Photometric stereo

Photometric stereo is a technique in computer vision for estimating the surface normals of objects by observing that object under different lighting conditions (photometry). It is based on the fact that the amount of light reflected by a surface is dependent on the orientation of the surface in relation to the light source and the observer. By measuring the amount of light reflected into a camera, the space of possible surface orientations is limited. Given enough light sources from different angles, the surface orientation may be constrained to a single orientation or even overconstrained. The technique was originally introduced by Woodham in 1980. The special case where the data is a single image is known as shape from shading, and was analyzed by B. K. P. Horn in 1989. Photometric stereo has since been generalized to many other situations, including extended light sources and non-Lambertian surface finishes. Current research aims to make the method work in the presence of projected shadows, highlights, and non-uniform lighting. Photometric stereo is widely used in various fields, including archaeology, cultural heritage conservation, and quality control. It is now integrated into widely used open-source software, such as Meshroom. == Basic method == Under Woodham's original assumptions — Lambertian reflectance, known point-like distant light sources, and uniform albedo — the problem can be solved by inverting the linear equation I = L ⋅ n {\displaystyle I=L\cdot n} , where I {\displaystyle I} is a (known) vector of m {\displaystyle m} observed intensities, n {\displaystyle n} is the (unknown) surface normal, and L {\displaystyle L} is a (known) 3 × m {\displaystyle 3\times m} matrix of normalized light directions. This model can easily be extended to surfaces with non-uniform albedo, while keeping the problem linear. Taking an albedo reflectivity of k {\displaystyle k} , the formula for the reflected light intensity becomes I = k ( L ⋅ n ) . {\displaystyle I=k(L\cdot n).} If L {\displaystyle L} is square (there are exactly 3 lights) and non-singular, it can be inverted, giving L − 1 I = k n . {\displaystyle L^{-1}I=kn.} Since the normal vector is known to have length 1, k {\displaystyle k} must be the length of the vector k n {\displaystyle kn} , and n {\displaystyle n} is the normalised direction of that vector. If L {\displaystyle L} is not square (there are more than 3 lights), a generalisation of the inverse can be obtained using the Moore–Penrose pseudoinverse, by simply multiplying both sides with L T {\displaystyle L^{T}} , giving L T I = L T k ( L ⋅ n ) , {\displaystyle L^{T}I=L^{T}k(L\cdot n),} ( L T L ) − 1 L T I = k n , {\displaystyle (L^{T}L)^{-1}L^{T}I=kn,} after which the normal vector and albedo can be solved as described above. == Non-Lambertian surfaces == The classical photometric stereo problem concerns itself only with Lambertian surfaces, with perfectly diffuse reflection. This is unrealistic for many types of materials, especially metals, glass and smooth plastics, and will lead to aberrations in the resulting normal vectors. Many methods have been developed to lift this assumption. In this section, a few of these are listed. === Specular reflections === Historically, in computer graphics, the commonly used model to render surfaces started with Lambertian surfaces and progressed first to include simple specular reflections. Computer vision followed a similar course with photometric stereo. Specular reflections were among the first deviations from the Lambertian model. These are a few adaptations that have been developed. Many techniques ultimately rely on modelling the reflectance function of the surface, that is, how much light is reflected in each direction. This reflectance function has to be invertible. The reflected light intensities towards the camera is measured, and the inverse reflectance function is fit onto the measured intensities, resulting in a unique solution for the normal vector. === General BRDFs and beyond === According to the Bidirectional reflectance distribution function (BRDF) model, a surface may distribute the amount of light it receives in any outward direction. This is the most general known model for opaque surfaces. Some techniques have been developed to model (almost) general BRDFs. In practice, all of these require many light sources to obtain reliable data. These are methods in which surfaces with general BRDFs can be measured. Determine the explicit BRDF prior to scanning. To do this, a different surface is required that has the same or a very similar BRDF, of which the actual geometry (or at least the normal vectors for many points on the surface) is already known. The lights are then individually shone upon the known surface, and the amount of reflection into the camera is measured. Using this information, a look-up table can be created that maps reflected intensities for each light source to a list of possible normal vectors. This puts constraints on the possible normal vectors the surface may have, and reduces the photometric stereo problem to an interpolation between measurements. Typical known surfaces to calibrate the look-up table with are spheres for their wide variety of surface orientations. Restricting the BRDF to be symmetrical. If the BRDF is symmetrical, the direction of the light can be restricted to a cone about the direction to the camera. Which cone this is depends on the BRDF itself, the normal vector of the surface, and the measured intensity. Given enough measured intensities and the resulting light directions, these cones can be approximated and therefore the normal vectors of the surface. Some progress has been made towards modelling an even more general surfaces, such as Spatially Varying Bidirectional Distribution Functions (SVBRDF), Bidirectional surface scattering reflectance distribution functions (BSSRDF), and accounting for interreflections. However, such methods are still fairly restrictive in photometric stereo. Better results have been achieved with structured light. == Uncalibrated photometric stereo == Uncalibrated Photometric Stereo is an approach in photometric stereo that aims to reconstruct the 3D shape of an object from images captured under unknown lighting conditions. Unlike classical methods, which often assume controlled or known lighting setups, this approach removes these constraints, making it adaptable to diverse and real-world environments. The advent of deep learning has revolutionized universal PS by replacing handcrafted assumptions with data-driven models. Recent approaches leverage Transformer-based architectures and multi-scale encoder–decoder networks to directly estimate surface normals from input images. Uncalibrated Photometric Stereo is inherently an ill-posed problem, as it attempts to recover 3D shape and lighting conditions simultaneously from images alone. This leads to fundamental ambiguities in the reconstruction process, which manifest as systematic errors in the recovered geometry, including global distortions in the object's overall shape, and misinterpretation of surface orientation, where concave regions may appear convex and vice versa. To address the challenges of uncalibrated photometric stereo, hybrid methods have emerged that combine multi-view stereo and photometric stereo. These approaches leverage the strengths of both techniques, including geometric reliability and resolution.

Textual case-based reasoning

Textual case-based reasoning (TCBR) is a subtopic of case-based reasoning, in short CBR, a popular area in artificial intelligence. CBR suggests the ways to use past experiences to solve future similar problems, requiring that past experiences be structured in a form similar to attribute-value pairs. This leads to the investigation of textual descriptions for knowledge exploration whose output will be, in turn, used to solve similar problems. == Subareas == Textual case-base reasoning research has focused on: measuring similarity between textual cases mapping texts into structured case representations adapting textual cases for reuse automatically generating representations.

Plant Nanny

Plant Nanny is a water tracker mobile application which reminds users to drink water. It was developed by Taiwanese app maker Fourdesire. The app was first released in 2013 and is available on the Apple App Store for iPhones and the Google Play Store for Android devices. == Description == Play Nanny uses a game method that allows users to turn their virtual selves into plants, which grows and thrives as the user drinks more water. The app sends occasional push notifications to remind users to drink water throughout the day. Users can choose from a wide range of plants, including cacti and carnations, and track their water intake. The app uses two resources, How to calculate how much water you should drink by Jennifer Stone (2018) and Human energy requirements by the Food and Agriculture Organization (2004), to calculate the recommended daily water intake for its users. Upon downloading the app, users are prompted to input basic personal information which is then used to calculate the recommended daily water intake and prompts them to drink the appropriate amount. == Accolades ==

Chirplet transform

In signal processing, the chirplet transform is an inner product of an input signal with a family of analysis primitives called chirplets. Similar to the wavelet transform, chirplets are usually generated from (or can be expressed as being from) a single mother chirplet (analogous to the so-called mother wavelet of wavelet theory). == Definitions == The term chirplet transform was coined by Steve Mann, as the title of the first published paper on chirplets. The term chirplet itself (apart from chirplet transform) was also used by Steve Mann, Domingo Mihovilovic, and Ronald Bracewell to describe a windowed portion of a chirp function. In Mann's words: A wavelet is a piece of a wave, and a chirplet, similarly, is a piece of a chirp. More precisely, a chirplet is a windowed portion of a chirp function, where the window provides some time localization property. In terms of time–frequency space, chirplets exist as rotated, sheared, or other structures that move from the traditional parallelism with the time and frequency axes that are typical for waves (Fourier and short-time Fourier transforms) or wavelets. The chirplet transform thus represents a rotated, sheared, or otherwise transformed tiling of the time–frequency plane. Although chirp signals have been known for many years in radar, pulse compression, and the like, the first published reference to the chirplet transform described specific signal representations based on families of functions related to one another by time–varying frequency modulation or frequency varying time modulation, in addition to time and frequency shifting, and scale changes. In that paper, the Gaussian chirplet transform was presented as one such example, together with a successful application to ice fragment detection in radar (improving target detection results over previous approaches). The term chirplet (but not the term chirplet transform) was also proposed for a similar transform, apparently independently, by Mihovilovic and Bracewell later that same year. == Applications == The first practical application of the chirplet transform was in water-human-computer interaction (WaterHCI) for marine safety, to assist vessels in navigating through ice-infested waters, using marine radar to detect growlers (small iceberg fragments too small to be visible on conventional radar, yet large enough to damage a vessel). Other applications of the chirplet transform in WaterHCI include the SWIM (Sequential Wave Imprinting Machine). More recently other practical applications have been developed, including image processing (e.g. where there is periodic structure imaged through projective geometry), as well as to excise chirp-like interference in spread spectrum communications, in EEG processing, and Chirplet Time Domain Reflectometry. == Extensions == The warblet transform is a particular example of the chirplet transform introduced by Mann and Haykin in 1992 and now widely used. It provides a signal representation based on cyclically varying frequency modulated signals (warbling signals).

System appreciation

System appreciation is an activity often included in the maintenance phase of software engineering projects. Key deliverables from this phase include documentation that describes what the system does in terms of its functional features, and how it achieves those features in terms of its architecture and design. Software architecture recovery is often the first step within System appreciation.

Viola–Jones object detection framework

The Viola–Jones object detection framework is a machine learning object detection framework proposed in 2001 by Paul Viola and Michael Jones. It was motivated primarily by the problem of face detection, although it can be adapted to the detection of other object classes. In short, it consists of a sequence of classifiers. Each classifier is a single perceptron with several binary masks (Haar features). To detect faces in an image, a sliding window is computed over the image. For each image, the classifiers are applied. If at any point, a classifier outputs "no face detected", then the window is considered to contain no face. Otherwise, if all classifiers output "face detected", then the window is considered to contain a face. The algorithm is efficient for its time, able to detect faces in 384 by 288 pixel images at 15 frames per second on a conventional 700 MHz Intel Pentium III. It is also robust, achieving high precision and recall. While it has lower accuracy than more modern methods such as convolutional neural network, its efficiency and compact size (only around 50k parameters, compared to millions of parameters for typical CNN like DeepFace) means it is still used in cases with limited computational power. For example, in the original paper, they reported that this face detector could run on the Compaq iPAQ at 2 fps (this device has a low power StrongARM without floating point hardware). == Problem description == Face detection is a binary classification problem combined with a localization problem: given a picture, decide whether it contains faces, and construct bounding boxes for the faces. To make the task more manageable, the Viola–Jones algorithm only detects full view (no occlusion), frontal (no head-turning), upright (no rotation), well-lit, full-sized (occupying most of the frame) faces in fixed-resolution images. The restrictions are not as severe as they appear, as one can normalize the picture to bring it closer to the requirements for Viola-Jones. any image can be scaled to a fixed resolution for a general picture with a face of unknown size and orientation, one can perform blob detection to discover potential faces, then scale and rotate them into the upright, full-sized position. the brightness of the image can be corrected by white balancing. the bounding boxes can be found by sliding a window across the entire picture, and marking down every window that contains a face. This would generally detect the same face multiple times, for which duplication removal methods, such as non-maximal suppression, can be used. The "frontal" requirement is non-negotiable, as there is no simple transformation on the image that can turn a face from a side view to a frontal view. However, one can train multiple Viola-Jones classifiers, one for each angle: one for frontal view, one for 3/4 view, one for profile view, a few more for the angles in-between them. Then one can at run time execute all these classifiers in parallel to detect faces at different view angles. The "full-view" requirement is also non-negotiable, and cannot be simply dealt with by training more Viola-Jones classifiers, since there are too many possible ways to occlude a face. == Components of the framework == A full presentation of the algorithm is in. Consider an image I ( x , y ) {\displaystyle I(x,y)} of fixed resolution ( M , N ) {\displaystyle (M,N)} . Our task is to make a binary decision: whether it is a photo of a standardized face (frontal, well-lit, etc) or not. Viola–Jones is essentially a boosted feature learning algorithm, trained by running a modified AdaBoost algorithm on Haar feature classifiers to find a sequence of classifiers f 1 , f 2 , . . . , f k {\displaystyle f_{1},f_{2},...,f_{k}} . Haar feature classifiers are crude, but allows very fast computation, and the modified AdaBoost constructs a strong classifier out of many weak ones. At run time, a given image I {\displaystyle I} is tested on f 1 ( I ) , f 2 ( I ) , . . . f k ( I ) {\displaystyle f_{1}(I),f_{2}(I),...f_{k}(I)} sequentially. If at any point, f i ( I ) = 0 {\displaystyle f_{i}(I)=0} , the algorithm immediately returns "no face detected". If all classifiers return 1, then the algorithm returns "face detected". For this reason, the Viola-Jones classifier is also called "Haar cascade classifier". === Haar feature classifiers === Consider a perceptron f w , b {\displaystyle f_{w,b}} defined by two variables w ( x , y ) , b {\displaystyle w(x,y),b} . It takes in an image I ( x , y ) {\displaystyle I(x,y)} of fixed resolution, and returns f w , b ( I ) = { 1 , if ∑ x , y w ( x , y ) I ( x , y ) + b > 0 0 , else {\displaystyle f_{w,b}(I)={\begin{cases}1,\quad {\text{if }}\sum _{x,y}w(x,y)I(x,y)+b>0\\0,\quad {\text{else}}\end{cases}}} A Haar feature classifier is a perceptron f w , b {\displaystyle f_{w,b}} with a very special kind of w {\displaystyle w} that makes it extremely cheap to calculate. Namely, if we write out the matrix w ( x , y ) {\displaystyle w(x,y)} , we find that it takes only three possible values { + 1 , − 1 , 0 } {\displaystyle \{+1,-1,0\}} , and if we color the matrix with white on + 1 {\displaystyle +1} , black on − 1 {\displaystyle -1} , and transparent on 0 {\displaystyle 0} , the matrix is in one of the 5 possible patterns shown on the right. Each pattern must also be symmetric to x-reflection and y-reflection (ignoring the color change), so for example, for the horizontal white-black feature, the two rectangles must be of the same width. For the vertical white-black-white feature, the white rectangles must be of the same height, but there is no restriction on the black rectangle's height. ==== Rationale for Haar features ==== The Haar features used in the Viola-Jones algorithm are a subset of the more general Haar basis functions, which have been used previously in the realm of image-based object detection. While crude compared to alternatives such as steerable filters, Haar features are sufficiently complex to match features of typical human faces. For example: The eye region is darker than the upper-cheeks. The nose bridge region is brighter than the eyes. Composition of properties forming matchable facial features: Location and size: eyes, mouth, bridge of nose Value: oriented gradients of pixel intensities Further, the design of Haar features allows for efficient computation of f w , b ( I ) {\displaystyle f_{w,b}(I)} using only constant number of additions and subtractions, regardless of the size of the rectangular features, using the summed-area table. === Learning and using a Viola–Jones classifier === Choose a resolution ( M , N ) {\displaystyle (M,N)} for the images to be classified. In the original paper, they recommended ( M , N ) = ( 24 , 24 ) {\displaystyle (M,N)=(24,24)} . ==== Learning ==== Collect a training set, with some containing faces, and others not containing faces. Perform a certain modified AdaBoost training on the set of all Haar feature classifiers of dimension ( M , N ) {\displaystyle (M,N)} , until a desired level of precision and recall is reached. The modified AdaBoost algorithm would output a sequence of Haar feature classifiers f 1 , f 2 , . . . , f k {\displaystyle f_{1},f_{2},...,f_{k}} . The details of the modified AdaBoost algorithm is detailed below. ==== Using ==== To use a Viola-Jones classifier with f 1 , f 2 , . . . , f k {\displaystyle f_{1},f_{2},...,f_{k}} on an image I {\displaystyle I} , compute f 1 ( I ) , f 2 ( I ) , . . . f k ( I ) {\displaystyle f_{1}(I),f_{2}(I),...f_{k}(I)} sequentially. If at any point, f i ( I ) = 0 {\displaystyle f_{i}(I)=0} , the algorithm immediately returns "no face detected". If all classifiers return 1, then the algorithm returns "face detected". === Learning algorithm === The speed with which features may be evaluated does not adequately compensate for their number, however. For example, in a standard 24x24 pixel sub-window, there are a total of M = 162336 possible features, and it would be prohibitively expensive to evaluate them all when testing an image. Thus, the object detection framework employs a variant of the learning algorithm AdaBoost to both select the best features and to train classifiers that use them. This algorithm constructs a "strong" classifier as a linear combination of weighted simple “weak” classifiers. h ( x ) = sgn ⁡ ( ∑ j = 1 M α j h j ( x ) ) {\displaystyle h(\mathbf {x} )=\operatorname {sgn} \left(\sum _{j=1}^{M}\alpha _{j}h_{j}(\mathbf {x} )\right)} Each weak classifier is a threshold function based on the feature f j {\displaystyle f_{j}} . h j ( x ) = { − s j if f j < θ j s j otherwise {\displaystyle h_{j}(\mathbf {x} )={\begin{cases}-s_{j}&{\text{if }}f_{j}<\theta _{j}\\s_{j}&{\text{otherwise}}\end{cases}}} The threshold value θ j {\displaystyle \theta _{j}} and the polarity s j ∈ ± 1 {\displaystyle s_{j}\in \pm 1} are determined in the training, as well as the coefficients α j {\displaystyle \alpha _{j}} . Here a simplified version of the lea

Charge-coupled device

A charge-coupled device (CCD) is an integrated circuit containing an array of linked, or coupled, capacitors. Under the control of an external circuit, each capacitor can transfer its electric charge to a neighboring capacitor. CCD sensors are a major technology used in digital imaging. In a CCD image sensor, pixels are represented by p-doped metal–oxide–semiconductor (MOS) capacitors. These MOS capacitors, the basic building blocks of a CCD, are biased above the threshold for inversion when image acquisition begins, allowing the conversion of incoming photons into electron charges at the semiconductor-oxide interface; the CCD is then used to read out these charges. Although CCDs are not the only technology to allow for light detection, CCD image sensors are widely used in professional, medical, and scientific applications where high-quality image data are required. In applications with less exacting quality demands, such as consumer and professional digital cameras, active pixel sensors, also known as CMOS sensors (complementary MOS sensors), are generally used. However, the large quality advantage CCDs enjoyed early on has narrowed over time and since the late 2010s CMOS sensors are the dominant technology, having largely if not completely replaced CCD image sensors. == History == The basis for the CCD is the metal–oxide–semiconductor (MOS) structure, with MOS capacitors being the basic building blocks of a CCD, and a depleted MOS structure used as the photodetector in early CCD devices. In the late 1960s, Willard Boyle and George E. Smith at Bell Labs were researching MOS technology while working on semiconductor bubble memory. They realized that an electric charge was the analog of the magnetic bubble and that it could be stored on a tiny MOS capacitor. As it was fairly straightforward to fabricate a series of MOS capacitors in a row, they connected a suitable voltage to them so that the charge could be stepped along from one to the next. This led to the invention of the charge-coupled device by Boyle and Smith in 1969. They conceived of the design of what they termed, in their notebook, "Charge 'Bubble' Devices". The initial paper describing the concept in April 1970 listed possible uses as memory, a delay line, and an imaging device. The device could also be used as a shift register. The essence of the design was the ability to transfer charge along the surface of a semiconductor from one storage capacitor to the next. The first experimental device demonstrating the principle was a row of closely spaced metal squares on an oxidized silicon surface electrically accessed by wire bonds. It was demonstrated by Gil Amelio, Michael Francis Tompsett and George Smith in April 1970. This was the first experimental application of the CCD in image sensor technology, and used a depleted MOS structure as the photodetector. The first patent (U.S. patent 4,085,456) on the application of CCDs to imaging was assigned to Tompsett, who filed the application in 1971. The first working CCD made with integrated circuit technology was a simple 8-bit shift register, reported by Tompsett, Amelio and Smith in August 1970. This device had input and output circuits and was used to demonstrate its use as a shift register and as a crude eight pixel linear imaging device. Development of the device progressed at a rapid rate. By 1971, Bell researchers led by Michael Tompsett were able to capture images with simple linear devices. Several companies, including Fairchild Semiconductor, RCA and Texas Instruments, picked up on the invention and began development programs. Fairchild's effort, led by ex-Bell researcher Gil Amelio, was the first with commercial devices, and by 1974 had a linear 500-element device and a 2D 100 × 100 pixel device. Peter L. P. Dillon, a scientist at Kodak Research Labs, invented the first color CCD image sensor by overlaying a color filter array on this Fairchild 100 x 100 pixel Interline CCD starting in 1974. Steven Sasson, an electrical engineer working for the Kodak Apparatus Division, invented a digital still camera using this same Fairchild 100 × 100 CCD in 1975. The interline transfer (ILT) CCD device was proposed by L. Walsh and R. Dyck at Fairchild in 1973 to reduce smear and eliminate a mechanical shutter. To further reduce smear from bright light sources, the frame-interline-transfer (FIT) CCD architecture was developed by K. Horii, T. Kuroda and T. Kunii at Matsushita (now Panasonic) in 1981. The first KH-11 KENNEN reconnaissance satellite equipped with charge-coupled device array (800 × 800 pixels) technology for imaging was launched in December 1976. Under the leadership of Kazuo Iwama, Sony started a large development effort on CCDs involving a significant investment. Eventually, Sony managed to mass-produce CCDs for their camcorders. Before this happened, Iwama died in August 1982. Subsequently, a CCD chip was placed on his tombstone to acknowledge his contribution. The first mass-produced consumer CCD video camera, the CCD-G5, was released by Sony in 1983, based on a prototype developed by Yoshiaki Hagiwara in 1981. Early CCD sensors suffered from shutter lag. This was largely resolved with the invention of the pinned photodiode (PPD). It was invented by Nobukazu Teranishi, Hiromitsu Shiraki and Yasuo Ishihara at NEC in 1980. They recognized that lag can be eliminated if the signal carriers could be transferred from the photodiode to the CCD. This led to their invention of the pinned photodiode, a photodetector structure with low lag, low noise, high quantum efficiency and low dark current. It was first publicly reported by Teranishi and Ishihara with A. Kohono, E. Oda and K. Arai in 1982, with the addition of an anti-blooming structure. The new photodetector structure invented at NEC was given the name "pinned photodiode" (PPD) by B.C. Burkey at Kodak in 1984. In 1987, the PPD began to be incorporated into most CCD devices, becoming a fixture in consumer electronic video cameras and then digital still cameras. Since then, the PPD has been used in nearly all CCD sensors and then CMOS sensors. In January 2006, Boyle and Smith were awarded the National Academy of Engineering Charles Stark Draper Prize, and in 2009 they were awarded the Nobel Prize for Physics for their invention of the CCD concept. Michael Tompsett was awarded the 2010 National Medal of Technology and Innovation, for pioneering work and electronic technologies including the design and development of the first CCD imagers. He was also awarded the 2012 IEEE Edison Medal for "pioneering contributions to imaging devices including CCD Imagers, cameras and thermal imagers". == Basics of operation == In a CCD for capturing images, there is a photoactive region (an epitaxial layer of silicon), and a transmission region made out of a shift register (the CCD, properly speaking). An image is projected through a lens onto the capacitor array (the photoactive region), causing each capacitor to accumulate an electric charge proportional to the light intensity at that location. A one-dimensional array, used in line-scan cameras, captures a single slice of the image, whereas a two-dimensional array, used in video and still cameras, captures a two-dimensional picture corresponding to the scene projected onto the focal plane of the sensor. Once the array has been exposed to the image, a control circuit causes each capacitor to transfer its contents to its neighbor (operating as a shift register). The last capacitor in the array dumps its charge into a charge amplifier, which converts the charge into a voltage. By repeating this process, the controlling circuit converts the entire contents of the array in the semiconductor to a sequence of voltages. In a digital device, these voltages are then sampled, digitized, and usually stored in memory; in an analog device (such as an analog video camera), they are processed into a continuous analog signal (e.g. by feeding the output of the charge amplifier into a low-pass filter), which is then processed and fed out to other circuits for transmission, recording, or other processing. == Detailed physics of operation == === Charge generation === Before the MOS capacitors are exposed to light, they are biased into the depletion region; in n-channel CCDs, the silicon under the bias gate is slightly p-doped or intrinsic. The gate is then biased at a positive potential, above the threshold for strong inversion, which will eventually result in the creation of an n channel below the gate as in a MOSFET. However, it takes time to reach this thermal equilibrium: up to hours in high-end scientific cameras cooled at low temperature. Initially after biasing, the holes are pushed far into the substrate, and no mobile electrons are at or near the surface; the CCD thus operates in a non-equilibrium state called deep depletion. Then, when electron–hole pairs are generated in the depletion region, they are separated by the electric field, the elec