Orthogonal Polyhedra in <italic>3D Time-Color Space</italic> as a Geometric Model for Representation of Video Sequences with Low or Inexistent Redundancy between Frames

Abstract

Several video compression methods have in common their conciseness depends of the degree of redundancy between the frames associated to the sequences they describe. Cartoon animations are a good example of animations with an elevated redundancy and from which an elevated compression is expected. However, scientific sequences provide us with a huge set of examples where the degree of redundancy is very low or inexistent. Because of the accuracy required when these sequences are analyzed, any kind of threshold, which could elevate the redundancy degree, is prohibited. In this work, a proposed solution to the addressed problem considers the linearization of each frame. That is, a frame can be considered as a matrix but by stacking its columns on top of one another a vector is obtained. In this way each pixel can be referenced by only one coordinate in the vector. Starting from these considerations a geometric representation is built: A video sequence will be associated to a unique 3D Orthogonal Pseudo-Polyhedron (3D-OPP). Such 3D-OPP is embedded in a 3D Time-Color Space where X1-axis corresponds to the position of pixels in the linearization, the second spatial dimension (X2-axis) is associated to the color value of a pixel, and finally, X3-axis describes the displaying time of frames in the original animation. Such 3D-OPP can be compressed, manipulated, and displayed in screen by expressing it according to the Extreme Vertices Model in the n-Dimensional Space (nD-EVM). The nD-EVM shares the representation of n-Dimensional Orthogonal Pseudo-Polytopes (nD-OPPs) by considering only a subset of their vertices.