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Image Analysis Based on Tensor Representations

Mohamad Jouni 1
1 GIPSA-SIGMAPHY - GIPSA - Signal Images Physique
GIPSA-PSD - GIPSA Pôle Sciences des Données
Abstract : We consider an image in which every pixel n is defined by a vector y(n) of dimension m, containing m observations of a varying quantity. This variable is measured sequentially and could be the spectrum of light (e.g., hyperspectral images), time (i.e., a video), different angles of acquisition etc. For example, a RGB image is composed of three (i.e., m = 3) channels adjacent in the spectral domain ranging from approximatively red to blue wavelengths. It is often meaningful to express this vector as a linear combination of the compact form as: Y = X*A where Y, X and A are of dimension m×n, m×p and p×n. It is clear that with this writing, the exact position of pixels is not taken into account, nor is the order of the measured values. Even the size of the image is not explicit; if the image is n1×n2, only the product n=n1*n2 indeed appears. More importantly, if pixels and measured variables are permuted, rows of X and columns of A are permuted accordingly. One of the goals of this research topic is to fix these indeterminacies, because permutations are relevant (i.e., the position of pixels and sequential order of values are meaningful features). At least two attempts can be found in the literature. This idea has started to be investigated in the framework of the internship of M. Jouni (supervised by M. Dalla Mura and P. Comon) during the summer 2017 at Gipsa-Lab. Extensions: - For the sake of simplicity, this description has been made for images in 2D, that is, for data depending on two variables, but this extends to a larger number of variables; - Optimization criteria can include penalties aiming at imposing a desired structure on factor matrices (sparsity, spatial regularization, . . . ); - When several data arrays are given and are related in some partially known way, we are facing a particular fusion problem that can also be addressed via tensor tools.
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Contributor : Mohamad Jouni <>
Submitted on : Monday, May 10, 2021 - 5:50:55 PM
Last modification on : Friday, May 28, 2021 - 3:29:55 PM


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  • HAL Id : tel-03223274, version 1


Mohamad Jouni. Image Analysis Based on Tensor Representations. Signal and Image processing. Université Grenoble Alpes, 2021. English. ⟨tel-03223274v1⟩



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