A fast vector quantization encoding algorithm based on projection pyramid with Hadamard transformation

The Hadamard transform (also known as the Walsh¿Hadamard transform, Hadamard¿Rademacher¿Walsh transform, Walsh transform, or Walsh¿Fourier transform) is an example of a generalized class of Fourier transforms. It is named for the French mathematician Jacques Hadamard, the German-American mathematician Hans Rademacher, and the American mathematician Joseph Leonard Walsh. Vector quantization is a classical quantization technique from signal processing which allows the modeling of probability density functions by the distribution of prototype vectors. It was originally used for data compression. It works by dividing a large set of points into groups having approximately the same number of points closest to them. Each group is represented by its centroid point, as in k-means and some other clustering algorithms. In mathematics, a transformation could be any function mapping a set X on to another set or on to itself. However, often the set X has some additional algebraic or geometric structure and the term 'transformation' refers to a function from X to itself that preserves this structure. Examples include linear transformations and affine transformations, rotations, reflections and translations. These can be carried out in Euclidean space, particularly in dimensions 2 and 3. In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle. It is a conic solid with polygonal base. A pyramid with an n-sided base will have n + 1 vertices, n + 1 faces, and 2n edges. All pyramids are self-dual. When unspecified, the base is usually assumed to be square. If the base is a regular polygon and the apex is above the center of the polygon, an n-gonal pyramid will have Cnv symmetry. 3D projection is any method of mapping three-dimensional points to a two-dimensional plane. As most current methods for displaying graphical data are based on planar two-dimensional media, the use of this type of projection is widespread, especially in computer graphics, engineering and drafting. The objective of image compression is to reduce irrelevance and redundancy of the image data in order to be able to store or transmit data in an efficient form. Source.

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