Tensors in Image Processing and Computer Vision

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Editors

Asst. Prof. Santiago Aja-Fern

andez

Universidad de Valladolid

Escuela T

ecnica Superior de

Ingenieros de

Telecomunicaci

Campus Miguel Delibes

47011 Valladolid

Spain

sanaja@tel.uva.es

Dr. Dacheng Tao

Blk N4, 02b-67

School of Computer Engineering

Nanyang Technological University

Singapore 639798

dctao@ntu.edu.sg

Series editor

Professor Sameer Singh, PhD

Research School of Informatics

Loughborough University

Loughborough, UK

Asst. Prof. Rodrigo de Luis Garc

ıa

Universidad de Valladolid

Escuela T

ecnica Superior de

Ingenieros de

Telecomunicaci

Campus Miguel Delibes

47011 Valladolid

Spain

rodlui@tel.uva.es

Dr. Xuelong Li

University of London

Birkbeck College

School of Computer Science &

Information Systems

Malet Street

London WC1E 7HX

United Kingdom

xuelong

li@ieee.org

ISSN 1617-7916

ISBN 978-1-84882-298-6 e-ISBN 978-1-84882-299-3

DOI 10.1007/978-1-84882-299-3

Springer Dordrecht Heidelberg London New York

British Library Cataloguing in Publication Data

A catalogue record for this book is available from the British Library

Library of Congress Control Number: 2009926807

 Springer-Verlag London Limited 2009

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as

permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced,

stored or transmitted, in any form or by any means, with the prior permission in writing of the

publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued

by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be

sent to the publishers.

The use of registered names, trademarks, etc., in this publication does not imply, even in the absence of a

speciﬁc statement, that such names are exempt from the relevant laws and regulations and therefore free

for general use.

The publisher makes no representation, express or implied, with regard to the accuracy of the information

contained in this book and cannot accept any legal responsibility or liability for any errors or omissions

that may be made.

Printed on acid-free paper

Springer is part of Springer Science+Business Media (www.springer.com)

Preface

Over the past few years, tensor processing tools have become more and more popu-

lar in the ﬁelds of computer vision and image processing, and tensor-valued image

modalities have also been more commonly employed, with the remarkable example

of Diffusion Tensor Magnetic Resonance Imaging.

However, tensor applications and tensor processing tools arise from very dif-

ferent areas. This can prevent important advances from rapidly spreading over the

scientiﬁc community. Even though novel discoveries can greatly beneﬁt many het-

erogeneous ﬁelds such as medical image processing or multilinear analysis, these

advances are too often kept within the areas of knowledge where they were ﬁrst

employed.

Given this fact, a compilation of some of the most recent advances in tensor

processing can be a valuable tool for the scientiﬁc community, thus providing a

useful reference state of the artfor tensor processing applications as well as a general

insight on the areas where tensor processing is being successfully applied.

The idea behind this book started after the Tensor Workshop held at the IEEE

Computer Society Conference on Computer Vision and Pattern Recognition held in

Anchorage, Alaska, in June 2008. This workshop gathered experts from different

ﬁelds working on tensor processing, and some of the ideas presented there were

further developed toghether with the results of the Tensor Workshop held earlier in

Gran Canaria (Spain) in November 2006, which was sponsored by the SIMILAR

Network of Excellence of the European 6th Framework Programme.

As this book comprises theoretical advances and applications regarding very het-

erogeneous areas of image processing and computer vision, it has been organized

into ﬁve parts, which are nevertheless preceeded by an introductory chapter about

the different applications of the use of tensors in signal processing. Part I is devoted

to the use of tensors and tensor ﬁeld processing in general. The processing tools

described in these chapters can be applied in a number of different applications. In

Part II, two tensor techniques for image processing are presented. Later, Part III fo-

cuses on the use of tensors in computer vision applications, such as camera models

or multilinear applications. As medical imaging is one of the areas that has taken

more advantage of the advances of tensor processing, Part IV is dedicated to this

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Tensors in Image Processing and Computer Vision

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structure tensors

only Tensors of floating point and complex dtype can require gradients

Sizes of tensors must match except in dimension 1. Expected size 2 but got size 1 for tensor number 1 in the list.

RuntimeError: Sizes of tensors must match except in dimension 1. Expected size 7 but got size 6 for tensor number 1 in the list

izes of tensors must match except in dimension 0. Got 2 and 640 (The offending index is 0)

RuntimeError: Sizes of tensors must match except in dimension 1. Expected size 64 but got size 63 for tensor number 1 in the list.

tf.nn.conv2d

tf.meshgrid

pytorch pandas

element 0 of tensors does not require grad and does not have a grad_fn

Expected all tensors to be on the same device, but found at least two devices, cpu and cuda:0! (when checking argument for argument index in method wrapper_CUDA__index_select)

RuntimeError: Expected all tensors to be on the same device, but found at least two devices, cpu and cuda:0! (when checking argument for argument tensors in method wrapper_cat)

RuntimeError: Expected all tensors to be on the same device, but found at least two devices, cuda:0 and cpu! (when checking argument for argument tensors in method wrapper_cat)

RuntimeError: element 0 of tensors does not require grad and does not have a grad_fn

TypeError: tensor or list of tensors expected, got <class 'PIL.Image.Image'>

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