Color science is the scientific study of color including lighting and optics; measurement of light and color; the physiology, psychophysics, and modeling of color vision; and color reproduction. It is the modern extension of traditional color theory. == Organizations == International Commission on Illumination (CIE) Illuminating Engineering Society (IES) Inter-Society Color Council (ISCC) Society for Imaging Science and Technology (IS&T) International Colour Association (AIC) Optica, formerly the Optical Society of America (OSA) The Colour Group Society of Dyers and Colourists (SDC) American Association of Textile Chemists and Colorists (AATCC) Association for Research in Vision and Ophthalmology (ARVO) ACM SIGGRAPH Vision Sciences Society (VSS) Council for Optical Radiation Measurements (CORM) == Journals == The preeminent scholarly journal publishing research papers in color science is Color Research and Application, started in 1975 by founding editor-in-chief Fred Billmeyer, along with Gunter Wyszecki, Michael Pointer and Rolf Kuehni, as a successor to the Journal of Colour (1964–1974). Previously most color science work had been split between journals with broader or partially overlapping focus such as the Journal of the Optical Society of America (JOSA), Photographic Science and Engineering (1957–1984), and the Journal of the Society of Dyers and Colourists (renamed Coloration Technology in 2001). Other journals where color science papers are published include the Journal of Imaging Science & Technology, the Journal of Perceptual Imaging, the Journal of the International Colour Association (JAIC), the Journal of the Color Science Association of Japan, Applied Optics, and the Journal of Vision. == Conferences == Congress of the International Color Association IS&T Color and Imaging Conference (CIC) SIGGRAPH International Symposium for Color Science and Art == Selected books == Berns, Roy S. (2019). Billmeyer and Saltzman's Principles of Color Technology (4th ed.). Wiley. doi:10.1002/9781119367314. 3rd ed. (2000). Daw, Nigel (2012). How Vision Works: The Physiological Mechanisms Behind What We See. Oxford. doi:10.1093/acprof:oso/9780199751617.001.0001. Elliot, Andrew J.; Fairchild, Mark D.; Franklin, Anna, eds. (2015). Handbook of Color Psychology. Cambridge. doi:10.1017/CBO9781107337930. Fairchild, Mark D. (2013). Color Appearance Models (3rd ed.). Wiley. doi:10.1002/9781118653128. Author's website. 2nd ed. (2005). Hunt, Robert W. G. (2004). The Reproduction of Colour (6th ed.). Wiley. doi:10.1002/0470024275. Kuehni, Rolf G. (2012). Color: An Introduction to Practice and Principles (3rd ed.). Wiley. doi:10.1002/9781118533567. 1st ed. (1997). Luo, Ming R., ed. (2016). Encyclopedia of Color Science and Technology. Springer. doi:10.1007/978-1-4419-8071-7. MacAdam, David L., ed. (1970). Sources of Color Science. MIT Press. Reinhard, Erik; Khan, Erum Arif; Akyuz, Ahmet Oguz; Johnson, Garrett (2008). Color Imaging: Fundamentals and Applications. CRC Press. doi:10.1201/b10637. Schanda, János, ed. (2007). Colorimetry: Understanding the CIE System. Wiley. doi:10.1002/9780470175637. Shamey, Renzo; Kuehni, Rolf G. (2020). Pioneers of Color Science. Springer. doi:10.1007/978-3-319-30811-1. Wyszecki, Günter; Stiles, Walter S. (1982). Color Science: Concepts and Methods, Quantitative Data and Formulae (2nd ed.). Wiley.
Cygwin
Cygwin ( SIG-win) is a free and open-source Unix-like environment and command-line interface (CLI) for Microsoft Windows. The project also provides a software repository containing open-source packages. Cygwin allows source code for Unix-like operating systems to be compiled and run on Windows. Cygwin provides native integration of Windows-based applications. The terminal emulator mintty is the default command-line interface provided to interact with the environment. The Cygwin installation directory layout mimics the root file system of Unix-like systems, with directories such as /bin, /home, /etc, /usr, and /var. Cygwin is released under the GNU Lesser General Public License version 3. It was originally developed by Cygnus Solutions, which was later acquired by Red Hat (now part of IBM), to port the GNU toolchain to Win32, including the GNU Compiler Suite. Rather than rewrite the tools to use the Win32 runtime environment, Cygwin implemented a POSIX-compatible environment in the form of a DLL. The brand motto is "Get that Linux feeling – on Windows", although Cygwin doesn't have Linux in it. == History == Cygwin began in 1995 as a project of Steve Chamberlain, a Cygnus engineer who observed that Windows NT and 95 used COFF as their object file format, and that GNU already included support for x86 and COFF, and the C library newlib. He thought that it would be possible to retarget GCC and produce a cross compiler generating executables that could run on Windows. A prototype was later developed. Chamberlain bootstrapped the compiler on a Windows system, to emulate Unix to let the GNU configure shell script run. Initially, Cygwin was called Cygwin32. When Microsoft registered the trademark Win32, the "32" was dropped to simply become Cygwin. In 1999, Cygnus offered Cygwin 1.0 as a commercial product. Subsequent versions have not been released, instead relying on continued open source releases. Geoffrey Noer was the project lead from 1996 to 1999. Christopher Faylor was lead from 1999 to 2004; he left Red Hat and became co-lead with Corinna Vinschen. Corinna Vinschen has been the project lead from mid-2014 to date (as of September, 2024). From June 23, 2016, the Cygwin library version 2.5.2 was licensed under the GNU Lesser General Public License (LGPL) version 3. == Description == Cygwin is provided in two versions: the full 64-bit version and a stripped-down 32-bit version, whose final version was released in 2022. Cygwin consists of a library that implements the POSIX system call API in terms of Windows system calls to enable the running of a large number of application programs equivalent to those on Unix systems, and a GNU development toolchain (including GCC and GDB). Programmers have ported the X Window System, K Desktop Environment 3, GNOME, Apache, and TeX. Cygwin permits installing inetd, syslogd, sshd, Apache, and other daemons as standard Windows services. Cygwin programs have full access to the Windows API and other Windows libraries. Cygwin programs are installed by running Cygwin's "setup" program, which downloads them from repositories on the Internet. The Cygwin API library is licensed under the GNU Lesser General Public License version 3 (or later), with an exception to allow linking to any free and open-source software whose license conforms to the Open Source Definition. Cygwin consists of two parts: A dynamic-link library in the form of a C standard library that acts as a compatibility layer for the POSIX API and A collection of software tools and applications that provide a Unix-like look and feel. Cygwin supports POSIX symbolic links, representing them as plain-text files with the system attribute set. Cygwin 1.5 represented them as Windows Explorer shortcuts, but this was changed for reasons of performance and POSIX correctness. Cygwin also recognises NTFS junction points and symbolic links and treats them as POSIX symbolic links, but it does not create them. The POSIX API for handling access control lists (ACLs) is supported. === Technical details === A Cygwin-specific version of the Unix mount command allows mounting Windows paths as "filesystems" in the Unix file space. Initial mount points can be configured in /etc/fstab, which has a format very similar to Unix systems, except that Windows paths appear in place of devices. Filesystems can be mounted in binary mode (by default), or in text mode, which enables automatic conversion between LF and CRLF endings (which only affects programs that open files without explicitly specifying text or binary mode). Cygwin 1.7 introduced comprehensive support for POSIX locales, and the UTF-8 Unicode encoding became the default. The fork system call for duplicating a process is fully implemented, but the copy-on-write optimization strategy could not be used. Cygwin's default user interface is the bash shell running in the mintty terminal emulator. The DLL also implements pseudo terminal (pty) devices, and Cygwin ships with a number of terminal emulators that are based on them, including rxvt/urxvt and xterm. The version of GCC that comes with Cygwin has various extensions for creating Windows DLLs, such as specifying whether a program is a windowing or console-mode program. Support for compiling programs that do not require the POSIX compatibility layer provided by the Cygwin DLL used to be included in the default GCC, but as of 2014, it is provided by cross-compilers contributed by the MinGW-w64 project. == Software packages == Cygwin's base package selection is approximately 100MB, containing the bash (interactive user) and dash (installation) shells and the core file and text manipulation utilities. Additional packages are available as optional installs from within the Cygwin "setup" program and package manager ("setup-x86_64.exe" – 64 bit). The Cygwin Ports project provided additional packages that were not available in the Cygwin distribution itself. Examples included GNOME, K Desktop Environment 3, MySQL database, and the PHP scripting language. Most ports have been adopted by volunteer maintainers as Cygwin packages, and Cygwin Ports are no longer maintained. Cygwin ships with GTK+ and Qt. The Cygwin/X project allows graphical Unix programs to display their user interfaces on the Windows desktop for both local and remote programs.
Pixel-art scaling algorithms
Pixel art scaling algorithms are graphical filters that attempt to enhance the appearance of hand-drawn 2D pixel art graphics. These algorithms are a form of automatic image enhancement. Pixel art scaling algorithms employ methods significantly different than the common methods of image rescaling, which have the goal of preserving the appearance of images. As pixel art graphics are commonly used at very low resolutions, they employ careful coloring of individual pixels. This results in graphics that rely on a high amount of stylized visual cues to define complex shapes. Several specialized algorithms have been developed to handle re-scaling of such graphics. These specialized algorithms can improve the appearance of pixel-art graphics, but in doing so they introduce changes. Such changes may be undesirable, especially if the goal is to faithfully reproduce the original appearance. Since a typical application of this technology is improving the appearance of fourth-generation and earlier video games on arcade and console emulators, many pixel art scaling algorithms are designed to run in real-time for sufficiently small input images at 60-frames per second. This places constraints on the type of programming techniques that can be used for this sort of real-time processing. Many work only on specific scale factors. 2× is the most common scale factor, while 3×, 4×, 5×, and 6× exist but are less used. == Algorithms == === SAA5050 'Diagonal Smoothing' === The Mullard SAA5050 Teletext character generator chip (1980) used a primitive pixel scaling algorithm to generate higher-resolution characters on the screen from a lower-resolution representation from its internal ROM. Internally, each character shape was defined on a 5 × 9 pixel grid, which was then interpolated by smoothing diagonals to give a 10 × 18 pixel character, with a characteristically angular shape, surrounded to the top and the left by two pixels of blank space. The algorithm only works on monochrome source data, and assumes the source pixels will be logically true or false depending on whether they are 'on' or 'off'. Pixels 'outside the grid pattern' are assumed to be off. The algorithm works as follows: A B C --\ 1 2 D E F --/ 3 4 1 = B | (A & E & !B & !D) 2 = B | (C & E & !B & !F) 3 = E | (!A & !E & B & D) 4 = E | (!C & !E & B & F) Note that this algorithm, like the Eagle algorithm below, has a flaw: If a pattern of 4 pixels in a hollow diamond shape appears, the hollow will be obliterated by the expansion. The SAA5050's internal character ROM carefully avoids ever using this pattern. The degenerate case: becomes: === EPX/Scale2×/AdvMAME2× === Eric's Pixel Expansion (EPX) is an algorithm developed by Eric Johnston at LucasArts around 1992, when porting the SCUMM engine games from the IBM PC (which ran at 320 × 200 × 256 colors) to the early color Macintosh computers, which ran at more or less double that resolution. The algorithm works as follows, expanding P into 4 new pixels based on P's surroundings: 1=P; 2=P; 3=P; 4=P; IF C==A => 1=A IF A==B => 2=B IF D==C => 3=C IF B==D => 4=D IF of A, B, C, D, three or more are identical: 1=2=3=4=P Later implementations of this same algorithm (as AdvMAME2× and Scale2×, developed around 2001) are slightly more efficient but functionally identical: 1=P; 2=P; 3=P; 4=P; IF C==A AND C!=D AND A!=B => 1=A IF A==B AND A!=C AND B!=D => 2=B IF D==C AND D!=B AND C!=A => 3=C IF B==D AND B!=A AND D!=C => 4=D AdvMAME2× is available in DOSBox via the scaler=advmame2x dosbox.conf option. The AdvMAME4×/Scale4× algorithm is just EPX applied twice to get 4× resolution. ==== Scale3×/AdvMAME3× and ScaleFX ==== The AdvMAME3×/Scale3× algorithm (available in DOSBox via the scaler=advmame3x dosbox.conf option) can be thought of as a generalization of EPX to the 3× case. The corner pixels are calculated identically to EPX. 1=E; 2=E; 3=E; 4=E; 5=E; 6=E; 7=E; 8=E; 9=E; IF D==B AND D!=H AND B!=F => 1=D IF (D==B AND D!=H AND B!=F AND E!=C) OR (B==F AND B!=D AND F!=H AND E!=A) => 2=B IF B==F AND B!=D AND F!=H => 3=F IF (H==D AND H!=F AND D!=B AND E!=A) OR (D==B AND D!=H AND B!=F AND E!=G) => 4=D 5=E IF (B==F AND B!=D AND F!=H AND E!=I) OR (F==H AND F!=B AND H!=D AND E!=C) => 6=F IF H==D AND H!=F AND D!=B => 7=D IF (F==H AND F!=B AND H!=D AND E!=G) OR (H==D AND H!=F AND D!=B AND E!=I) => 8=H IF F==H AND F!=B AND H!=D => 9=F There is also a variant improved over Scale3× called ScaleFX, developed by Sp00kyFox, and a version combined with Reverse-AA called ScaleFX-Hybrid. === Eagle === Eagle works as follows: for every in pixel, we will generate 4 out pixels. First, set all 4 to the color of the pixel we are currently scaling (as nearest-neighbor). Next look at the three pixels above, to the left, and diagonally above left: if all three are the same color as each other, set the top left pixel of our output square to that color in preference to the nearest-neighbor color. Work similarly for all four pixels, and then move to the next one. Assume an input matrix of 3 × 3 pixels where the centermost pixel is the pixel to be scaled, and an output matrix of 2 × 2 pixels (i.e., the scaled pixel) first: |Then . . . --\ CC |S T U --\ 1 2 . C . --/ CC |V C W --/ 3 4 . . . |X Y Z | IF V==S==T => 1=S | IF T==U==W => 2=U | IF V==X==Y => 3=X | IF W==Z==Y => 4=Z Thus if we have a single black pixel on a white background it will vanish. This is a bug in the Eagle algorithm but is solved by other algorithms such as EPX, 2xSaI, and HQ2x. === 2×SaI === 2×SaI, short for 2× Scale and Interpolation engine, was inspired by Eagle. It was designed by Derek Liauw Kie Fa, also known as Kreed, primarily for use in console and computer emulators, and it has remained fairly popular in this niche. Many of the most popular emulators, including ZSNES and VisualBoyAdvance, offer this scaling algorithm as a feature. Several slightly different versions of the scaling algorithm are available, and these are often referred to as Super 2×SaI and Super Eagle. The 2xSaI family works on a 4 × 4 matrix of pixels where the pixel marked A below is scaled: I E F J G A B K --\ W X H C D L --/ Y Z M N O P For 16-bit pixels, they use pixel masks which change based on whether the 16-bit pixel format is 565 or 555. The constants colorMask, lowPixelMask, qColorMask, qLowPixelMask, redBlueMask, and greenMask are 16-bit masks. The lower 8 bits are identical in either pixel format. Two interpolation functions are described: INTERPOLATE(uint32 A, UINT32 B). -- linear midpoint of A and B if (A == B) return A; return ( ((A & colorMask) >> 1) + ((B & colorMask) >> 1) + (A & B & lowPixelMask) ); Q_INTERPOLATE(uint32 A, uint32 B, uint32 C, uint32 D) -- bilinear interpolation; A, B, C, and D's average x = ((A & qColorMask) >> 2) + ((B & qColorMask) >> 2) + ((C & qColorMask) >> 2) + ((D & qColorMask) >> 2); y = (A & qLowPixelMask) + (B & qLowPixelMask) + (C & qLowPixelMask) + (D & qLowPixelMask); y = (y >> 2) & qLowPixelMask; return x + y; The algorithm checks A, B, C, and D for a diagonal match such that A==D and B!=C, or the other way around, or if they are both diagonals or if there is no diagonal match. Within these, it checks for three or four identical pixels. Based on these conditions, the algorithm decides whether to use one of A, B, C, or D, or an interpolation among only these four, for each output pixel. The 2xSaI arbitrary scaler can enlarge any image to any resolution and uses bilinear filtering to interpolate pixels. Since Kreed released the source code under the GNU General Public License, it is freely available to anyone wishing to utilize it in a project released under that license. Developers wishing to use it in a non-GPL project would be required to rewrite the algorithm without using any of Kreed's existing code. It is available in DOSBox via scaler=2xsai option. === hqnx family === Maxim Stepin's hq2x, hq3x, and hq4x are for scale factors of 2:1, 3:1, and 4:1 respectively. Each work by comparing the color value of each pixel to those of its eight immediate neighbors, marking the neighbors as close or distant, and using a pre-generated lookup table to find the proper proportion of input pixels' values for each of the 4, 9 or 16 corresponding output pixels. The hq3x family will perfectly smooth any diagonal line whose slope is ±0.5, ±1, or ±2 and which is not anti-aliased in the input; one with any other slope will alternate between two slopes in the output. It will also smooth very tight curves. Unlike 2xSaI, it anti-aliases the output. hqnx was initially created for the Super NES emulator ZSNES. The author of bsnes has released a space-efficient implementation of hq2x to the public domain. A port to shaders, which has comparable quality to the early versions of xBR, is available. Before the port, a shader called "scalehq" has often been confused for hqx. === xBR family === There are 6 filters in this family: xBR , xBRZ, xBR-Hybrid, Super xBR, xBR+3D and Super xBR+3D. xBR ("scale by rules"), cre
PANGU (software)
The PANGU (Planet and Asteroid Natural scene Generation Utility) is a computer graphics utility of which the development was funded by ESA and performed by University of Dundee. It generates scenes of planets, moons, asteroids, spacecraft and rovers. The main purpose of the tool is to test and validate navigation techniques based on the processing of images coming from on-board sensors, such as a camera or imaging LIDAR on a planetary lander.
Microsoft Fresh Paint
Fresh Paint is a painting app developed by Microsoft and released on May 25, 2012. == History == Fresh Paint originated from a Microsoft Research project known as Project Gustav, an endeavor to reproduce the behavior of physical oil paint on a digital medium. To push the boundaries of simulating oil on a digital medium, the research team created a physics model that precisely replicated on a screen what would happen in the real world if you combined oil, a surface and a tool such as a paint brush. Two publications, Detail-Preserving Paint Modeling for 3D Brushes and Simple Data-Driven Modeling of Brushes, were released as a result of the team’s findings. After a variety of internal testing Project, Gustav was codenamed Digital Art. Partnering with The Museum of Modern Art, Digital Art was tested for a year by 60,000 people. With feedback culled from MoMA, developers expanded the existing physics model, experimenting with how real oil paint blended and reacted to the texture of a canvas. After final adjustments were made, Digital Art was rebranded as Fresh Paint. It was released to the public on 25 May 2012.
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
PNGOUT
PNGOUT is a freeware command line optimizer for PNG images written by Ken Silverman. The transformation is lossless, meaning that the resulting image is visually identical to the source image. According to its author, this program can often get higher compression than other optimizers by 5–10%. It is possible to compress some inflated PNGs to a size below 1% of the original file. PNGOUT was also available as a plug-in for the freeware image viewer IrfanView and can be enabled as an option when saving files. It allows editing of various PNGOUT settings via a dialog box. PNGOUT integration was removed in IrfanView version 4.58 in favour of OptiPNG. In 2006, a commercial version of PNGOUT with a graphical user interface, known as PNGOUTWin, was released by Ardfry Imaging, a small company Silverman co-founded in 2005. There is also a freeware GUI frontend to PNGOUT available, known as PNGGauntlet. == Main operation == The main function of PNGOUT is to reduce the size of image data contained in the IDAT chunk. This chunk is compressed using the deflate algorithm. Deflate algorithms can vary in speed and compression ratio, with higher compression ratios generally implying lower speed. Ken Silverman wrote a deflate compressor for PNGOUT that is slower than the ones used in most graphics software, but produces smaller files. PNGOUT also performs automatic bit depth, color, and palette reduction where appropriate.