”Volume 6.No.4,A_u-gust1994
`.
`7
`.
`.
`or"
`i
`
`
`
`
`
`'
`iS‘lGNAL PROCESSth
`
`
`
`V
`
`f
`
`iss~0923-5965
`
`SM) 231 37s (1994)
`
`
`
`
`
`
`
`
`IMAGE
`
`COMMUNICATION
`
`CONTENTS
`
`
`
`Paper:
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`A publication of the European Association for Signal Processing (EURASIP)
`
`J P Fillard, JM. Lussert, M Castagné and H. M'timet
`
`
`
`
`
`
`
`
`
`Fourier phase shift location estimation 0! unfocused optical point spread functions
`
`
`
`
`
`
`
`
`
`
`R-J, Chen and 8 Ci Chieu
`
`
`
`
`
`A fully adaptive DCT based color image sequence coders .
`
`
`
`
`
`
`
`
`
`A Neri. Gr Russo and P Talone
`
`
`
`
`
`
`
`Inter-block liltering and downsampling in DCT domain .....
`
`
`
`
`
`
`
`
`J -H Moon and J -K Kim
`
`
`
`
`
`On the accuracy and convergence of 20 motion models usmg minimum MSE motion estimation .
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`M W Mak and WG. Allen
`
`
`
`
`
`A lip-tracking system based on morphological processing and block matching techniques .
`
`
`
`
`
`
`
`
`
`
`
`5. Chang, C..W Jen and C L Lee
`
`
`
`
`
`
`
`A motion detection scheme for motion adaptive pro—scan conversmn V
`
`
`
`
`
`
`
`
`
`Z. Sivan and Dr Malah
`
`
`
`
`
`Change detection and texture analysns for image sequence coding
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`_
`_
`
`
`
`
`
`
`Announcement
`
`.
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Theory. Techniques & Applications
`
`
`
`
`
`
`
`
`
`
`
`
`
`Page 1 of 18
`
`GOOGLE EXHIBIT 1006
`
`

`

`SIGNAL PROCESSING
`
`
`
`
`IMAGE COMMUNICATION
`
`
`
`
`
`Theory, Techniques 5 Applications
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`A publication at the European Association lor Signal Processrng (EURASIP)
`
`
`
`
`
`
`
`
`
`EditorAin-Chief
`
`Leonardo CHIAHIGLIONE
`
`
`Centro Studi e Laboratori
`
`
`
`
`Telecommunicaziont (CSELT)
`
`
`
`Via Guglielmo Raise-Homo". 274
`
`
`
`MOMS Torino. Italy
`
`
`
`Telephone (II) 2286 120
`
`
`
`Telefax. (11) 2288 299
`
`
`
`
`Editorial Board
`
`
`J. Biemond (Univ. Delft. The Netherlands)
`
`
`
`
`
`6. Boerger (HI-II, Germany)
`
`
`
`
`E Dubois (Univ. Quebec. Canada)
`
`
`
`
`E. Girod (Keir). Germany)
`
`
`
`
`H. Harashima (Univ. Tokyo. Japan)
`
`
`
`
`
`C N. Judice (Bellcore. USA)
`
`
`
`
`
`J -K Kim (KAIST. South Korea)
`
`
`
`
`
`AB. Lippman (MIT. USA)
`
`
`
`
`H.G. Musmann (Univ Hannover. Germany)
`
`
`
`
`D Nasse (CCETT, France)
`
`
`
`
`A. Netravali (ATT. USA)
`
`
`
`
`Y Ninomiya (NHK. Japan)
`
`
`
`
`D Pearson (Univ. Essex. United Kingdom)
`
`
`
`
`
`H. Seguin (CNET. France)
`
`
`
`
`L Stenger (FI/DBP, Germany)
`
`
`
`
`H. Tominaga (Waseda Unlv.. Japan)
`
`
`
`
`M. Vetterli (Columbia Univ . USA)
`
`
`
`
`
`LT Wu (ITFII, Taiwan)
`
`
`
`
`t-l. Yasuda (NTT. Japan)
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Guest Editors
`
`
`5 A Benton (MIT. USA)
`
`
`
`
`6 De Haan (Philips, The Netherlands)
`
`
`
`
`
`T Fujii (NTT. Japan)
`
`
`
`
`J Guichard (CNET France)
`
`
`
`
`J Hamasalu (Univ Tokyo, Japan)
`
`
`
`
`
`J Johann (Deutsche Bundespost. Germany)
`
`
`
`
`T Kurita (NHK, Japan)
`
`
`
`
`0 LeGaII (C-Cube. USA)
`
`
`
`
`8 Liu (Princeton Univ . USA)
`
`
`
`
`
`6 Morrison (81’ Labs. United Kingdom)
`
`
`
`
`
`5. Okubo (NTT. Japan)
`
`
`
`
`T. Omachi (NEG. Japan)
`
`
`
`W. Verbiest (Belgium)
`
`
`
`
`
`
`
`
`
`
`
`
`IMAGE COMMUNI»
`Editorial Policy. SIGNAL PROCESSING:
`
`
`
`
`
`CATION is an international journal tor the development of the
`
`
`
`
`
`
`
`
`
`
`theory and practice of image communication. Its primary objec—
`
`
`
`
`
`
`
`
`tives are the tollowing:
`
`
`
`
`To present a forum for the advancement ol the theory and
`
`
`
`
`
`
`
`
`
`
`practice at Image communication.
`
`
`
`
`. To stimulate cross~lertilizalion between areas similar In nature
`
`
`
`
`
`
`
`which have traditionally been separated. Ior example. various
`
`
`
`
`
`
`
`aspects of visual communications and inlormation systems.
`
`
`
`
`
`
`
`- To contribute to a rapid intormation exchange between the
`
`
`
`
`
`
`
`
`industrial and academic environments
`
`
`
`
`The editorial policy and the technical content at the journal are
`
`
`
`
`
`
`
`
`
`
`the responsibility at the Editor-InoChiet and the Editorial Board
`
`
`
`
`
`
`
`
`
`The Journal
`is sell-supporting from subscription income and
`
`
`
`
`
`
`
`
`contains a minimum amount ol advertisements. Advertisements
`
`
`
`
`
`
`
`are subject to the prior approval of the Editor-in-Chief. The journal
`
`
`
`
`
`
`
`
`
`
`
`welcomes contributions from every country in the world,
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Scope. SIGNAL PROCESSING IMAGE COMMUNICATION pub-
`
`
`
`
`
`lishes articles relating to aspects ol the design. implementation
`
`
`
`
`
`
`
`
`and use of image communication sy3tems.
`
`
`
`
`
`
`SIGNAL PROCESSING: IMAGE COMMUNICATION features orig-
`
`
`
`
`
`inal research work. tutorial and review articles. and accounts at
`
`
`
`
`
`
`
`
`
`practical developments
`
`
`
`
`
`
`
`
`Subjects. Subject areas covered by the journal include:
`
`
`
`
`
`
`
`TV. HDTV and 30-TV systems
`Image Transmission
`
`
`
`
`
`
`
`Visual Science
`Interactive Image
`
`
`
`
`
`Image Coding Communication
`
`
`
`
`
`
`TV and Advanced TV
`
`
`
`
`Broadcasting
`
`Image Storage and Retrieval
`
`
`
`Graphic Arts
`
`
`Electronic Printing
`
`
`
`
`
`
`
`
`Imaging Technology
`
`Display Technology
`
`
`VLSI Processors lor
`
`
`
`Image Communications
`
`
`
`
`Membership and Subscription Information.
`
`
`
`
`SIGNAL PROCESSING IMAGE COMMUNICATION (ISBN 0923.
`
`
`
`
`
`5965) is published in one volume (six issues) a year For I994
`
`
`
`
`
`
`
`
`
`
`
`
`Volume 6 is scheduled Ior publication. Subscription prices are
`
`
`
`
`
`
`
`
`
`available upon request lrom the publisher. Subscriptions are
`
`
`
`
`
`
`
`
`accepted on a prepaid basis only and are entered on a calendar
`
`
`
`
`
`
`
`
`
`
`
`
`year basis. Issues are sent by surface mail except to the lollowing
`
`
`
`
`
`
`
`
`
`
`
`
`countries where air delivery (SAL
`Surlace Air Lifted) is
`
`
`
`
`
`
`
`
`
`ensured: Argentina. Australia. Brazil. Canada. Hong Kong. India.
`
`
`
`
`
`
`
`
`Israel. Japan. Malaysia. Mexico. New Zealand. Pakistan. People‘s
`
`
`
`
`
`
`
`
`Republic of China. Singapore. South Africa. South Korea. Taiwan.
`
`
`
`
`
`
`
`
`
`Thailand. USA For the rest oi the world. airmail charges are
`
`
`
`
`
`
`
`
`
`
`
`available upon request Claims for missing issues will be honour-
`
`
`
`
`
`
`
`
`
`ed lree of charge it made wrlhin six months alter the publication
`
`
`
`
`
`
`
`
`
`
`
`date of the issues Mail orders and inquiries to: Elsevier Science
`
`
`
`
`
`
`
`
`
`
`BV Journals Department PO. Box 211 1000 AE Amsterdam.
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`The Netherlands For lull membership information of the Associ-
`ation possibly combined witha subscription at a reduced rate.
`
`
`
`
`
`
`
`
`
`please contact. EURASIP PO Box 134 CH 1000 Lausanne I3.
`
`
`
`
`
`
`
`
`
`Swrtzerland
`
`
`
`
`
`
`0 1994 Elsevier Science B.V. All right reserved
`
`
`
`
`
`
`
`
`
`No part at this publication may be'reproduced. stored In a retrieval system or transmitted in any term or by any means electronic. mechanical. photocopying recording or
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`otherwise. without the prior permission of the publisher. EIsevter Science B V.. Copyright and Permissions Department. P 0 Box 521. two AM Amsterdam. The Netherlands
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Special ragirmlons for authors Upon acceptance 0! an article by the journal. the authorts) wili be asked to transfer copyright oI iris article to the publisher This transler will
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`ensure the widest possible dissemination of information
`
`
`
`
`
`
`
`Special regulations for readers in the USA This journal has been registered with the Copyright Clearance Center. Inc Consent is given lor copying ol articles tor personal or
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`internal use. or lor the personal use DI spectIIc clients This consent Ia given on thecoridilion that the copier pays through the Center the per-copy tee stated in the code on the
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`met page at each article Ior copying beyond that permitted by Sections 107 or 1“ ol Ihe US Copyright Law The appropriate lee should be Iorwarded wrlh a copy at the first
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`page of the article In the Copyright Clearance Center. Inc. 27 Congress Street. Salem. MA 01970. USA II no code appears in an article, the author has not given broadconsent
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`to copy and permission tocopy must be obtained directly from the author. The lens indicated on the first page oI an article in this issue will apply retroactively In all articles
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`DUOIISMG In "I! Journal, regardless oi the year at publication This consent does not extend to other kinds olcopying. such as for general distribution. resale. advertising and
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`promotion purposes. or Ior creating new collective wortis Special written permissrcn must be obtained from the publisher tor such copying
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`or operation of any methods. products instructions or ideas contained in the material herein
`No responsibilityis assumed by the Publisher tor any Injury end/or damage to persons or property as a matter at products liability. negligence or otherwise. or ircm any use
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Although all advertising material is expected to contorn'l to ethical standards. inclusion in this publication does not constitute a guarantee or endorsement ol the quality or
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`value at such product or 0! the claims made ol It by its menuiactursr.
`‘
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`as. The paper used in this publication meets the requirements of ANSI/NISO 23948-1992 (Permanence ol Paper).
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`0923-5965/94/50700
`Printed in The Netherlands
`Published 6 times a year
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Page 2 of 18
`
`Page 2 of 18
`
`

`

`
`
`
`Signal Processing: IMAGE COMMUNICATION
`
`
`
`
`
`
`Volume 6, No. 4, August 1994
`
`
`
`CONTENTS
`
`
`
`Papers
`
`
`
`
`
`
`
`
`
`
`
`
`.
`J.P. Fillard, JM Lussert, M. Castagné and H. M'timet
`
`
`
`
`
`
`
`
`
`
`
`Fourier phase shift location estimation of unfocused optical point spread functions .....
`R.-J. Chen and B.-C. Chieu
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`A fully adaptive DCT based color image sequence coder .....................
`A. Neri, G. Russo and P. Talone
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Inter-block filtering and downsampling in DCT domain .....................
`J.-H. Moon and J.-K. Kim
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`On the accuracy and convergence of 2-D motion models using minimum MSE motion
`estimation ................................................
`
`
`MW. Mak and W.G. Allen
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`A lip-tracking system based on morphological processing and block matching
`
`
`techniques ................................................
`
`
`
`
`
`
`
`S. Chang, C.-W. Jen and CL. Lee
`
`
`
`
`
`
`
`
`
`A motion detection scheme for motion adaptive pro-scan conversion .
`Z. Sivan and D. Malah
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Change detection and texture analysis for image sequence coding ...............
`
`.
`
`.
`
`.
`
`.
`
`.
`
`.
`
`.
`
`.
`
`.
`
`.
`
`.
`
`.
`
`Announcement .............................................
`
`
`
`
`
`281
`
`
`289
`
`
`303
`
`
`
`319
`
`
`
`335
`
`
`
`349
`
`
`
`357
`
`377
`
`
`
`
`
`a complete checklist wrth each diskette. Additional copies ol the guide and the checklist are available lrom the publisher
`
`Authors may now accompany their manuscripts with text: in electronic form
`
`
`
`
`
`
`
`
`
`
`
`
`
`Please see the notes on the msrde back cover and the guide at the back at the issue Authors are requested to submit
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`ANNOUNCEMENT
`
`
`Page 3 of 18
`
`Page 3 of 18
`
`

`

`rm; material my be wormed byCopyrighl law time 17 u 5 (me)
`
`
`
` .I‘n .’.
`FLS EVIER
`
`
`Signal
`
`I’:
`
`
`
`'xt'wIIt-J
`
`
`
`
`Inuit/i
`
`t mimmztuuwvi (i ll'l‘Hi
`
`
`
`
`
`
`
`ill}
`
`
`
`‘1‘
`
`
`
`SIG‘IAI. PROCI-Sfillsti-
`
`IMAGE
`COMMUNICATION
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Inter—block filtering and downsampling in DCT domain1
`
`
`
`
`
`
`
`A. Neri‘. G. Russo". P. Talonel”
`
`'Rqu' III. Rumv, I/u/i
`‘ L'mtt'riiri' u/
`
`
`
`
`
`
`
`
`hI'mulu:imu' L'gu Bun/um I'm 8 ('m/iz/mm 5‘). “0143 Rome. lm/i‘
`
`
`
`
`
`
`
`
`
`
`Received 16 December 1992
`
`
`
`
`
`
`
`
`Abstract
`
`
`The extensive use of discrete cosine transform (DCT) techniques in image coding suggests the investigation on filtering
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`and do“ nsampling methods directly acting on the I)(‘I' domain. As DCT image transforms Usually operate on blocks, it
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`is useful that the I)("I filtering techniques preserve the block dimension. In this context the present paper first revises the
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`intra-block filtering techniques to enlighten the limitations implied by small block dimensions. To overcome the artefacts
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Introduced by this method and to satisfy the filtering design constraints which are usually defined in the hiurier domain.
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`inter-block techniques are developed starting from the implementation of HR filtering. Inter-block schemes do not
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`e\hihit an) limitation but their computational cost has to be taken into account. In addition. hybrid techniques. using
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`tariable length F IR filters after the discard of low order DCT coefiiucnts, are introduced to increase the computational
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`etIicienci; in lhh case. the introduced aliasing has to he kept at tolerable values. The amount of the tolerable aliasing
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`\IFIL‘II) depends on the subsequent operations applied to the tiltered and downsaiiipled image. The numerical examples
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`reported could form a basis for error estimation and eialuation of trade-off between performance and computational
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`completit}.
`
`
`Kl’l‘ nun/x.
`
`
`
`
`I)I\CI'L‘IC cosine transform; Block operation Filtering: Downsampling
`
`
`
`
`
`
`
`
`
`
`
`
`
`I. Introduction
`
`
`
`
`
`
`
`
`
`
`Filtering and downsampling of image signals are
`
`
`
`
`
`
`basic operations normally performed in image pro—
`
`cessing.
`
`
`
`
`
`
`
`
`
`
`
`'1 his is. for instance. the case of spatial scalabil-
`
`
`
`
`
`
`
`
`ity (cg. MPEU High 1440x1152 a» C(‘IR 601
`
`
`
`
`
`
`
`
`
`
`
`720 x 576 => M PEG SIF 352 x 288 [2. 6] and
`
`
`
`
`
`
`
`
`JI’LZG Progressive Hierarchical Mode [7]l as well
`
`
`
`
`
`
`as of chrominance downsampling (cg.
`(‘CIR
`
`
`
`
`
`
`4:4:4 ->CIR 423:2 :> MPEG 4:2:0 [16]),
`
`
`
`
`
`I‘iltering and downsampling are usually carried
`
`
`
`
`
`
`
`
`
`
`out in the space domain by means of FIR filters.
`
`
`
`
`
`
`
`
`However. the extensive use of DCT techniques in
`
`
`
`
`
`
`
`
`image coding suggested the investigation on filter-
`
`
`
`
`
`
`ing and downsampling directly in the transformed
`
`
`
`
`
`
`tDCTt domain. As DCT image transforms usually
`
`
`
`
`
`
`
`
`
`‘(‘orresponding author. Tel
`
`
`
`
`SJXIMJIN
`
`in the framework of the
`' [his work has been carried out
`
`
`
`
`
`
`
`
`
`
`
`agreement between I'nnda/ionc Bordoni and the Italian PT
`
`
`
`
`
`
`
`.'\t.imlnlSIrtiIlun.
`
`+39-6-54XIHJNI.
`
`
`
`
`
`
`Inn
`
`
`
`+3‘}»b-
`
`
`
`
`tW-t Iflsei'ier Science B V. All rights resencd
`0971 Sam 94 8700 C:
`
`
`
`
`
`
`
`SS‘DI 0921 S‘HsipltflltHH'KD
`
`
`
`
`
`Page 4 of 18
`
`

`

`304
`
`
`
`.4. Nor: ('f u/ . Sign”! Protr'tving Image ('ummu/imrlr'un o . [994; 303 317
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`~
`
`
`
`
`
`
`
`
`
`operate on square blocks of small dimension (8, 16).
`
`
`
`
`
`
`DCT operations are usually intra-block oriented.
`
`
`
`
`
`
`In particular, the above mentioned operations can
`
`
`
`
`
`
`
`
`
`
`be realized as matrix products [1.5.8 10.12.13].
`
`
`
`
`
`
`
`
`The possibility to combine into a unique oper-
`
`
`
`
`
`
`ator (acting on spatial or
`transformed blocks)
`
`
`
`
`
`
`
`
`a series of block operations such as direct and
`
`
`
`
`
`
`inverse transforms. intra-block filtering and down-
`
`
`
`
`
`sampling was demonstrated in [l].
`
`
`
`
`
`
`The matrix based operations allow to directly
`
`produce
`
`
`
`
`
`
`— the DCT transform of a filtered or downsampled
`
`
`
`
`
`image from the original image.
`
`
`
`
`
`
`
`the DCT transform ofa filtered or downsampled
`
`
`
`
`image from its DCT.
`
`
`
`
`
`
`
`, a filtered or downsampled image from its DCT.
`
`
`
`
`
`
`
`
`
`This paper presents a brief review of the intra-
`
`
`
`
`
`
`
`block filtering methods in DCT domain and dis-
`
`
`
`cusses their performance.
`Then,-in order to overcome the intra-block tech-
`
`
`
`
`
`
`
`
`
`
`
`nique drawbacks, an inter-block filtering method
`
`
`
`
`
`
`
`and some hybrid techniques are presented and dis-
`
`
`
`
`
`
`
`
`
`cussed. The use ofan inter-block technique is neces-
`
`
`
`
`
`
`
`sary to satisfy the filtering design constraints which
`
`
`
`
`
`
`
`
`are usually defined in the Fourier domain.
`
`
`
`
`
`All the above-mentioned techniques are present-
`
`
`
`
`
`
`
`
`
`ed in a context that aims at preserving the trans-
`
`
`
`
`
`
`formed block dimension; this means that. manipu-
`
`
`
`
`
`
`
`
`
`lating image blocks of N x N pixels, a transformed
`
`
`
`
`
`
`
`
`
`kN x hN macroblock is considered as a set of (hk)
`transformed blocks of dimension N x N and not as
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`a single kN x hN transformed block.
`
`
`
`
`
`
`
`The paper is organized as follows. Sections 2
`
`
`
`
`
`
`
`
`
`
`
`and 3 report a concise review of some basic con-
`
`
`
`
`
`cepts and definitions regarding spatial filtering,
`
`
`
`
`
`
`downsampling and DCT transform. Moreover, no—
`
`
`
`
`
`
`
`
`tation used in the following description is introduc-
`
`
`
`
`
`
`
`
`
`ed. ln Section 4 a method to perform spatial down-
`
`
`
`
`
`
`sampling in DCT domain is presented. Section
`
`
`
`
`
`
`5 presents a review of‘the intra-block filtering tech-
`
`
`
`
`
`
`
`
`niques in DCT domain and illustrates their perfor—
`
`
`
`
`
`
`
`mance. In Section 6. an inter-block filtering tech-
`
`
`
`
`
`
`
`nique is proposed and its properties are discussed.
`
`
`
`
`
`
`
`Finally, in Section 7. hybrid methods to increase
`
`
`
`
`
`the computational efficiency of the inter-block
`
`
`
`
`
`
`technique are suggested and their performance are
`
`
`
`
`
`
`
`directly derived from the results illustrated in Sec-
`tions 5 and 6.
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`2. Spatial filtering and downsampling
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Image filtering is usually carried out in the space
`
`
`
`
`
`
`
`
`domain by means of FIR filters. Simple methods
`
`
`
`
`
`
`
`
`
`based on pixel averaging are reported in [6. 7].
`
`
`
`
`
`
`
`The well established FIR design techniques allow
`
`
`
`
`
`
`
`to easily satisfy the frequency filtering constraints.
`
`
`
`
`
`
`
`
`
`As a matter of fact.
`these constraints are usually
`
`
`
`
`
`
`
`
`given in terms of templates in the Fourier domain.
`
`
`
`
`
`
`
`For instance.
`the template for insertion loss/fre-
`
`
`
`
`
`quency characteristic of the CC IR recommended
`
`
`
`
`
`
`
`
`
`low-pass filter for the 4:4 :4 =>4:2:2 format con-
`
`
`
`
`
`version is reported in [2].
`
`
`
`
`
`
`A usual method to perform spatial bidimensional
`
`
`
`
`
`
`
`
`
`2:1 downsampling on an image is to serially oper-
`ate on columns and on rows.
`
`
`
`
`
`
`
`
`
`
`
`
`Executing a 2: 1
`column downsampling on
`
`
`
`
`
`
`
`
`
`
`a N x 2N block [g] means essentially to assemble
`
`
`
`
`
`
`
`
`
`
`
`an N x N matrix with the odd columns of [g].
`
`
`
`
`
`
`
`The assembly must be preceded by a low-pass
`
`
`
`
`
`
`
`
`
`filter on [g] rows to reduce aliasing efiects on the
`
`
`downsampled image.
`
`
`
`
`
`
`
`
`
`Similarly, a 221 row downsampling on a 2N x N
`
`
`
`
`
`
`
`
`
`
`block [9] means to assemble an N x N matrix with
`
`
`
`
`
`the odd rows of [g].
`
`
`
`
`
`
`
`
`
`Obviously the choice of odd columns or rows is
`
`
`
`
`
`
`
`
`a conventional matter: the operations on the even
`
`
`
`
`components are totally equivalent.
`
`
`
`
`
`
`3. DCT operator
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Let g” be the r'j-element of the N x N image block
`
`
`
`
`
`
`
`
`
`
`[g] and G...
`the tic-element of the N x N two-
`
`
`
`dimensional DCT [G].
`
`
`
`
`
`
`
`As well known. G... has the following expression
`
`[ll]:
`
`
`
`
`
`
`
`
`
`
`
`
`2((u)c(i> N l” ‘
`(21' + Hurt
`:4) 1209.] cos—2N
`
`
`
`
`
`
`
`
`
`(Zj + llvrr
`
`
`
`xcosT (l)
`
`
`
`
`G,,.=
`
`
`
`where
`
`
`
`
`’
`
`
`
`
`
`(M(v) {WV/2".
`
`_ 1,
`
`u,v=0,...,N— 1.
`
`
`
`
`
`
`
`
`
`
`
`if u.v = 0,
`otherwise.
`
`
`
`
`
`Page 5 of 18
`
`Page 5 of 18
`
`

`

`A.
`
`.VI’N or a! - Signal Prm‘evxing. Image Communication 0 4 I 994, 103 1/7
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`305
`
`
`
`
`
`
`
`Applying the two-dimensional [DCT transform
`
`
`
`
`
`
`
`
`
`
`
`
`[ii] to the matrix [G].
`the element gU can be
`
`
`expressed as
`
`
`
`
`
`
`._"“"'1-"1
`
`
`
`
`
`9;,- = N (go ”go ('lulc‘lt‘le. cos (
`
`
`
`.,.
`
`
`
`.j + Hurt
`
`
`xcosT,
`
`
`
`2i+lzn
`iNii‘ ,
`
`
`
`
`
`
`7
`
`t.)
`
`
`2N]=Ex~]1 OCT block
`[W] x [
`
`
`Mal“ operator
`
`
`
`
`
`2 vertical adjacent
`
`
`
`DCT blocks
`
`
`
`
`
`
`
`
`
`IN
`
`
`[mm :1 X
`
`2 horizontal amatent
`
`
`DCT 5‘06“
`
`
`
`
`
`=
`E
`(V
`
`Matrix operator
`
`
`
`
`
`
`
`
`Em]
`\ DCT b ack
`
`
`
`
`
`
`
`
`
`i,j=0,...,N— l.
`
`
`
`Fig.
`
`
`l. DCT row or column downsampling.
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Eqs. (1) and (2) may be, respectively, written in
`matrix notation as
`
`
`
`
`
`
`
`
`
`
`
`
`(the subscript s indicates the row or column down-
`
`
`sampled blocks):
`
`[s1"""””]s = [Um]. I [g""’“];]
`
`
`
`
`
`= [[g‘"’] | [9"H “1] [S] .
`
`
`
`
`
`
`
`
`
`where [g""" " "], is the downsampled N x N block
`
`
`
`
`
`
`
`
`and [S] is a 2N x N downsampling matrix oper-
`ator defined as follows:
`
`
`
`
`
`
`
`(5)
`
`
`
`
`
`
`
`[G] = [T] [a] [Ti H
`
`
`
`
`[g] = ”1“ [G] [T],
`
`
`
`
`
`
`(3)
`
`
`(4)
`
`
`
`
`
`
`
`
`
`
`
`
`
`where [T] is the NXN DCT transform matrix
`
`
`
`
`
`
`
`that
`[I l]. The DCT unitary property assures
`
`
`
`
`
`
`
`
`[T]" = [T]T where [T]T means the transpose of .
`
`[T].
`
`
`
`
`
`
`
`
`
`In the following of this work we will use lower-
`
`
`
`
`
`
`
`
`case letters to indicate variables in the spatial do-
`
`
`
`
`
`
`
`
`
`main. and capital letters for variables in the DCT or
`DFT domain.
`
`
`
`
`
`
`
`
`
`
`
`4. The 2:1 downsampling in DCT domain
`
`
`
`
`
`
`
`As mentioned in Section 2. column and row
`
`
`
`
`
`
`
`
`
`
`
`
`
`downsampling are separately considered. First col~
`
`
`
`
`
`umn downsampling will be illustrated.
`
`
`
`
`
`
`In the present section a downsampling operator
`
`
`
`
`
`
`
`equivalent to the one operating a spatial row down-
`
`
`
`
`
`
`
`
`
`
`sampling, but acting on two N x N ZD~DCT blocks
`
`
`
`
`
`
`will be examined. Obviously, a horizontal down-
`
`
`
`
`
`
`
`sampling operator acting on lD-DCTS could be
`
`
`
`
`
`
`
`
`
`derived in a similar way; however. we focus our
`attention on the 2D case because the 2D-DCT
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`defined by Eq. (3) is more frequently applied in
`
`
`image coding.
`
`
`
`
`
`
`
`
`In any case. the operator produces one DCT
`
`
`
`
`
`
`block as shown in Fig. 1.
`
`
`
`
`
`
`
`Column downsampling can be obtained just by
`
`
`
`
`
`
`
`
`applying the same operator in its transposed form.
`
`
`
`
`
`
`The 2:1 downsampling performed on a couple of
`
`
`
`
`
`
`
`
`
`
`adjacent N x N blocks [[g"”] | [g"H I’]] can be ex-
`
`
`
`
`
`
`
`
`pressed (in space domain) in the following manner
`
`
`
`
`
`
`
`Page 6 of 18
`
`1
`
`0
`
`i
`
`0
`
`
`[S] =
`
`l
`
`0 0 0
`
`
`
`0 0 0 0
`
`
`
`
`
`
`0
`0 0
`
`
`
`O 0
`
`
`
`0
`O 0
`
`
`
`0 0 0
`
`
`
`
`
`
`
`
`
`
`
`
`0
`
`
`0
`
`
`
`
`
`
`
`0
`
`0
`
`0
`
`0
`
`O
`
`0
`
`0
`
`0
`
`O
`
`l
`
`0
`
`0 0 0
`
`
`
`0 0 0 0
`
`
`
`
`
`
`
`
`l
`
`0
`
`
`
`
`
`
`
`
`
`
`The [S] operator performs the odd columns
`
`
`
`
`
`
`
`
`discard. From Eqs. (3) and (5). the 2D-DCT trans-
`
`
`
`
`form of [g"""+”]s is
`
`
`
`
`
`
`
`
`
`[Gmn ’ ”J. = [T][[9‘"’] lfg‘” ”]][S][T]"'
`
`
`
`
`= [T][[9‘"’]l[g‘"‘ ”D [723’1
`
`
`
`XEfzISJET]
`
`
`
`
`I
`
`
`
`
`= [[G‘"']|[G‘" "]][7"2][S][T]" ',
`
`
`
`
`
`(6)
`
`Page 6 of 18
`
`

`

`
`
`.,
`
`
`
`
`
`
`
`
`
`
`HF('!J)={0
`
`
`1, —W<j<W,
`
`
`
`
`otherwise.
`
`
`
`l
`
`l
`
`
`
`
`
`
`
`
`
`where [7'2] is a 2Nx2N block DCT transform
`matrix defined as follows:
`
`
`
`
`
`
`
`
`
`
`Wile? [iii
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`Hence, Eq, (6) can be rewritten as
`
`
`
`
`
`[OMWL=n0un0“wnF1
`
`
`
`where
`
`
`
`UJ=UUUHU”.
`
`
`a;
`
`
`to
`
`
`
`
`
`
`
`
`
`
`
`[F] is a 2N x N operator which can be applied
`
`
`
`
`
`
`
`
`
`
`to a couple of consecutive DCT transformed N x N
`
`
`
`
`
`
`
`
`
`
`blocks to obtain a single N x N transformed block
`
`
`
`
`
`
`of the horizontal 2:1 downsampled image.
`
`
`
`
`
`
`
`
`Considering the row downsampling it
`is easily
`
`
`
`
`
`
`
`shown that the required operator is just the trans—
`
`
`
`pose of [F ].
`
`
`
`
`
`
`
`
`
`5. Inna-block filtering in DCT domain
`
`
`
`
`
`
`
`
`As mentioned in Section 2, to reduce aliasing
`
`
`
`
`
`
`effects on the downsampled image, the downsamp-
`
`
`
`
`
`
`
`
`ling operation must be preceded by a low-pass
`
`
`
`filtering on [g].
`
`
`
`
`
`
`Intra-block filtering in DCT domain has been
`
`
`
`
`
`
`
`
`investigated in [3, 8] where a filter is derived via the
`
`
`
`
`convolution-multiplication property of the circular
`
`
`
`
`
`
`
`convolution in space domain that can be sum-
`marized as follows.
`
`
`
`
`
`
`
`
`Given a filter with symmetrical impulse response
`
`
`
`
`
`
`
`
`
`h(i,j)
`(with
`h(i,j) = htl —-i,j) = h(i,l —j)=
`
`
`
`
`
`
`
`
`
`
`h(l — i, l — j)) and a real sequence x, the 2D circu-
`lar convolution
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`y(n,k) = fin, k)*h(n.k),
`
`
`
`
`
`
`
`n. k = 0.1, 2.
`
`
`
`N — 1,
`(9)
`
`where 2m k) is the 2D symmetrical sequence de-
`
`
`
`
`
`
`
`
`fined by
`
`
`
`
`
`.106
`
`
`
`.4. NW! 1'! al.
`
`
`
`
`'Signul Pltlt‘t’leng. Image ('ommmm-alion 6 f 1994 l 303 J17
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`has the following DCT transform [3]:
`
`
`
`
`
`YCUJ) = XclillleFl'lll
`
`
`
`
`
`
`
`
`
`
`i.j= —N,—N+l....,N——2‘N—l:
`
`
`
`
`
`(11)
`
`
`
`
`
`
`
`
`
`
`
`
`
`where YCUJ) and Xc(i.j) are the ANN DCT
`
`
`
`
`
`
`
`
`
`symmetrically extended to the [—N. ..., N — l;
`
`
`
`
`
`
`
`
`
`
`—N..... N—l]
`range as defined in
`[3] of
`
`
`
`
`
`
`
`
`the sequences y and x respectively. while H,~(i.j)
`
`
`
`
`
`
`
`
`the bidimensional DFT of the filter impulse
`is
`response.
`
`
`
`
`
`
`
`[deal low-pass filtering in horizontal direction
`
`
`
`
`
`
`corresponds to a frequency operator Hpti. j) of the
`
`
`following type:
`
`
`
`
`
`
`
`
`
`
`
`
`
`Based on the sequences product of Eq. (H),
`
`
`
`
`
`
`
`a simple intra-block low-pass filtering operator in
`DCT domain can be written in matrix form as
`
`
`
`
`
`
`
`
`
`
`
`follows [1]:
`
`
`
`[Y]=[X3[P]~
`
`
`
`(12)
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`where [X] and [Y] are the N x N DCT of x and y,
`
`
`
`
`
`
`
`
`
`respectively. and [P] is the following N x N matrix:
`
`
`_[H m]
`”1'hm NJ
`
`
`
`
`
`
`
`
`
`
`
`
`
`where [I] is a W, x W, unity matrix.
`
`
`
`
`
`
`
`
`lntra-block filtering operation defined by (12)
`
`
`
`
`
`
`
`
`
`and column downsampling defined in Section 4 can
`
`
`
`
`
`
`
`
`
`be combined in a unique 2N x N operator acting in
`
`
`
`
`
`
`
`
`the DCT domain on a couple of transformed
`
`
`
`
`
`
`blocks, thus giving the DCT block:
`
`
`
`
`
`[G"""“ ’L = [[G‘”"’] l [G"”]] [Q],
`
`where
`_
`~
`1
`[Q] = [P2][T2][S][T] '
`
`
`
`,
`
`
`(13)
`
`
`(14)
`
`
`
`x(n.k)
`
`
`
`
`,1(—l —n,k)
`
`
`
`fin.k)=
`
`
`
`x(n,—l—k)
`
`
`
`
`
`
`
`
`n,k=0.l.2....,N—l;
`
`
`
`
`
`
`
`
`
`k=0.l,2, ...,N— 1; n= —N, -—N+ l,
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`n=0.l,2,...,N—l:k=—N.—N+l....,—l;
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`x(-i-n.-—l—k) n.k=—N,—N+l.....—l;
`
`—l;
`
`(10)
`
`
`
`Page 7 of 18
`
`Page 7 of 18
`
`

`

`.-I. New at (1/ Signal Prm‘armig: Image ('ommummlion o ( [994) 5‘!!! 3/7
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`307
`
`
`
`and
`
`
`
`
`~
`= [P]
`rm [[0]
`
`
`
`
`
`[01
`[Hi
`
`
`
`
`
`
`
`
`
`
`
`
`in the vertical
`It could be easily shown that.
`
`
`
`
`
`
`
`
`
`filtering and row downsampling case. the N x 2N
`
`
`
`
`
`
`
`
`
`operator is just the transpose of [Q].
`
`
`
`
`
`
`5. I. Performance
`
`
`
`
`
`
`
`
`
`
`For real images, each N x N image block is not
`
`
`
`
`
`
`
`
`
`approximated by using Eq. (10) written for N/2
`instead of N.
`
`
`
`
`
`
`
`
`
`
`
`In particular for small N. expressions (11) and
`
`
`
`
`
`
`
`
`(12) cannot be considered approximations of the
`
`
`
`
`spatial circular convolution (9).
`
`
`
`
`
`
`
`To understand better the behaviour of the [P]
`
`
`
`
`
`
`operator, let us consider a monodimensional single
`
`
`
`
`
`
`
`
`tone with variable phase shift 4). centred at fre-
`
`
`
`quency (m,(l,./2N)):
`
`
`
`
`
`
`
`
`
`
`_
`(2n + ”mm
`
`
`
`
`X" — COS W—-“— ‘i‘
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`In order to illustrate this effect better.
`
`
`
`
`
`
`
`
`
`
`
`
`
`express the filter output in DFT domain:
`
`
`
`let us
`
`
`
`
`
`
`
`
`
`
`[Yon] = [XDFTHDFTMJ[fzrwfiz]
`
`
`
`x [filtDFhJ ‘.
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`where [XDn] and [Yun] are the 2N points input
`
`and output DFTs. respectively: [72] and [F2] are
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`defined in Sections 3 and 4 while matrix [DFsz] is
`
`
`
`
`
`
`
`
`
`the 2N points DFT transform matrix defined in
`
`
`
`
`
`
`
`
`
`
`[4]. The 2N points extension is necessary to map all
`
`
`
`
`
`
`
`
`
`the DCT components in the DFT domain [5] for
`a block size of N.
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`In Figs. 2 and 3 two examples of the output
`
`
`
`
`
`
`
`
`spectra [Yon] for both in-band and out-band sig—
`
`
`
`
`
`
`
`
`
`
`
`nals are reported for N = 8. It comes clear that the
`
`
`
`
`
`
`
`
`[P] operator in DCT domain is not equivalent to
`
`
`
`
`
`
`
`
`a sharp low-pass filter in the DFT domain.
`
`
`
`
`
`
`
`The precise mapping. in DCT domain, of a gen-
`
`
`
`
`
`
`eric DFT block operation, corresponding to a spa-
`
`
`
`
`
`
`
`
`tial circular convolution. was carried out in [5].
`
`
`
`
`
`Nevertheless, all the filtering techniques above
`
`
`
`
`
`
`
`are based on intra-block operators and. for this
`
`
`
`
`
`
`
`
`reason, they do not correspond to a spatial linear
`
`
`
`
`
`
`
`convolution. As a consequence,
`the block tech-
`
`
`
`
`
`
`
`
`
`
`
`
`niques are not helpful in the usual filter design task
`
`
`
`
`
`
`
`
`
`when the performances are assigned in the Fourier
`domain.
`
`
`
`
`
`
`
`Strictly speaking. the matrix product techniques
`
`
`
`
`
`
`
`
`
`should not be named filtering when applied, in the
`
`
`
`
`
`
`
`
`
`
`real cases, to adjacent signal blocks. As noted in [l]
`
`
`
`
`
`
`
`
`a matrix product corresponds to a shift variant
`
`
`
`
`
`
`linear operation: consequently. it cannot be repres-
`
`
`
`
`
`
`ented by means of a transfer function.
`
`
`
`
`
`
`
`
`
`When the input signal is not a DCT frequency
`
`
`
`
`
`
`
`
`
`and the matrix operator is applied to a long se-
`
`
`
`
`
`
`
`
`
`quence of blocks, the method of analysis proposed
`
`
`
`
`
`in [I] can be applied.
`
`
`
`
`
`
`
`
`
`
`
`the input assumes
`In fact,
`if this is the case.
`
`
`
`
`
`
`
`
`
`a different phase in each block and the long-term
`
`
`
`
`spectrum is phase independent.
`
`
`
`
`
`
`The number of output components produced by
`
`
`
`
`
`
`
`
`
`
`an input tone is equal to the block size N. Their
`
`
`
`
`
`
`
`position in the baseband spectrum can be deter-
`
`
`
`
`
`
`
`
`mined as function of the input frequency f.
`
`
`
`
`
`
`
`
`
`
`Let A be the distance of f from the nearest DCT
`
`
`
`
`
`
`frequency DCT". Then the output components are
`
`
`
`
`
`
`
`
`
`
`
`
`
`l
`
`>< i u E
`
`
`
`
`
`
`xcos
`
`
`
`
`
`-— — k <‘(ml sin pmgosin M—+2—:M
`
`
`
`
`(2n+ llnlft
`
`
`—— =0....,N.
`
`
`
`
`
`2N
`, m
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`3
`
`
`
`
`
`
`
`')
`
`
`
`N '1
`
`
`
`
`
`
`
`
`
`
`
`
`~
`
`
`
`
`
`
`
`
`
`
`
`
`
`
`The previous expressions show that the X m coef-
`
`
`
`
`
`
`
`
`ficients depend on the input sequence phase :15 with
`sinusoidal law.
`
`
`
`
`
`
`
`
`Discarding the coefficient X m corresponds to
`
`
`
`
`
`
`
`
`
`completely deleting the x sequence only if the initial
`
`
`
`
`
`
`
`
`
`
`
`phase is zero while.
`in the other cases (if) aé 0:
`
`
`
`
`
`
`
`
`
`
`X m M. at 0). only a part of x is deleted. Thus, this
`
`
`
`
`
`
`
`
`
`
`operation produces visible aliasing due to the addi-
`
`
`
`
`
`
`tional frequency components introduced in the re-
`
`
`
`
`
`
`
`
`
`constructed signal. We remark that aliasing can be
`
`
`
`
`
`
`generated even from in-band signals (in. < WI)
`
`
`
`
`
`
`
`
`
`since they usually exhibit non-zero high order
`
`
`
`
`(m, > W.)