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Robotics Research Technical Report: Review of Multifrequency Channel Decompositions, of Images and Wavelet Models (Classic Reprint) - Softcover

 
9781332190393: Robotics Research Technical Report: Review of Multifrequency Channel Decompositions, of Images and Wavelet Models (Classic Reprint)

Inhaltsangabe

Excerpt from Robotics Research Technical Report: Review of Multifrequency Channel Decompositions, of Images and Wavelet Models

In psychophysics and physiology of human vision. Many evidences have been gathered showing that the retina image is decomposed into several spatially oriented frequency channels. In the first section of this paper, we describe the experimental motivations of this model. Biolog ical studies of human vision have always been a source of ideas for computer vision and image processing research. Indeed. The human visual system is generally considered as an optimal image processor. The goal is not to imitate the processings immemented in the human brains but rather to understand the motivations of such processings and analyze their applications to computer vision problems. From this point of view. The recent experimental findings in psychophysics and physiology open challenging questions. In order to get a better understanding of multichannel decompositions. We review the main mathematical results in this domain. The best know decom position which is intermediate between a spatial and a frequency representation is the window Fourier transform. We describe its properties but also show from a mathematical point of view why it is not convenient to analyze images. The wavelet transfonn was introduced by J. Morlet to compensate the inconveniences of a window Fourier transform. It is computed by expanding the signal on a family of functions which are the dilate and translate of a unique function w(x)

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Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com

This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

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Reseña del editor

Excerpt from Robotics Research Technical Report: Review of Multifrequency Channel Decompositions, of Images and Wavelet Models

In psychophysics and physiology of human vision. Many evidences have been gathered showing that the retina image is decomposed into several spatially oriented frequency channels. In the first section of this paper, we describe the experimental motivations of this model. Biolog ical studies of human vision have always been a source of ideas for computer vision and image processing research. Indeed. The human visual system is generally considered as an optimal image processor. The goal is not to imitate the processings immemented in the human brains but rather to understand the motivations of such processings and analyze their applications to computer vision problems. From this point of view. The recent experimental findings in psychophysics and physiology open challenging questions. In order to get a better understanding of multichannel decompositions. We review the main mathematical results in this domain. The best know decom position which is intermediate between a spatial and a frequency representation is the window Fourier transform. We describe its properties but also show from a mathematical point of view why it is not convenient to analyze images. The wavelet transfonn was introduced by J. Morlet to compensate the inconveniences of a window Fourier transform. It is computed by expanding the signal on a family of functions which are the dilate and translate of a unique function w(x)

About the Publisher

Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com

This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Reseña del editor

Excerpt from Robotics Research Technical Report: Review of Multifrequency Channel Decompositions, of Images and Wavelet Models

In this paper we review the recent multichannel models developed in psycho-physiology, computer vision and image processing. In psychophysiology. multichannel models have been particularly successful for explaining some low-level processing tn the visual cortex. The expansion of a function in several frequency channels provides a representation which is intermediate between a spatial and a Fourier representation We describe the mathematical properties of such decompositions and introduce the wavelet transform. We review the classical multircsolution pyramidal transforms developed in computer vision and show how they relate to the decomposition of an image in a wavelet orthonormal basis. In the last section we discuss the properties of the zcro-crossings of multifrcqocncy channels. Zcro-crossings representations arc particularly well adapted for pattern recognition in computer vision.

1. Introduction

Within the last 10 years, multi-frequency channel decompositions have found many applications in image processing. In psycho-physiology of human vision, multichannel models have also been particularly successful for explaining some low-level biological processings.

About the Publisher

Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com

This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

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9780483052901: Robotics Research Technical Report: Review of Multifrequency Channel Decompositions, of Images and Wavelet Models (Classic Reprint)

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ISBN 10:  0483052906 ISBN 13:  9780483052901
Verlag: Forgotten Books, 2018
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Stephane G. Mallat
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ISBN 10: 1332190391 ISBN 13: 9781332190393
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