Polygonal Approximation and Scale-Space Analysis of Closed Digital Curves

382 Pages·2013·5.57 MB·English

by  Kumar S. Ray

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of CPloolsyegdoo nDf aCigl lAoitpasepl Cdro uDxriivmgeitasatli oCnu arvneds Scale-Space Analysis
Thiso bfo Cokl ocosvTeehridss tbDhoeoi gkm ciotosavt elim rCsp touhrerta vmneto tssotp iimcsp oinr ttahnet atorpeiac so fi np athttee ranr erae coofg pnaittitoenr,n recognition,
object recogonbitjeiocnt , rceocmogpnuitteiorn , viscoiomn,p urteorb otv isvioisnio, n,r obmoet divciasli onc,o mmpeudtiincga,l computing,
This book covers the most important topics in the area of pattern recognition,
computationacl ogmepoumtaettioryn, aal ngde obmioeintrfyo, rmanadtic sb iosiynsfotermmas.t icRs esaydsetresm ws.i ll Rfeinadd ears will find a
object recognition, computer vision, robot vision, medical computing,
comprehensivceo mtprereahtmenesnivt e oft repaotlmygeonnt alo f appporloygxiomnaatli ona pparnodx imitast iorne ala nldif e its real life
computational geometry, and bioinformatics systems. Readers will find a
applications. aTphpeli cbaotioonk s.n oTt hoen lbyo oekx pnlaoitn so nthlye etxhpeloarinesti cathl ea sthpeeocrtes ticbault aaslspoe cts but also
comprehensive treatment of polygonal approximation and its real life
presents applpicraetsioennsts w aipthp dliceatatiiolends dweitshig dne ptaairleadm deetesrigsn. parameters.
applications. The book not only explains the theoretical aspects but also
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researchers, rbeuste iatsr cshcearlse,- sbpuat cites asncaallyes-sisp ahcaes annoat lbyesiesn h tahso rnooutg bhelye nd isthcoursosuegdh. ly discussed.
Polygonal approximation of digital curves has been cultivated by many
Hence, a systHeemnacteic, dae svyesltoepmmaetinct doef vpeolloypgmoneanlt aopf pproolxyigmoantaiol na papnrdo xsicmaaleti-osnp aacned scale-space
researchers, but its scale-space analysis has not been thoroughly discussed.
analysis of daigniatalyl scisu rovef disig ivtaelr yc uersvsee nist iavle froyr efsustuernet iawl ofrokr. fAultsuore t hweorerk .i sA nlsoo there is no
Hence, a systematic development of polygonal approximation and scale-space
comprehensivceo mboporekh oenn spivoely gboonoakl oanp pproolyxgimoantaiol na papnrdo xsicmaaleti-osnp aacned asncaallyes-sisp aocf e analysis of
analysis of digital curve is very essential for future work. Also there is no
digital curves.d Tighitisa lb couorkv ewsi.l lT bhei sv ebroyo uks weiflul bl fero vmer tyh uesoerefutilc farol man tdh eporarecttiiccaall apnodin pt oraf ctical point of
comprehensive book on polygonal approximation and scale-space analysis of
view. The lasvt ipeawr.t Tohf eth lea sbt opoakr th oafn tdhlee sb oao ske hriaens dolef sa pap sliecariteiosn osf ianp tphleic aatrieoan so fin the area of
digital curves. This book will be very useful from theoretical and practical point of
structural pattsetrrnu cctluarsasli pficaattteiornn calnads soibficjeacttio renc aongdn oitbiojenc.t recognition.
view. The last part of the book handles a series of applications in the area of
structural pattern classification and object recognition.
About the AuAthboorust the Authors
KumAabro uSt. tRheaK yAu, umPtahhroD rS,s .i sR aa yp, rPofheDss, oisr ian pthroef eEslseocrtr oinn icthse aEnlde cCtroomnimcsu naincda tiCono mmunication
Science Unit Sact itehnec Ien dUinaint aStt athties tIicnadli aInns Stittuatteis,t iKcaoll kIantsati,t uInted,i aK. oHlkea htaa,s I nwdriiatt.e Hn ea has written a
Kumar S. Ray, PhD, is a professor in the Electronics and Communication
number of arntiucmlebse pr uobfl isahrteicdle isn pinutbelrisnhaetido nianl ijnotuerrnnaaltsio annadl johuarsn aplrse saenndt ehda sa t presented at
Science Unit at the Indian Statistical Institute, Kolkata, India. He has written a
several professesvioenraall mpreoefetisnsgios.n aHli sm ceuertrienngts .r eHsiesa cruchrr einntte rreessetsa rinchcl uindtee raersttifsic iinacl lude artificial
number of articles published in international journals and has presented at
intelligence, cinotmelpliguetenrc vei,s icoonm, pcoumtemr voinsisoenn, sceo mremasoonnsienngs, es orfet acsoomnipnugt,i nsgo,f tn coonm- puting, non-
several professional meetings. His current research interests include artificial
monotonic demduocntoivteo ndiact daebdauscet sivyes dteamtasb, aasned s DyNstAe mcosm, apnudti nDgN. A computing.
intelligence, computer vision, commonsense reasoning, soft computing, non-
Bimmalo KnoutmonairBc Rdimeadyau,l PcKthuivDme, daisar taRa pabryao,s fPee shssDyos,r tie sam ta ts hp,e rao Snfedcs hDsoNoorAl ao ctf o tIhmnefpo Surmctihnaogtio.o ln o Tf eIncfhonrmolaotgioyn Technology
and Engineerainngd, EVnegllionreee Irninsgti,t uVtee lloofr eT eIncshtnitoultoeg yo,f VTeelclohrneo, loIngdyi,a V. eHlliosr ere, sIenadriac.h His research
Bimal Kumar Ray, PhD, is a professor at the School of Information Technology
interests incluindtee rceosmtsp iuntcelur dgera cpohmicpsu, tceor mgprauptehric vsi,s icoonm, pauntde rim vaisgioen p, raoncde simsinagg.e processing.
and Engineering, Vellore Institute of Technology, Vellore, India. His research
He has publisHheed h aa sn upmubbliesrh oefd r eas neuamrcbhe pr aopf ererss eina prcehe pr-arepveiresw ine pde joeur-rrneavlise.wed journals.
interests include computer graphics, computer vision, and image processing.
He has published a number of research papers in peer-reviewed journals.
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POLYGONAL APPROXIMATION
AND SCALE-SPACE ANALYSIS OF
CLOSED DIGITAL CURVES
TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
POLYGONAL APPROXIMATION
AND SCALE-SPACE ANALYSIS OF
CLOSED DIGITAL CURVES
Kumar S. Ray, PhD, and Bimal Kumar Ray, PhD
Apple Academic Press
TORONTO NEW JERSEY
CRC Press Apple Academic Press, Inc
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Version Date: 20130318
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About the Authors
Kumar S. Ray, PhD
Kumar S. Ray, PhD, is a professor in the Electronics and Communication Science Unit
at the Indian Statistical Institute, Kolkata, India. He has written a number of articles
published in international journals and has presented at several professional meetings.
His current research interests include artificial intelligence, computer vision, com-
monsense reasoning, soft computing, non-monotonic deductive database systems, and
DNA computing.
Bimal Kumar Ray, PhD
Bimal Kumar Ray is a professor at the School of Information Technology and Engi-
neering, Vellore Institute of Technology, Vellore, India. He received his PhD degree in
computer science from the Indian Statistical Institute, Kolkata, India. He received his
master’s degree in applied mathematics from Calcutta University and his bachelor's
degree in mathematics from St. Xavier’s College, Kolkata. His research interests in-
clude computer graphics, computer vision, and image processing. He has published a
number of research papers in peer-reviewed journals.
TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
Contents
List of Abbreviations ...........................................................................................xi
Preface ..............................................................................................................xiii
1. Polygonal Approximation ....................................................................................1
2. A Split and Merge Technique ............................................................................11
3. A Sequential One-pass Method .........................................................................21
4. Another Sequential One-pass Method ...............................................................31
5. A Data-driven Method .......................................................................................45
6. Another Data-driven Method ............................................................................57
7. A Two-pass Sequential Method .........................................................................67
8. Polygonal Approximation Using Reverse Engineering on Bresenham’s
Line Drawing Technique ...................................................................................95
9. Polygonal Approximation as Angle Detection ................................................103
10. Polygonal Approximation as Angle Detection Using Asymmetric
Region of Support ............................................................................................113
11. Scale Space Analysis with Application to Corner Detection ...........................125
12. Scale Space Analysis and Corner Detection on Chain Coded Curves ............129
13. Scale Space Analysis and Corner Detection Using Iterative Gaussian
Smoothing with Constant Window Size ..........................................................143
14. Corner Detection Using Bessel Function as Smoothing Kernel .....................175
15. Adaptive Smoothing Using Convolution with Gaussian Kernel .....................191
16. Application of Polygonal Approximation for Pattern Classifi cation and
Object Recognition ..........................................................................................199
17. Polygonal Dissimilarity and Scale Preserving Smoothing ..............................203
18. Matching Polygon Fragments ..........................................................................221
19. Polygonal Approximation to Recognize and Locate Partially Occluded
Objects Hypothesis Generation and Verifi cation Paradigm ............................235
20. Object Recognition with Belief Revision: Hypothesis Generation
and Belief Revision Paradigm .........................................................................259
viii Polygonal Approximation and Scale-Space Analysis of Closed Digital Curves
21. Neuro-fuzzy Reasoning for Occluded Object Recognition: A Learning
Paradigm through Neuro-fuzzy Concept .........................................................311
22. Conclusion .......................................................................................................341
(cid:37)(cid:76)(cid:69)(cid:79)(cid:76)(cid:82)(cid:74)(cid:85)(cid:68)(cid:83)(cid:75)(cid:92)(cid:3)....................................................................................................36(cid:20)
Index ................................................................................................................369
List of Abbreviation
AI Artificial intelligence
ATM Assumption based truth maintenance
CR Compression ratio
CV Computer vision
DFI Decomposed fuzzy implication
FOM Figure of merit
ISE Integral square error
LMPP Linear minimum perimeter polygon
MOM Measure of merit
MPP Minimum perimeter polygon
MLP Multilayer perceptron
QT Query table
SLS Smoothed local symmetries