Publication
Methods and apparatuses for encoding and decoding digital images or video streams
Abstract
The invention relates to a method and an apparatus for encoding and/or decoding digital images, wherein said encoding apparatus (1100) comprises processing means (1110) configured for determining weights of a graph related to an image by minimizing a cost function, transforming said weights through a graph Fourier transform, quantizing the transformed weights, computing transformed coefficients through a graph Fourier transform of a graph having said the transformed weights as weights, de-quantizing the quantized transformed weights, computing a reconstructed image through an inverse graph Fourier transform on the basis of the de-quantized transformed weights, computing a distortion cost on the basis of the reconstructed image and the original image, generating a final encoded image on the basis of said distortion cost.
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Related concepts (35)
Fast Fourier transform
A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis converts a signal from its original domain (often time or space) to a representation in the frequency domain and vice versa. The DFT is obtained by decomposing a sequence of values into components of different frequencies. This operation is useful in many fields, but computing it directly from the definition is often too slow to be practical.
Fourier transform
In physics and mathematics, the Fourier transform (FT) is a transform that converts a function into a form that describes the frequencies present in the original function. The output of the transform is a complex-valued function of frequency. The term Fourier transform refers to both this complex-valued function and the mathematical operation. When a distinction needs to be made the Fourier transform is sometimes called the frequency domain representation of the original function.
Graph theory
In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called links or lines). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics.
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