An operational taxonomic unit (OTU) is an operational definition used to classify groups of closely related individuals. The term was originally introduced in 1963 by Robert R. Sokal and Peter H. A. Sneath in the context of numerical taxonomy, where an "operational taxonomic unit" is simply the group of organisms currently being studied. In this sense, an OTU is a pragmatic definition to group individuals by similarity, equivalent to but not necessarily in line with classical Linnaean taxonomy or modern evolutionary taxonomy. Nowadays, however, the term is commonly used in a different context and refers to clusters of (uncultivated or unknown) organisms, grouped by DNA sequence similarity of a specific taxonomic marker gene (originally coined as mOTU; molecular OTU). In other words, OTUs are pragmatic proxies for "species" at different taxonomic levels, in the absence of traditional systems of biological classification as are available for macroscopic organisms. For several years, OTUs have been the most commonly used units of diversity, especially when analysing small subunit 16S (for prokaryotes) or 18S rRNA (for eukaryotes) marker gene sequence datasets. == Molecular OTU by clustering of marker gene sequences == In the approach represented by DNA barcoding, a particular locus is chosen to be used as the marker gene for classification. This locus should be universally present in the scope selected, variable enough to be different among close-related species, and be flanked by conservative sequences that allow for easy amplification and detection. There are databases containing sequences for such marker genes from many different species, allowing for comparison. (Sometimes only using one locus does not provide sufficient resolution, so multiple marker genes are used. This is the case for plants, where rbcL+matK is common.) Sequences obtained this way can be clustered according to their similarity to one another, and operational taxonomic units are defined based on the similarity threshold set by the researcher. The exact threshold depends on the taxa in question and the mutational rates of the selected locus in the taxon. 97–99% are commonly used, but "it is now recognized to be somewhat arbitrary as sequence variation within and among species varies across taxa". 100% similarity (fully identical) is also common, also known as single variants. It remains debatable how well this commonly used method recapitulates true microbial species phylogeny or ecology. Although OTUs can be calculated differently when using different algorithms or thresholds, research by Schmidt et al. (2014) demonstrated that 16S-derived microbial OTUs were generally ecologically consistent across habitats and several clustering approaches. The number of OTUs defined may be inflated due to errors in DNA sequencing. === OTU clustering approaches === There are three main approaches to clustering OTUs: De novo, for which the clustering is based on similarities between sequencing reads. Closed-reference, for which the clustering is performed against a reference database of sequences. Open-reference, where clustering is first performed against a reference database of sequences, then any remaining sequences that could not be mapped to the reference are clustered de novo. Using a reference provides taxonomic context for the OTUs found. Alternatively, taxonomic context can be found after the construction of clusters by comparing representative sequences from clusters against a reference database. There are also specialized classifiers for this purpose which are much faster than naive comparison using BLAST. === OTU clustering algorithms === Hierarchical clustering algorithms (HCA): uclust & cd-hit & ESPRIT Bayesian clustering: CROP == Molecular OTU by other methods == In addition to similarity-based grouping, marker gene sequences can be sorted into OTUs using molecular phylogeny, k-mer composition, or hybrid methods combining these methods with similarity. There are also Bayesian tree-less methods and machine learning approaches. Using phylogeny often involves manually assigning terminal clades or single nodes to an OTU, so this is usually only done for refinement. Genome skimming can be used to obtain high-copy DNA without the need to choose marker genes or to design PCR primers for the chosen genes. It can provide fairly good coverage of organelle DNA and repetitive elements such as ribosomal DNA, both of which can be used like marker genes in OTU analysis. Whole-genome sequencing is more expensive and involves the production and processing of more data. By considering the entire genome, many (sometimes over 100) marker genes can be used at the same time, producing highly resolved phylogenies that correctly identify problematic taxa. It is also possible to use entire genomes for OTU assignment. For example, genomes from different bacterial species almost always have an average nucleotide identity lower than 95%, a fact that can be used to define new OTUs (and likely new species).
Progressive Graphics File
PGF (Progressive Graphics File) is a wavelet-based bitmapped image format that employs lossless and lossy data compression. PGF was created to improve upon and replace the JPEG format. It was developed at the same time as JPEG 2000 but with a focus on speed over compression ratio. PGF can operate at higher compression ratios without taking more encoding/decoding time and without generating the characteristic "blocky and blurry" artifacts of the original DCT-based JPEG standard. It also allows more sophisticated progressive downloads. == Color models == PGF supports a wide variety of color models: Grayscale with 1, 8, 16, or 31 bits per pixel Indexed color with palette size of 256 RGB color image with 12, 16 (red: 5 bits, green: 6 bits, blue: 5 bits), 24, or 48 bits per pixel ARGB color image with 32 bits per pixel Lab color image with 24 or 48 bits per pixel CMYK color image with 32 or 64 bits per pixel == Technical discussion == PGF claims to achieve an improved compression quality over JPEG adding or improving features such as scalability. Its compression performance is similar to the original JPEG standard. Very low and very high compression rates (including lossless compression) are also supported in PGF. The ability of the design to handle a very large range of effective bit rates is one of the strengths of PGF. For example, to reduce the number of bits for a picture below a certain amount, the advisable thing to do with the first JPEG standard is to reduce the resolution of the input image before encoding it — something that is ordinarily not necessary for that purpose when using PGF because of its wavelet scalability properties. The PGF process chain contains the following four steps: Color space transform (in case of color images) Discrete Wavelet Transform Quantization (in case of lossy data compression) Hierarchical bit-plane run-length encoding === Color components transformation === Initially, images have to be transformed from the RGB color space to another color space, leading to three components that are handled separately. PGF uses a fully reversible modified YUV color transform. The transformation matrices are: [ Y r U r V r ] = [ 1 4 1 2 1 4 1 − 1 0 0 − 1 1 ] [ R G B ] ; [ R G B ] = [ 1 3 4 − 1 4 1 − 1 4 − 1 4 1 − 1 4 3 4 ] [ Y r U r V r ] {\displaystyle {\begin{bmatrix}Y_{r}\\U_{r}\\V_{r}\end{bmatrix}}={\begin{bmatrix}{\frac {1}{4}}&{\frac {1}{2}}&{\frac {1}{4}}\\1&-1&0\\0&-1&1\end{bmatrix}}{\begin{bmatrix}R\\G\\B\end{bmatrix}};\qquad \qquad {\begin{bmatrix}R\\G\\B\end{bmatrix}}={\begin{bmatrix}1&{\frac {3}{4}}&-{\frac {1}{4}}\\1&-{\frac {1}{4}}&-{\frac {1}{4}}\\1&-{\frac {1}{4}}&{\frac {3}{4}}\end{bmatrix}}{\begin{bmatrix}Y_{r}\\U_{r}\\V_{r}\end{bmatrix}}} The chrominance components can be, but do not necessarily have to be, down-scaled in resolution. === Wavelet transform === The color components are then wavelet transformed to an arbitrary depth. In contrast to JPEG 1992 which uses an 8x8 block-size discrete cosine transform, PGF uses one reversible wavelet transform: a rounded version of the biorthogonal CDF 5/3 wavelet transform. This wavelet filter bank is exactly the same as the reversible wavelet used in JPEG 2000. It uses only integer coefficients, so the output does not require rounding (quantization) and so it does not introduce any quantization noise. === Quantization === After the wavelet transform, the coefficients are scalar-quantized to reduce the amount of bits to represent them, at the expense of a loss of quality. The output is a set of integer numbers which have to be encoded bit-by-bit. The parameter that can be changed to set the final quality is the quantization step: the greater the step, the greater is the compression and the loss of quality. With a quantization step that equals 1, no quantization is performed (it is used in lossless compression). In contrast to JPEG 2000, PGF uses only powers of two, therefore the parameter value i represents a quantization step of 2i. Just using powers of two makes no need of integer multiplication and division operations. === Coding === The result of the previous process is a collection of sub-bands which represent several approximation scales. A sub-band is a set of coefficients — integer numbers which represent aspects of the image associated with a certain frequency range as well as a spatial area of the image. The quantized sub-bands are split further into blocks, rectangular regions in the wavelet domain. They are typically selected in a way that the coefficients within them across the sub-bands form approximately spatial blocks in the (reconstructed) image domain and collected in a fixed size macroblock. The encoder has to encode the bits of all quantized coefficients of a macroblock, starting with the most significant bits and progressing to less significant bits. In this encoding process, each bit-plane of the macroblock gets encoded in two so-called coding passes, first encoding bits of significant coefficients, then refinement bits of significant coefficients. Clearly, in lossless mode all bit-planes have to be encoded, and no bit-planes can be dropped. Only significant coefficients are compressed with an adaptive run-length/Rice (RLR) coder, because they contain long runs of zeros. The RLR coder with parameter k (logarithmic length of a run of zeros) is also known as the elementary Golomb code of order 2k. === Comparison with other file formats === JPEG 2000 is slightly more space-efficient in handling natural images. The PSNR for the same compression ratio is on average 3% better than the PSNR of PGF. It has a small advantage in compression ratio but longer encoding and decoding times. PNG (Portable Network Graphics) is more space-efficient in handling images with many pixels of the same color. There are several self-proclaimed advantages of PGF over the ordinary JPEG standard: Superior compression performance: The image quality (measured in PSNR) for the same compression ratio is on average 3% better than the PSNR of JPEG. At lower bit rates (e.g. less than 0.25 bits/pixel for gray-scale images), PGF has a much more significant advantage over certain modes of JPEG: artifacts are less visible and there is almost no blocking. The compression gains over JPEG are attributed to the use of DWT. Multiple resolution representation: PGF provides seamless compression of multiple image components, with each component carrying from 1 to 31 bits per component sample. With this feature there is no need for separately stored preview images (thumbnails). Progressive transmission by resolution accuracy, commonly referred to as progressive decoding: PGF provides efficient code-stream organizations which are progressive by resolution. This way, after a smaller part of the whole file has been received, it is possible to see a lower quality of the final picture, the quality can be improved monotonically getting more data from the source. Lossless and lossy compression: PGF provides both lossless and lossy compression in a single compression architecture. Both lossy and lossless compression are provided by the use of a reversible (integer) wavelet transform. Side channel spatial information: Transparency and alpha planes are fully supported ROI extraction: Since version 5, PGF supports extraction of regions of interest (ROI) without decoding the whole image. == Available software == The author published libPGF via a SourceForge, under the GNU Lesser General Public License version 2.0. Xeraina offers a free Windows console encoder and decoder, and PGF viewers based on WIC for 32bit and 64bit Windows platforms. Other WIC applications including File Explorer are able to display PGF images after installing this viewer. Digikam is a popular open-source image editing and cataloging software that uses libPGF for its thumbnails. It makes use of the progressive decoding feature of PGF images to store a single version of each thumbnail, which can then be decoded to different resolutions without loss, thus allowing users to dynamically change the size of the thumbnails without having to recalculate them again.
Conduit (company)
Conduit Ltd. is an international software company. From its founding in 2005 to 2013, its most well-known product was the Conduit toolbar, which was widely-described as malware. In 2013, it spun off its toolbar business; today, its main product is a mobile development platform that allows users to create native and web mobile applications for smartphones. == Products == From 2005 to 2013, the company's most well-known product was the Conduit toolbar, which is flagged by most antivirus software as potentially unwanted and adware. Conduit's toolbar software is often downloaded by malware packages from other publishers. The company spun off the toolbar division that manages the Conduit toolbar in 2013. Today, the company's main product is a mobile development platform that allows users to create native and web mobile applications for smartphones. App creation for its App Gallery is free, but it charges a monthly subscription fee to place apps on the App Store or Google Play. == History == Conduit was founded in 2005 by Shilo, Dror Erez, and Gaby Bilcyzk. Between years 2005 and 2013, it ran a successful but controversial toolbar platform business. Conduit was part of the so-called Download Valley companies monetizing free software and downloads by bundling adware. The toolbars were criticized by some as being very difficult to uninstall. The toolbar software was referred to as a "potentially unwanted program" by some in the computer industry because it could be used to change browser settings. The company had more than 400 employees in 2013. In September same year, Conduit spun off its entire website toolbar business division, which combined with Perion Network. After the deal, Conduit shareholders owned 81% of Perion's existing shares and both Perion and Conduit remained independent companies. The substantial size of the Conduit user base allowed Perion to immediately surpass AOL in U.S. searches. In 2015, Conduit announced it would purchase Keeprz, a mobile customer loyalty platform, for $45 million.
Oculus Quill
Quill is a painting and animation software for virtual reality. It runs on Microsoft Windows with Oculus Rift headsets. It is used to create 3D paintings and animated cartoons. Quill was released on November 29, 2016, on the Oculus Store. Theater Elsewhere(formerly Quill Theater), an application for viewing creations made in Quill, was later made available following the release of the Oculus Quest. In September 2021, Facebook, now known as Meta Platforms, and the owner of Oculus, sold Quill to its original creator, who continues to develop and support the app. == Development == Quill was originally developed by Oculus Story Studio as an internal tool for the creative needs of the studio's project Dear Angelica directed by Saschka Unseld along with its art-director Wesley Allsbrook. == Controls == The software works on Oculus Rift utilizing its 6DoF motion controllers. Users can paint in 3D space using their hands naturally, and animate those paintings with keyframes. They can also capture videos and photos of their creations. == Reception == Dear Angelica, a VR story fully painted in Quill, was nominated for an Emmy Award in 2017.
Paint.NET
Paint.NET (sometimes stylized as paint.net) is a freeware general-purpose raster graphics editor program for Microsoft Windows, developed with the .NET platform. Paint.NET was originally created by Rick Brewster as a Washington State University student project, and has evolved from a simple replacement for the Microsoft Paint program into a program for editing mainly graphics, with support for plugins. == History == Paint.NET originated as a computer science senior design project by Rick Brewster during spring 2004 at Washington State University. Version 1.0 consisted of 36,000 lines of code and was written in four months. In contrast, version 3.35 has approximately 162,000 lines of code. The Paint.NET project continued over the summer and into the autumn 2004 semester for both the version 1.1 and 2.0 releases. Development continued with one programmer who worked on previous versions of Paint.NET while he was a student at WSU. As of May 2006 the program had been downloaded at least 2 million times, at a rate of about 180,000 per month. Initially, Paint.NET was released under a modified version of the MIT License, with the exclusion of the installer, text, and graphics. However, citing issues with the open source code being plagiarized by others that had rebranded the software as their own and bundled user content without their permission, the availability of the source code was restricted, in December 2007 Brewster announced his intent to restrict access to components of the program (including its installer, resources, and user interface). In November 2009, the software was made proprietary, restricting the sale or creation of derivative works of the software. Starting with version 4.0.18, Paint.NET is published in two editions: A classic edition remains freeware, similar to all other versions since 3.5. Another edition, however, is published to Microsoft Store under a trialware license and is available to purchase for US$14.99. According to the developer, this was done to enable the users to contribute to the development with more convenience, even though the old avenue of donation was not closed. In May 2026, Brewster revealed that he obtained the paint.net domain after attempting to do so for 22 years. Historically, the editor was hosted on getpaint.net, and according to Brewster, the previous owners of paint.net would not sell the domain and asked for "lots and lots of money". In December of the previous year, paint.net began hosting content that impersonated Paint.NET, therefore becoming a clear case of trademark infringement and domain squatting. Brewster stated that he was able to obtain the domain afterwards with the help of a lawyer. == Overview == Paint.NET is primarily programmed in the C# programming language. Its native image format, .PDN, is a compressed representation of the application's internal object format, which preserves layering and other information. == Plugins == Paint.NET supports plugins, which add image adjustments, effects, and support for additional file types. They can be programmed using any .NET Framework programming language, though they are most commonly written in C#. These are created by volunteer coders on the program's discussion board, the Paint.NET Forum. Though most are simply published via the discussion board, some have been included with a later release of the program. For instance, a DirectDraw Surface file type plugin, (originally by Dean Ashton) and an Ink Sketch and Soften Portrait effect (originally by David Issel) were added to Paint.NET in version 3.10. Hundreds of plugins have been produced; such as Shape3D, which renders a 2D drawing into a 3D shape. Some plugins expand on the functionality that comes with Paint.NET, such as Curves+ and Sharpen+, which extend the included tools Curves and Sharpen, respectively. Examples of file type plugins include an Animated Cursor and Icon plugin and an Adobe Photoshop file format plugin. Several of these plugins are based on existing open source software, such as a raw image format plugin that uses dcraw and a PNG optimization plugin that uses OptiPNG. == Forks == === paint-mono === Paint.NET was created exclusively for Windows and has no native support for other operating systems. Due to its former open-source licensing, the development of alternative versions was possible. In May 2007, Miguel de Icaza officially started a porting project called paint-mono. This project had partially ported Paint.NET 3.0 to Mono, an open-source implementation of the Common Language Infrastructure on which the .NET Framework is based. This allowed Paint.NET to be run on Mono-supported platforms, such as Linux. This port is no longer maintained and has not been updated since March 2009. Newer Mono runtime 6 versions are able to run original Paint.NET releases up to 3.5.11 with only minor issues. === Pinta === In 2010, developer Jonathan Pobst started a project called Pinta, describing it as a clone of Paint.NET for Mono and Gtk#. Pinta reused the adjustments and effects code from Paint.NET but otherwise is original code.
Transduction (machine learning)
In logic, statistical inference, and supervised learning, transduction or transductive inference is reasoning from observed, specific (training) cases to specific (test) cases. In contrast, induction is reasoning from observed training cases to general rules, which are then applied to the test cases. The distinction is most interesting in cases where the predictions of the transductive model are not achievable by any inductive model. Note that this is caused by transductive inference on different test sets producing mutually inconsistent predictions. Transduction was introduced in a computer science context by Vladimir Vapnik in the 1990s, motivated by his view that transduction is preferable to induction since, according to him, induction requires solving a more general problem (inferring a function) before solving a more specific problem (computing outputs for new cases): "When solving a problem of interest, do not solve a more general problem as an intermediate step. Try to get the answer that you really need but not a more general one.". An example of learning which is not inductive would be in the case of binary classification, where the inputs tend to cluster in two groups. A large set of test inputs may help in finding the clusters, thus providing useful information about the classification labels. The same predictions would not be obtainable from a model which induces a function based only on the training cases. Some people may call this an example of the closely related semi-supervised learning, since Vapnik's motivation is quite different. The most well-known example of a case-bases learning algorithm is the k-nearest neighbor algorithm, which is related to transductive learning algorithms. Another example of an algorithm in this category is the Transductive Support Vector Machine (TSVM). A third possible motivation of transduction arises through the need to approximate. If exact inference is computationally prohibitive, one may at least try to make sure that the approximations are good at the test inputs. In this case, the test inputs could come from an arbitrary distribution (not necessarily related to the distribution of the training inputs), which wouldn't be allowed in semi-supervised learning. An example of an algorithm falling in this category is the Bayesian Committee Machine (BCM). == Historical context == The mode of inference from particulars to particulars, which Vapnik came to call transduction, was already distinguished from the mode of inference from particulars to generalizations in part III of the Cambridge philosopher and logician W.E. Johnson's 1924 textbook, Logic. In Johnson's work, the former mode was called 'eduction' and the latter was called 'induction'. Bruno de Finetti developed a purely subjective form of Bayesianism in which claims about objective chances could be translated into empirically respectable claims about subjective credences with respect to observables through exchangeability properties. An early statement of this view can be found in his 1937 La Prévision: ses Lois Logiques, ses Sources Subjectives and a mature statement in his 1970 Theory of Probability. Within de Finetti's subjective Bayesian framework, all inductive inference is ultimately inference from particulars to particulars. == Example problem == The following example problem contrasts some of the unique properties of transduction against induction. A collection of points is given, such that some of the points are labeled (A, B, or C), but most of the points are unlabeled (?). The goal is to predict appropriate labels for all of the unlabeled points. The inductive approach to solving this problem is to use the labeled points to train a supervised learning algorithm, and then have it predict labels for all of the unlabeled points. With this problem, however, the supervised learning algorithm will only have five labeled points to use as a basis for building a predictive model. It will certainly struggle to build a model that captures the structure of this data. For example, if a nearest-neighbor algorithm is used, then the points near the middle will be labeled "A" or "C", even though it is apparent that they belong to the same cluster as the point labeled "B", compared to semi-supervised learning. Transduction has the advantage of being able to consider all of the points, not just the labeled points, while performing the labeling task. In this case, transductive algorithms would label the unlabeled points according to the clusters to which they naturally belong. The points in the middle, therefore, would most likely be labeled "B", because they are packed very close to that cluster. An advantage of transduction is that it may be able to make better predictions with fewer labeled points, because it uses the natural breaks found in the unlabeled points. One disadvantage of transduction is that it builds no predictive model. If a previously unknown point is added to the set, the entire transductive algorithm would need to be repeated with all of the points in order to predict a label. This can be computationally expensive if the data is made available incrementally in a stream. Further, this might cause the predictions of some of the old points to change (which may be good or bad, depending on the application). A supervised learning algorithm, on the other hand, can label new points instantly, with very little computational cost. == Transduction algorithms == Transduction algorithms can be broadly divided into two categories: those that seek to assign discrete labels to unlabeled points, and those that seek to regress continuous labels for unlabeled points. Algorithms that seek to predict discrete labels tend to be derived by adding partial supervision to a clustering algorithm. Two classes of algorithms can be used: flat clustering and hierarchical clustering. The latter can be further subdivided into two categories: those that cluster by partitioning, and those that cluster by agglomerating. Algorithms that seek to predict continuous labels tend to be derived by adding partial supervision to a manifold learning algorithm. === Partitioning transduction === Partitioning transduction can be thought of as top-down transduction. It is a semi-supervised extension of partition-based clustering. It is typically performed as follows: Consider the set of all points to be one large partition. While any partition P contains two points with conflicting labels: Partition P into smaller partitions. For each partition P: Assign the same label to all of the points in P. Of course, any reasonable partitioning technique could be used with this algorithm. Max flow min cut partitioning schemes are very popular for this purpose. === Agglomerative transduction === Agglomerative transduction can be thought of as bottom-up transduction. It is a semi-supervised extension of agglomerative clustering. It is typically performed as follows: Compute the pair-wise distances, D, between all the points. Sort D in ascending order. Consider each point to be a cluster of size 1. For each pair of points {a,b} in D: If (a is unlabeled) or (b is unlabeled) or (a and b have the same label) Merge the two clusters that contain a and b. Label all points in the merged cluster with the same label. === Continuous Label Transduction === These methods seek to regress continuous labels, often via manifold learning techniques. The idea is to learn a low-dimensional representation of the data and infer values smoothly across the manifold. == Applications and related concepts == Transduction is closely related to: Semi-supervised learning – uses both labeled and unlabeled data but typically induces a model. Case-based reasoning – such as the k-nearest neighbor (k-NN) algorithm, often considered a transductive method. Transductive Support Vector Machines (TSVM) – extend standard SVMs to incorporate unlabeled test data during training. Bayesian Committee Machine (BCM) – an approximation method that makes transductive predictions when exact inference is too costly.
Radar geo-warping
Radar geo-warping is the adjustment of geo-referenced radar images and video data to be consistent with a geographical projection. This image warping avoids any restrictions when displaying it together with video from multiple radar sources or with other geographical data including scanned maps and satellite images which may be provided in a particular projection. There are many areas where geo warping has unique benefits: Single radar video signal displayed together with maps of different geographical projections. E.g. Mercator UTM stereographic Multiple radar video signals displayed simultaneously: Having the computing power to do so on one computer. Adapting the projection of all radar signals allowing the geographically correct display and accurate superimposition of those videos. Slant range correction: a modern 3D radar system can measure the height of a target and hence it is possible to correct the radar video by the real corrected range of the target. Slant Range Correction also allows to compensate the radar tower height e.g. for maritime surveillance radars. == Introduction == Radar video presents the echoes of electromagnetic waves a radar system has emitted and received as reflections afterwards. These echoes are typically presented on a computer screen with a color-coding scheme depicting the reflection strength. Two problems have to be solved during such a visualization process. The first problem arises from the fact that typically the radar antenna turns around its position and measures the reflection echo distances from its position in one direction. This effectively means that the radar video data are present in polar coordinates. In older systems the polar oriented picture has been displayed in so called plan position indicators (PPI). The PPI-scope uses a radial sweep pivoting about the center of the presentation. This results in a map-like picture of the area covered by the radar beam. A long-persistence screen is used so that the display remains visible until the sweep passes again. Bearing to the target is indicated by the target's angular position in relation to an imaginary line extending vertically from the sweep origin to the top of the scope. The top of the scope is either true north (when the indicator is operated in the true bearing mode) or ship's heading (when the indicator is operated in the relative bearing mode). For visualization on a modern computer screen the polar coordinates have to be converted into Cartesian coordinates. This process called radar scan conversion is presented with more detail in the next section. The second problem to solve arises from the fact that a radar system is placed in the real world and measures real world echo positions. These echoes have to be displayed together with other real world data like object positions, vector maps and satellite images in a consistent way. All this information refers to the curved earth surface but is displayed on a flat computer display. Building a link from real world earth positions to display pixels is commonly called geographical referencing or in short geo-referencing. Part of the geo-referencing process is to map the 3D earth surface onto a 2D display. This process of a geographical projection can be performed in many ways, but different data sources have their own 'natural' projection. E.g. Cartesian radar video data from a radar source on the earth surface are geo-referenced by a so-called radar projection. When using this radar projection the Cartesian radar video pixels can directly displayed on a computer screen (only being linearly transformed according to the current position on the screen and e.g. the current zoom level). A problem now arises if e.g. also a satellite map shall be shown together with the radar video data. The 'natural' geographical projection of a satellite image would be a satellite projection which depends on the satellite orbit, position and further parameters. Now either the satellite image has to be reprojected to a radar projection or the radar video has to use the satellite projection. This geographical re-projection is also called geographical warping or Geo Warping where each image pixel has to be transformed from one projection into another. This article describes in further detail the Geo Warping of radar video images in real time. It will also show that radar video Geo Warping is done most efficiently when it is integrated with the radar scan conversion process. == Radar-scan conversion == This section describes the principles of the radar-scan conversion (RSC) process. The radar supplies its measured data in polar coordinates (ρ,θ) directly from the rotating antenna. ρ defines the target/echo distance and θ the target angle in polar world coordinates. These data are measured, digitized and stored in a polar coordinate polar store or polar pixmap. The main RSC task is to convert these data to Cartesian (x, y) display coordinates, creating the necessary display pixels. The RSC process is influenced by the current zoom, shift and rotation settings defining which part of the 'world' shall be visible in the display image. As detailed later the RSC process also takes the currently used geographical projection into account when the radar video images are Geo Warped. The OpenGL RSC is implemented using a reverse scan conversion approach which calculates for every image pixel the most appropriate radar amplitude value in the polar store. This approach generates an optimal image without any artifacts known from forward spoke fill algorithms. By applying bi-linear filtering between adjacent pixels in the polar store during the conversion process the OpenGL RSC finally achieves a very high visual quality radar display image for every zoom level, creating smooth images of the radar echoes. == Radar projection == This section illustrates how radar video data are geo referenced and displayed on a computer screen. The radar sensor is positioned on the earth surface with a height h above the ground. It measures the direct distance d to the target (and not e.g. the distance the target is away from the radar if one would move on the earth surface). This distance is then used in the display plane after adjustment to the current display zoom level by the radar scan converter (RSC). Now it has to be clarified how the radar video data is geo referenced. This basically means, that if we want to display a geographical real world object (like e.g. a light house) which is at the same real world position as the radar target, that it also shall appear at the same position in the display plane. This is realized by calculating the distance from the radar sensor to the respective real world object and use that distance in the display plane. The position of the real world object is typically given in geographical coordinates (latitude, longitude and height above the earth surface). In other words, using a radar projection with geographical data is done by simulating a radar measurement process with the real world objects and use the resulting range and azimuth in the display plane. The second picture to the right shows an example radar projection with the center of projection (COP) at latitude 50.0° and longitude 0.0° which is also the radar position. The dashed lines are the equal-latitude and equal-longitude lines on top of the background map. The solid lines show equal-range and equal-azimuth with the respect to the radar position. It is a feature of the radar projection that equal-range lines are circles and equal-azimuth lines are straight lines. This is necessary to display radar video consistently with other map data when using a radar projection where the projection center has to be the radar position. == Geo Warping process == This section explains the actual geo warping or re-projection process when applied to radar video in real time. Assume we want to display radar video on top of a satellite image. As an example we use the CIB projection which is used to display satellite data in CIB (Controlled Image Base) format. The Figure Geo Warping Radar to CIB Projection shows dashed the maximal range circle for a range of 111 km or 60 miles using the radar projection. Such a range is typical for long range coastal surveillance radars. As stated in the last section this is a perfect circle also on the computer screen. The solid line ellipse shows the same range circle for the CIB projection. Typically the errors occurring without Geo Warping are smallest near the radar position if at least the projection center (COP) coincides with the radar position, as realized in our example. Otherwise the error distribution depends both on the used projection and also on the projection parameters. Thus, in our case the errors are most significant near the maximum radar range. The CIB projection error corrected in east–west direction at half the radar range is 2.6 km and is 5.3 km at the full radar range of 111 km. An error of 5.3 km is