++, CoffeeScript, Delphi, Elm, Erlang, F#, Gleam, Go, Java, JavaScript, Julia, Kotlin, Objective-C, PHP, Python, Raku, Red, Ruby, Rust, Scala, Swift, and V (Vlang). In 2023, the site launched a "12 in 23" challenge for users to learn the basics of 12 different languages - one per month in 2023. == Open source == The Exercism codebase is open source. In April 2016, it consisted of 50 repositories including website code, API code, command-line code and, most of all, over 40 stand-alone repositories for different language tracks. As of February 2024 Exercism has 14,344 contributors, maintains 366 repositories, and 19,603 mentors.

  Read more →
• 

  DBGallery

  DBGallery, short for Database Gallery, is a cloud-based Software as a Service (SaaS) and on-prem webserver for teams of various sizes. DBGallery enables users to centrally store, manage, catalog, archive, and securely share image, video, and document files. It facilitates version control, detects duplicates, and offers an intuitive and advanced search functionality, making assets easily accessible to all users. It takes advantage of current AI technologies to automatically add significant metadata to images, facilitates custom-trained AI models, and offers bespoke AI features. Additionally, DBGallery provides team management tools, workflow management, an activity audit trail, and other collaborative features that foster a productive environment for both internal and external stakeholders. == History == DBGallery's first public release was December 2007. Since then each year has seen continuous enhancements. 2013 added support for additional non-English languages in its meta-data. 2014 added support for creating custom data fields for tagging and search. In 2015 included the ability to auto-tag images using Reverse Geocoding. 2018 added artificial intelligence (AI) image recognition as a further addition to auto-tagging. March 2020 added complete image collection management via the web (e.g. file and folder drag and drop), a new collection dashboard, custom data layouts, and an improved audit trail. 2021 saw user experience improvements provided by improved styling and performance enhancements. Version 12 was released in October 2021. It added the ability to upload unlimited file sizes and made significant performance improvements for very large collections. June 2022 saw the release of a global duplicate images search. In late 2022, DBGallery began offering significantly reduced cloud storage cost, at a third of its previous prices, which played into its recent high-volume/high-capacity capabilities and its clients' subsequent demand for additional storage. 2023 saw improvements in user and role management, introduced it's mobile app (PWA), and improved custom-trained object detection. Release 14.0 in the spring of 2024 had large sharing improvements and a new find related images feature. Winter 2025's v15 release introduced AI-generated image descriptions, image-to-text, and facial recognition.

  Read more →
• 

  Augmented Analytics

  Augmented Analytics is an approach of data analytics that employs the use of machine learning and natural language processing to automate analysis processes normally done by a specialist or data scientist. The term was introduced in 2017 by Rita Sallam, Cindi Howson, and Carlie Idoine in a Gartner research paper. Augmented analytics is based on business intelligence and analytics. In the graph extraction step, data from different sources are investigated. == Defining Augmented Analytics == Machine Learning – a systematic computing method that uses algorithms to sift through data to identify relationships, trends, and patterns. It is a process that allows algorithms to dynamically learn from data instead of having a set base of programmed rules. Natural language generation (NLG) – a software capability that takes unstructured data and translates it into plain-English, readable, language. Automating Insights – using machine learning algorithms to automate data analysis processes. Natural Language Query – enabling users to query data using business terms that are either typed onto a search box or spoken. == Data Democratization == Data Democratization is the democratizing data access in order to relieve data congestion and get rid of any sense of data "gatekeepers". This process must be implemented alongside a method for users to make sense of the data. This process is used in hopes of speeding up company decision making and uncovering opportunities hidden in data. There are three aspects to democratising data: Data Parameterisation and Characterisation. Data Decentralisation using an OS of blockchain and DLT technologies, as well as an independently governed secure data exchange to enable trust. Consent Market-driven Data Monetisation. When it comes to connecting assets, there are two features that will accelerate the adoption and usage of data democratisation: decentralized identity management and business data object monetization of data ownership. It enables multiple individuals and organizations to identify, authenticate, and authorize participants and organizations, enabling them to access services, data or systems across multiple networks, organizations, environments, and use cases. It empowers users and enables a personalized, self-service digital onboarding system so that users can self-authenticate without relying on a central administration function to process their information. Simultaneously, decentralized identity management ensures the user is authorized to perform actions subject to the system’s policies based on their attributes (role, department, organization, etc.) and/ or physical location. == Use cases == Agriculture – Farmers collect data on water use, soil temperature, moisture content and crop growth, augmented analytics can be used to make sense of this data and possibly identify insights that the user can then use to make business decisions. Smart Cities – Many cities across the United States, known as Smart Cities collect large amounts of data on a daily basis. Augmented analytics can be used to simplify this data in order to increase effectiveness in city management (transportation, natural disasters, etc.). Analytic Dashboards – Augmented analytics has the ability to take large data sets and create highly interactive and informative analytical dashboards that assist in many organizational decisions. Augmented Data Discovery – Using an augmented analytics process can assist organizations in automatically finding, visualizing and narrating potentially important data correlations and trends. Data Preparation – Augmented analytics platforms have the ability to take large amounts of data and organize and "clean" the data in order for it to be usable for future analyses. Business – Businesses collect large amounts of data, daily. Some examples of types of data collected in business operations include; sales data, consumer behavior data, distribution data. An augmented analytics platform provides access to analysis of this data, which could be used in making business decisions.

  Read more →
• 

  Shape context

  Shape context is a feature descriptor used in object recognition. Serge Belongie and Jitendra Malik proposed the term in their paper "Matching with Shape Contexts" in 2000. == Theory == The shape context is intended to be a way of describing shapes that allows for measuring shape similarity and the recovering of point correspondences. The basic idea is to pick n points on the contours of a shape. For each point pi on the shape, consider the n − 1 vectors obtained by connecting pi to all other points. The set of all these vectors is a rich description of the shape localized at that point but is far too detailed. The key idea is that the distribution over relative positions is a robust, compact, and highly discriminative descriptor. So, for the point pi, the coarse histogram of the relative coordinates of the remaining n − 1 points, h i ( k ) = # { q ≠ p i : ( q − p i ) ∈ bin ( k ) } {\displaystyle h_{i}(k)=\#\{q\neq p_{i}:(q-p_{i})\in {\mbox{bin}}(k)\}} is defined to be the shape context of p i {\displaystyle p_{i}} . The bins are normally taken to be uniform in log-polar space. The fact that the shape context is a rich and discriminative descriptor can be seen in the figure below, in which the shape contexts of two different versions of the letter "A" are shown. (a) and (b) are the sampled edge points of the two shapes. (c) is the diagram of the log-polar bins used to compute the shape context. (d) is the shape context for the point marked with a circle in (a), (e) is that for the point marked as a diamond in (b), and (f) is that for the triangle. As can be seen, since (d) and (e) are the shape contexts for two closely related points, they are quite similar, while the shape context in (f) is very different. For a feature descriptor to be useful, it needs to have certain invariances. In particular it needs to be invariant to translation, scaling, small perturbations, and, depending on the application, rotation. Translational invariance comes naturally to shape context. Scale invariance is obtained by normalizing all radial distances by the mean distance α {\displaystyle \alpha } between all the point pairs in the shape although the median distance can also be used. Shape contexts are empirically demonstrated to be robust to deformations, noise, and outliers using synthetic point set matching experiments. One can provide complete rotational invariance in shape contexts. One way is to measure angles at each point relative to the direction of the tangent at that point (since the points are chosen on edges). This results in a completely rotationally invariant descriptor. But of course this is not always desired since some local features lose their discriminative power if not measured relative to the same frame. Many applications in fact forbid rotational invariance e.g. distinguishing a "6" from a "9". == Use in shape matching == A complete system that uses shape contexts for shape matching consists of the following steps (which will be covered in more detail in the Details of Implementation section): Randomly select a set of points that lie on the edges of a known shape and another set of points on an unknown shape. Compute the shape context of each point found in step 1. Match each point from the known shape to a point on an unknown shape. To minimize the cost of matching, first choose a transformation (e.g. affine, thin plate spline, etc.) that warps the edges of the known shape to the unknown (essentially aligning the two shapes). Then select the point on the unknown shape that most closely corresponds to each warped point on the known shape. Calculate the "shape distance" between each pair of points on the two shapes. Use a weighted sum of the shape context distance, the image appearance distance, and the bending energy (a measure of how much transformation is required to bring the two shapes into alignment). To identify the unknown shape, use a nearest-neighbor classifier to compare its shape distance to shape distances of known objects. == Details of implementation == === Step 1: Finding a list of points on shape edges === The approach assumes that the shape of an object is essentially captured by a finite subset of the points on the internal or external contours on the object. These can be simply obtained using the Canny edge detector and picking a random set of points from the edges. Note that these points need not and in general do not correspond to key-points such as maxima of curvature or inflection points. It is preferable to sample the shape with roughly uniform spacing, though it is not critical. === Step 2: Computing the shape context === This step is described in detail in the Theory section. === Step 3: Computing the cost matrix === Consider two points p and q that have normalized K-bin histograms (i.e. shape contexts) g(k) and h(k). As shape contexts are distributions represented as histograms, it is natural to use the χ2 test statistic as the "shape context cost" of matching the two points: C S = 1 2 ∑ k = 1 K [ g ( k ) − h ( k ) ] 2 g ( k ) + h ( k ) {\displaystyle C_{S}={\frac {1}{2}}\sum _{k=1}^{K}{\frac {[g(k)-h(k)]^{2}}{g(k)+h(k)}}} The values of this range from 0 to 1. In addition to the shape context cost, an extra cost based on the appearance can be added. For instance, it could be a measure of tangent angle dissimilarity (particularly useful in digit recognition): C A = 1 2 ‖ ( cos ⁡ ( θ 1 ) sin ⁡ ( θ 1 ) ) − ( cos ⁡ ( θ 2 ) sin ⁡ ( θ 2 ) ) ‖ {\displaystyle C_{A}={\frac {1}{2}}{\begin{Vmatrix}{\dbinom {\cos(\theta _{1})}{\sin(\theta _{1})}}-{\dbinom {\cos(\theta _{2})}{\sin(\theta _{2})}}\end{Vmatrix}}} This is half the length of the chord in unit circle between the unit vectors with angles θ 1 {\displaystyle \theta _{1}} and θ 2 {\displaystyle \theta _{2}} . Its values also range from 0 to 1. Now the total cost of matching the two points could be a weighted-sum of the two costs: C = ( 1 − β ) C S + β C A {\displaystyle C=(1-\beta )C_{S}+\beta C_{A}\!\,} Now for each point pi on the first shape and a point qj on the second shape, calculate the cost as described and call it Ci,j. This is the cost matrix. === Step 4: Finding the matching that minimizes total cost === Now, a one-to-one matching π ( i ) {\displaystyle \pi (i)} that matches each point pi on shape 1 and qj on shape 2 that minimizes the total cost of matching, H ( π ) = ∑ i C ( p i , q π ( i ) ) {\displaystyle H(\pi )=\sum _{i}C\left(p_{i},q_{\pi (i)}\right)} is needed. This can be done in O ( N 3 ) {\displaystyle O(N^{3})} time using the Hungarian method, although there are more efficient algorithms. To have robust handling of outliers, one can add "dummy" nodes that have a constant but reasonably large cost of matching to the cost matrix. This would cause the matching algorithm to match outliers to a "dummy" if there is no real match. === Step 5: Modeling transformation === Given the set of correspondences between a finite set of points on the two shapes, a transformation T : R 2 → R 2 {\displaystyle T:\mathbb {R} ^{2}\to \mathbb {R} ^{2}} can be estimated to map any point from one shape to the other. There are several choices for this transformation, described below. ==== Affine ==== The affine model is a standard choice: T ( p ) = A p + o {\displaystyle T(p)=Ap+o\!} . The least squares solution for the matrix A {\displaystyle A} and the translational offset vector o is obtained by: o = 1 n ∑ i = 1 n ( p i − q π ( i ) ) , A = ( Q + P ) t {\displaystyle o={\frac {1}{n}}\sum _{i=1}^{n}\left(p_{i}-q_{\pi (i)}\right),A=(Q^{+}P)^{t}} Where P = ( 1 p 11 p 12 ⋮ ⋮ ⋮ 1 p n 1 p n 2 ) {\displaystyle P={\begin{pmatrix}1&p_{11}&p_{12}\\\vdots &\vdots &\vdots \\1&p_{n1}&p_{n2}\end{pmatrix}}} with a similar expression for Q {\displaystyle Q\!} . Q + {\displaystyle Q^{+}\!} is the pseudoinverse of Q {\displaystyle Q\!} . ==== Thin plate spline ==== The thin plate spline (TPS) model is the most widely used model for transformations when working with shape contexts. A 2D transformation can be separated into two TPS function to model a coordinate transform: T ( x , y ) = ( f x ( x , y ) , f y ( x , y ) ) {\displaystyle T(x,y)=\left(f_{x}(x,y),f_{y}(x,y)\right)} where each of the ƒx and ƒy have the form: f ( x , y ) = a 1 + a x x + a y y + ∑ i = 1 n ω i U ( ‖ ( x i , y i ) − ( x , y ) ‖ ) , {\displaystyle f(x,y)=a_{1}+a_{x}x+a_{y}y+\sum _{i=1}^{n}\omega _{i}U\left({\begin{Vmatrix}(x_{i},y_{i})-(x,y)\end{Vmatrix}}\right),} and the kernel function U ( r ) {\displaystyle U(r)\!} is defined by U ( r ) = r 2 log ⁡ r 2 {\displaystyle U(r)=r^{2}\log r^{2}\!} . The exact details of how to solve for the parameters can be found elsewhere but it essentially involves solving a linear system of equations. The bending energy (a measure of how much transformation is needed to align the points) will also be easily obtained. ==== Regularized TPS ==== The TPS formulation above has exact matching requirement for the pairs of points on the two shapes. For noisy data, it is best to

  Read more →
• 

  Neighborhood operation

  In computer vision and image processing a neighborhood operation is a commonly used class of computations on image data which implies that it is processed according to the following pseudo code: Visit each point p in the image data and do { N = a neighborhood or region of the image data around the point p result(p) = f(N) } This general procedure can be applied to image data of arbitrary dimensionality. Also, the image data on which the operation is applied does not have to be defined in terms of intensity or color, it can be any type of information which is organized as a function of spatial (and possibly temporal) variables in p. The result of applying a neighborhood operation on an image is again something which can be interpreted as an image, it has the same dimension as the original data. The value at each image point, however, does not have to be directly related to intensity or color. Instead it is an element in the range of the function f, which can be of arbitrary type. Normally the neighborhood N is of fixed size and is a square (or a cube, depending on the dimensionality of the image data) centered on the point p. Also the function f is fixed, but may in some cases have parameters which can vary with p, see below. In the simplest case, the neighborhood N may be only a single point. This type of operation is often referred to as a point-wise operation. == Examples == The most common examples of a neighborhood operation use a fixed function f which in addition is linear, that is, the computation consists of a linear shift invariant operation. In this case, the neighborhood operation corresponds to the convolution operation. A typical example is convolution with a low-pass filter, where the result can be interpreted in terms of local averages of the image data around each image point. Other examples are computation of local derivatives of the image data. It is also rather common to use a fixed but non-linear function f. This includes median filtering, and computation of local variances. The Nagao-Matsuyama filter is an example of a complex local neighbourhood operation that uses variance as an indicator of the uniformity within a pixel group. The result is similar to a convolution with a low-pass filter with the added effect of preserving sharp edges. There is also a class of neighborhood operations in which the function f has additional parameters which can vary with p: Visit each point p in the image data and do { N = a neighborhood or region of the image data around the point p result(p) = f(N, parameters(p)) } This implies that the result is not shift invariant. Examples are adaptive Wiener filters. == Implementation aspects == The pseudo code given above suggests that a neighborhood operation is implemented in terms of an outer loop over all image points. However, since the results are independent, the image points can be visited in arbitrary order, or can even be processed in parallel. Furthermore, in the case of linear shift-invariant operations, the computation of f at each point implies a summation of products between the image data and the filter coefficients. The implementation of this neighborhood operation can then be made by having the summation loop outside the loop over all image points. An important issue related to neighborhood operation is how to deal with the fact that the neighborhood N becomes more or less undefined for points p close to the edge or border of the image data. Several strategies have been proposed: Compute result only for points p for which the corresponding neighborhood is well-defined. This implies that the output image will be somewhat smaller than the input image. Zero padding: Extend the input image sufficiently by adding extra points outside the original image which are set to zero. The loops over the image points described above visit only the original image points. Border extension: Extend the input image sufficiently by adding extra points outside the original image which are set to the image value at the closest image point. The loops over the image points described above visit only the original image points. Mirror extension: Extend the image sufficiently much by mirroring the image at the image boundaries. This method is less sensitive to local variations at the image boundary than border extension. Wrapping: The image is tiled, so that going off one edge wraps around to the opposite side of the image. This method assumes that the image is largely homogeneous, for example a stochastic image texture without large textons.

  Read more →
• 

  Natural language processing

  Natural language processing (NLP) is the processing of natural language information by a computer. NLP is a subfield of computer science and is closely associated with artificial intelligence. NLP is also related to information retrieval, knowledge representation, computational linguistics, and linguistics more broadly. Major processing tasks in an NLP system include: speech recognition, text classification, natural language understanding, and natural language generation. == History == Natural language processing has its roots in the 1950s. Already in 1950, Alan Turing published an article titled "Computing Machinery and Intelligence," which proposed what is now called the Turing test as a criterion of intelligence, though at the time that was not articulated as a problem separate from artificial intelligence. The proposed test includes a task that involves the automated interpretation and generation of natural language. === Symbolic NLP (1950s – early 1990s) === The premise of symbolic NLP is often illustrated using John Searle's Chinese room thought experiment: Given a collection of rules (e.g., a Chinese phrasebook, with questions and matching answers), the computer emulates natural language understanding (or other NLP tasks) by applying those rules to the data it confronts. 1950s: The Georgetown experiment in 1954 involved fully automatic translation of more than sixty Russian sentences into English. The authors claimed that within three or five years, machine translation would be a solved problem. However, real progress was much slower, and after the ALPAC report in 1966, which found that ten years of research had failed to fulfill the expectations, funding for machine translation was dramatically reduced. Little further research in machine translation was conducted in America (though some research continued elsewhere, such as Japan and Europe) until the late 1980s when the first statistical machine translation systems were developed. 1960s: Some notably successful natural language processing systems developed in the 1960s were SHRDLU, a natural language system working in restricted "blocks worlds" with restricted vocabularies, and ELIZA, a simulation of Rogerian psychotherapy, written by Joseph Weizenbaum between 1964 and 1966. Despite using minimal information about human thought or emotion, ELIZA was able to produce interactions that appeared human-like. When the "patient" exceeded the very small knowledge base, ELIZA might provide a generic response, for example, responding to "My head hurts" with "Why do you say your head hurts?". Ross Quillian's successful work on natural language was demonstrated with a vocabulary of only twenty words, because that was all that would fit in a computer memory at the time. 1970s: During the 1970s, many programmers began to write "conceptual ontologies", which structured real-world information into computer-understandable data. Examples are MARGIE (Schank, 1975), SAM (Cullingford, 1978), PAM (Wilensky, 1978), TaleSpin (Meehan, 1976), QUALM (Lehnert, 1977), Politics (Carbonell, 1979), and Plot Units (Lehnert 1981). During this time, the first chatterbots were written (e.g., PARRY). 1980s: The 1980s and early 1990s mark the heyday of symbolic methods in NLP. Focus areas of the time included research on rule-based parsing (e.g., the development of HPSG as a computational operationalization of generative grammar), morphology (e.g., two-level morphology), semantics (e.g., Lesk algorithm), reference (e.g., within Centering Theory) and other areas of natural language understanding (e.g., in the Rhetorical Structure Theory). Other lines of research were continued, e.g., the development of chatterbots with Racter and Jabberwacky. An important development (that eventually led to the statistical turn in the 1990s) was the rising importance of quantitative evaluation in this period. === Statistical NLP (1990s–present) === Up until the 1980s, most natural language processing systems were based on complex sets of hand-written rules. Starting in the late 1980s, however, there was a revolution in natural language processing with the introduction of machine learning algorithms for language processing. This shift was influenced by increasing computational power (see Moore's law) and a decline in the dominance of Chomskyan linguistic theories (e.g. transformational grammar), whose theoretical underpinnings discouraged the sort of corpus linguistics that underlies the machine-learning approach to language processing. 1990s: Many of the notable early successes in statistical methods in NLP occurred in the field of machine translation, due especially to work at IBM Research, such as IBM alignment models. These systems were able to take advantage of existing multilingual textual corpora that had been produced by the Parliament of Canada and the European Union as a result of laws calling for the translation of all governmental proceedings into all official languages of the corresponding systems of government. However, many systems relied on corpora that were specifically developed for the tasks they were designed to perform. This reliance has been a major limitation to their broader effectiveness and continues to affect similar systems. Consequently, significant research has focused on methods for learning effectively from limited amounts of data. 2000s: With the growth of the web, increasing amounts of raw (unannotated) language data have become available since the mid-1990s. Research has thus increasingly focused on unsupervised and semi-supervised learning algorithms. Such algorithms can learn from data that has not been hand-annotated with the desired answers or using a combination of annotated and non-annotated data. Generally, this task is much more difficult than supervised learning, and typically produces less accurate results for a given amount of input data. However, large quantities of non-annotated data are available (including, among other things, the entire content of the World Wide Web), which can often make up for the worse efficiency if the algorithm used has a low enough time complexity to be practical. 2003: word n-gram model, at the time the best statistical algorithm, is outperformed by a multi-layer perceptron (with a single hidden layer and context length of several words, trained on up to 14 million words, by Bengio et al.) 2010: Tomáš Mikolov (then a PhD student at Brno University of Technology) with co-authors applied a simple recurrent neural network with a single hidden layer to language modeling, and in the following years he went on to develop Word2vec. In the 2010s, representation learning and deep neural network-style (featuring many hidden layers) machine learning methods became widespread in natural language processing. This shift gained momentum due to results showing that such techniques can achieve state-of-the-art results in many natural language tasks, e.g., in language modeling and parsing. This is increasingly important in medicine and healthcare, where NLP helps analyze notes and text in electronic health records that would otherwise be inaccessible for study when seeking to improve care or protect patient privacy. == Approaches: Symbolic, statistical, neural networks == Symbolic approach, i.e., the hand-coding of a set of rules for manipulating symbols, coupled with a dictionary lookup, was historically the first approach used both by AI in general and by NLP in particular: such as by writing grammars or devising heuristic rules for stemming. Machine learning approaches, which include both statistical and neural networks, on the other hand, have many advantages over the symbolic approach: both statistical and neural network methods tend to focus more on the most common cases extracted from a corpus of texts, whereas the rule-based approach needs to provide rules for both rare and common cases equally. language models, produced by either statistical or neural networks methods, are more robust to both unfamiliar (e.g. containing words or structures that have not been seen before) and erroneous input (e.g. with misspelled words or words accidentally omitted) in comparison to the rule-based systems, which are also more costly to produce. the larger such a (probabilistic) language model is, the more accurate it becomes, in contrast to rule-based systems that can gain accuracy only by increasing the amount and complexity of the rules leading to intractability problems. Rule-based systems are commonly used: when the amount of training data is insufficient to successfully apply machine learning methods, e.g., for the machine translation of low-resource languages such as provided by the Apertium system, for preprocessing in NLP pipelines, e.g., tokenization, or for post-processing and transforming the output of NLP pipelines, e.g., for knowledge extraction from syntactic parses. === Statistical approach === In the late 1980s and mid-1990s, the statistical approach ended a peri

  Read more →
• 

  Shape context

  Shape context is a feature descriptor used in object recognition. Serge Belongie and Jitendra Malik proposed the term in their paper "Matching with Shape Contexts" in 2000. == Theory == The shape context is intended to be a way of describing shapes that allows for measuring shape similarity and the recovering of point correspondences. The basic idea is to pick n points on the contours of a shape. For each point pi on the shape, consider the n − 1 vectors obtained by connecting pi to all other points. The set of all these vectors is a rich description of the shape localized at that point but is far too detailed. The key idea is that the distribution over relative positions is a robust, compact, and highly discriminative descriptor. So, for the point pi, the coarse histogram of the relative coordinates of the remaining n − 1 points, h i ( k ) = # { q ≠ p i : ( q − p i ) ∈ bin ( k ) } {\displaystyle h_{i}(k)=\#\{q\neq p_{i}:(q-p_{i})\in {\mbox{bin}}(k)\}} is defined to be the shape context of p i {\displaystyle p_{i}} . The bins are normally taken to be uniform in log-polar space. The fact that the shape context is a rich and discriminative descriptor can be seen in the figure below, in which the shape contexts of two different versions of the letter "A" are shown. (a) and (b) are the sampled edge points of the two shapes. (c) is the diagram of the log-polar bins used to compute the shape context. (d) is the shape context for the point marked with a circle in (a), (e) is that for the point marked as a diamond in (b), and (f) is that for the triangle. As can be seen, since (d) and (e) are the shape contexts for two closely related points, they are quite similar, while the shape context in (f) is very different. For a feature descriptor to be useful, it needs to have certain invariances. In particular it needs to be invariant to translation, scaling, small perturbations, and, depending on the application, rotation. Translational invariance comes naturally to shape context. Scale invariance is obtained by normalizing all radial distances by the mean distance α {\displaystyle \alpha } between all the point pairs in the shape although the median distance can also be used. Shape contexts are empirically demonstrated to be robust to deformations, noise, and outliers using synthetic point set matching experiments. One can provide complete rotational invariance in shape contexts. One way is to measure angles at each point relative to the direction of the tangent at that point (since the points are chosen on edges). This results in a completely rotationally invariant descriptor. But of course this is not always desired since some local features lose their discriminative power if not measured relative to the same frame. Many applications in fact forbid rotational invariance e.g. distinguishing a "6" from a "9". == Use in shape matching == A complete system that uses shape contexts for shape matching consists of the following steps (which will be covered in more detail in the Details of Implementation section): Randomly select a set of points that lie on the edges of a known shape and another set of points on an unknown shape. Compute the shape context of each point found in step 1. Match each point from the known shape to a point on an unknown shape. To minimize the cost of matching, first choose a transformation (e.g. affine, thin plate spline, etc.) that warps the edges of the known shape to the unknown (essentially aligning the two shapes). Then select the point on the unknown shape that most closely corresponds to each warped point on the known shape. Calculate the "shape distance" between each pair of points on the two shapes. Use a weighted sum of the shape context distance, the image appearance distance, and the bending energy (a measure of how much transformation is required to bring the two shapes into alignment). To identify the unknown shape, use a nearest-neighbor classifier to compare its shape distance to shape distances of known objects. == Details of implementation == === Step 1: Finding a list of points on shape edges === The approach assumes that the shape of an object is essentially captured by a finite subset of the points on the internal or external contours on the object. These can be simply obtained using the Canny edge detector and picking a random set of points from the edges. Note that these points need not and in general do not correspond to key-points such as maxima of curvature or inflection points. It is preferable to sample the shape with roughly uniform spacing, though it is not critical. === Step 2: Computing the shape context === This step is described in detail in the Theory section. === Step 3: Computing the cost matrix === Consider two points p and q that have normalized K-bin histograms (i.e. shape contexts) g(k) and h(k). As shape contexts are distributions represented as histograms, it is natural to use the χ2 test statistic as the "shape context cost" of matching the two points: C S = 1 2 ∑ k = 1 K [ g ( k ) − h ( k ) ] 2 g ( k ) + h ( k ) {\displaystyle C_{S}={\frac {1}{2}}\sum _{k=1}^{K}{\frac {[g(k)-h(k)]^{2}}{g(k)+h(k)}}} The values of this range from 0 to 1. In addition to the shape context cost, an extra cost based on the appearance can be added. For instance, it could be a measure of tangent angle dissimilarity (particularly useful in digit recognition): C A = 1 2 ‖ ( cos ⁡ ( θ 1 ) sin ⁡ ( θ 1 ) ) − ( cos ⁡ ( θ 2 ) sin ⁡ ( θ 2 ) ) ‖ {\displaystyle C_{A}={\frac {1}{2}}{\begin{Vmatrix}{\dbinom {\cos(\theta _{1})}{\sin(\theta _{1})}}-{\dbinom {\cos(\theta _{2})}{\sin(\theta _{2})}}\end{Vmatrix}}} This is half the length of the chord in unit circle between the unit vectors with angles θ 1 {\displaystyle \theta _{1}} and θ 2 {\displaystyle \theta _{2}} . Its values also range from 0 to 1. Now the total cost of matching the two points could be a weighted-sum of the two costs: C = ( 1 − β ) C S + β C A {\displaystyle C=(1-\beta )C_{S}+\beta C_{A}\!\,} Now for each point pi on the first shape and a point qj on the second shape, calculate the cost as described and call it Ci,j. This is the cost matrix. === Step 4: Finding the matching that minimizes total cost === Now, a one-to-one matching π ( i ) {\displaystyle \pi (i)} that matches each point pi on shape 1 and qj on shape 2 that minimizes the total cost of matching, H ( π ) = ∑ i C ( p i , q π ( i ) ) {\displaystyle H(\pi )=\sum _{i}C\left(p_{i},q_{\pi (i)}\right)} is needed. This can be done in O ( N 3 ) {\displaystyle O(N^{3})} time using the Hungarian method, although there are more efficient algorithms. To have robust handling of outliers, one can add "dummy" nodes that have a constant but reasonably large cost of matching to the cost matrix. This would cause the matching algorithm to match outliers to a "dummy" if there is no real match. === Step 5: Modeling transformation === Given the set of correspondences between a finite set of points on the two shapes, a transformation T : R 2 → R 2 {\displaystyle T:\mathbb {R} ^{2}\to \mathbb {R} ^{2}} can be estimated to map any point from one shape to the other. There are several choices for this transformation, described below. ==== Affine ==== The affine model is a standard choice: T ( p ) = A p + o {\displaystyle T(p)=Ap+o\!} . The least squares solution for the matrix A {\displaystyle A} and the translational offset vector o is obtained by: o = 1 n ∑ i = 1 n ( p i − q π ( i ) ) , A = ( Q + P ) t {\displaystyle o={\frac {1}{n}}\sum _{i=1}^{n}\left(p_{i}-q_{\pi (i)}\right),A=(Q^{+}P)^{t}} Where P = ( 1 p 11 p 12 ⋮ ⋮ ⋮ 1 p n 1 p n 2 ) {\displaystyle P={\begin{pmatrix}1&p_{11}&p_{12}\\\vdots &\vdots &\vdots \\1&p_{n1}&p_{n2}\end{pmatrix}}} with a similar expression for Q {\displaystyle Q\!} . Q + {\displaystyle Q^{+}\!} is the pseudoinverse of Q {\displaystyle Q\!} . ==== Thin plate spline ==== The thin plate spline (TPS) model is the most widely used model for transformations when working with shape contexts. A 2D transformation can be separated into two TPS function to model a coordinate transform: T ( x , y ) = ( f x ( x , y ) , f y ( x , y ) ) {\displaystyle T(x,y)=\left(f_{x}(x,y),f_{y}(x,y)\right)} where each of the ƒx and ƒy have the form: f ( x , y ) = a 1 + a x x + a y y + ∑ i = 1 n ω i U ( ‖ ( x i , y i ) − ( x , y ) ‖ ) , {\displaystyle f(x,y)=a_{1}+a_{x}x+a_{y}y+\sum _{i=1}^{n}\omega _{i}U\left({\begin{Vmatrix}(x_{i},y_{i})-(x,y)\end{Vmatrix}}\right),} and the kernel function U ( r ) {\displaystyle U(r)\!} is defined by U ( r ) = r 2 log ⁡ r 2 {\displaystyle U(r)=r^{2}\log r^{2}\!} . The exact details of how to solve for the parameters can be found elsewhere but it essentially involves solving a linear system of equations. The bending energy (a measure of how much transformation is needed to align the points) will also be easily obtained. ==== Regularized TPS ==== The TPS formulation above has exact matching requirement for the pairs of points on the two shapes. For noisy data, it is best to

  Read more →