Compressed sensingCompressed sensing (also known as compressive sensing, compressive sampling, or sparse sampling) is a signal processing technique for efficiently acquiring and reconstructing a signal, by finding solutions to underdetermined linear systems. This is based on the principle that, through optimization, the sparsity of a signal can be exploited to recover it from far fewer samples than required by the Nyquist–Shannon sampling theorem. There are two conditions under which recovery is possible.
Image segmentationIn and computer vision, image segmentation is the process of partitioning a into multiple image segments, also known as image regions or image objects (sets of pixels). The goal of segmentation is to simplify and/or change the representation of an image into something that is more meaningful and easier to analyze. Image segmentation is typically used to locate objects and boundaries (lines, curves, etc.) in images. More precisely, image segmentation is the process of assigning a label to every pixel in an image such that pixels with the same label share certain characteristics.
Image tracingIn computer graphics, image tracing, raster-to-vector conversion or raster vectorization is the conversion of raster graphics into vector graphics. An image does not have any structure: it is just a collection of marks on paper, grains in film, or pixels in a bitmap. While such an image is useful, it has some limits. If the image is magnified enough, its artifacts appear. The halftone dots, film grains, and pixels become apparent. Images of sharp edges become fuzzy or jagged. See, for example, pixelation.
Sparse dictionary learningSparse dictionary learning (also known as sparse coding or SDL) is a representation learning method which aims at finding a sparse representation of the input data in the form of a linear combination of basic elements as well as those basic elements themselves. These elements are called atoms and they compose a dictionary. Atoms in the dictionary are not required to be orthogonal, and they may be an over-complete spanning set. This problem setup also allows the dimensionality of the signals being represented to be higher than the one of the signals being observed.
Sparse approximationSparse approximation (also known as sparse representation) theory deals with sparse solutions for systems of linear equations. Techniques for finding these solutions and exploiting them in applications have found wide use in , signal processing, machine learning, medical imaging, and more. Consider a linear system of equations , where is an underdetermined matrix and . The matrix (typically assumed to be full-rank) is referred to as the dictionary, and is a signal of interest.
Convex optimizationConvex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard.
Texture mappingTexture mapping is a method for mapping a texture on a . Texture here can be high frequency detail, surface texture, or color. The original technique was pioneered by Edwin Catmull in 1974. Texture mapping originally referred to diffuse mapping, a method that simply mapped pixels from a texture to a 3D surface ("wrapping" the image around the object).
Texture filteringIn computer graphics, texture filtering or texture smoothing is the method used to determine the texture color for a texture mapped pixel, using the colors of nearby texels (pixels of the texture). There are two main categories of texture filtering, magnification filtering and minification filtering. Depending on the situation texture filtering is either a type of reconstruction filter where sparse data is interpolated to fill gaps (magnification), or a type of anti-aliasing (AA), where texture samples exist at a higher frequency than required for the sample frequency needed for texture fill (minification).
Texture atlasIn computer graphics, a texture atlas (also called a spritesheet or an image sprite in 2d game development) is an image containing multiple smaller images, usually packed together to reduce overall dimensions. An atlas can consist of uniformly-sized images or images of varying dimensions. A sub-image is drawn using custom texture coordinates to pick it out of the atlas. In an application where many small textures are used frequently, it is often more efficient to store the textures in a texture atlas which is treated as a single unit by the graphics hardware.
Image editingImage editing encompasses the processes of altering s, whether they are digital photographs, traditional photo-chemical photographs, or illustrations. Traditional analog image editing is known as photo retouching, using tools such as an airbrush to modify photographs or editing illustrations with any traditional art medium. Graphic software programs, which can be broadly grouped into vector graphics editors, raster graphics editors, and 3D modelers, are the primary tools with which a user may manipulate, enhance, and transform images.
