Shape Detection in Computer Vision Using the Hough Transform

209 Pages·1992·15.635 MB·English

by  V. F. Leavers BSc, PhD (auth.)

Shape Detection in Computer Vision Using the
Hough Transform
Shape Detection
in Computer Vision
Using the
Hough Transform
V.F. LEAVERS
Springer-Verlag
London Berlin Heidelberg New York
Paris Tokyo Hong Kong
Barcelona Budapest
V.F. Leavers, BSc, PhD
DepartmentofPhysics
King's College London
TheStrand
London WC2R2LS, UK
BritishLibraryCataloguinginPublicationData
Leavers, V. F.
ShapeDetectioninComputerVisionUsingtheHoughTransform
I.Title
006.3
ISBN-13:978-3-540-19723-2 e-ISBN-13:978-1-4471-1940-1
DOl:10.1007/978-1-4471-1940-1
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PREFACE
Repeated visual inspection tasks, whether industrial or academic,
are often tedious and labour intensive but nevertheless require
specialist skill and careful judgement. There have- been many
attemptstoautomatesuchprocesses. However, fewhaveyetmade
the transition from research topic to production method. One
reasonforthisisthatscientistsseemtobeinfatuatedwithanything
mathematical. If something can be expressed as an equation we
treatitwith profound respect, ifitis merelydescriptive we tend to
be dismissive. Pure research in computer recognition tasks often
pursues theories ofshape representationand detectionas goalsin
themselveswithoutanyconcernbeinggiventotheircomputability
or to any application specific adaptations. In addition, the avail
ability and applicability of the results of such research is often
hampered by the computer vision community failing to recognize
that the potential user may lack some ofthe basic skills needed in
eithercomputingormathematics. Thisbookisaimed in particular
at two groups of potential users and the problems they may
encounter.
The first group consists of 'non-mathematical' academics who
simplywantto use computervisionasa tool in theirownresearch
programs. Such peoplemaybe, for example, cytologists orbiolog
ists whose only need for anything mathematical is a good know
ledge of statistics. The opportunity to relay useful work to these
peoplecanbelostifthecomputervisioncommunitydoesnotadopt
amoreenlightenedperspectiveonthecomprehensibilityofwhatit
is producing. In particular, those of us who routinely use math
ematicsinourworklosesightofthefactthatitisaskillwhichhasto
be developed. Some of the more advanced concepts are anything
butintuitivelyobvious, itisonlybyusing them thatweareable to
understand and manipulate them. Large sections of the book set
outtodevelopthenecessarymathematicalskillswithunashamedly
simple, whollypictorialexplanations. These areaimed atdevelop
ingastrongintuitiveunderstandingoftheunderlyingmathematics
before introducing any complicated notation. Anyone who does
not need these sections can simply skip them.
Thesecondgrouparethosepeopleinindustry.Itisoftendifficult
forsuchpeopletomakeuseofcurrentresearchbecausetheylackthe
background information needed. This makes it difficult to distin
guish between genuine trends and commercially inconsequential
developmentsinanareaofresearch. Forthisreasoncompaniesare
oftenreluctant to take on board new advances. Moreover, smaller
companiesmayhave to operatewithincostconstraintswhich may
well be the final arbiters in any decision to implement new
technology. If the vision community is to court the patronage of
these people we need to respect their situation and be realistic
concerningit. With thisinmind, thebookcontainsa reviewofthe
Hough Transform technique for shape detection. Care is taken to
distinguishbetweenresearchthataimstofurtherbasicunderstand
ing of the technique without necessarily being computationally
realisticandresearchthatmaybeapplicableinanindustrialcontext.
Whilst academically, the former may undoubtedly improve the
performance of the technique, it often adds significant computa
tional burdens to the overall processing load and this may not be
acceptableinindustrialorcommercialsituations.
Both groups of people may need to acquire some feel for the
technique. Thebookendsbyrecognisingthisneed. Acasestudyis
presentedinsomedetail. Thisshowsthenewuserhowtobeginan
implementationbyfollowing aparticularalgorithmstepbystep. It
includestheprefilteringoftheimageandtheuseofedgedetectors.
More importantly, the case study also shows what can go wrong
and how to deal withit. This can save much time and frustration.
This book aims to fill a gap by making available state-of-the-art
computervisiontechniquesusingtheHoughTransformmethodof
shape detection and recognition. Ifoffers the non-specialist easily
assimilated theory plus advice about implementing the technique.
It will also be useful to post-graduate students who need an
informal butthorough groundingin thisarea ofresearch.
ACKNOWLEDGEMENTS
Iwouldliketoexpressmygratitudeto ProfessorR.E. Burge, Head
ofthe Physics Departmentat King's College London, for allowing
meuseofthedepartmentalfacilities. IalsothankDr. HelenBerenyi
whoproofreadthefinaltext. MostofallIwouldliketothankNigel
Arnot, our departmental systems manager, for all the invaluable
help, supportand encouragement he has given me.
Thetextforthisbookwas preparedonequipmentprovidedbya
Science and Engineering Research Council Grant (SERC GRIF
92343), 'A buyer's guide to the Hough Transform'. It was typeset
using Donald Knuth's TeX.
vi
CONTENTS
1 ComputerVision: Shape Detection
1.1 Why ComputerVision? 1
1.1.1 Industrial Applications 2
1.1.2 MedicalApplications 2
1.1.3 Social Applications 3
1.1.4 Military Applications 3
1.2 WhyThis Book? 3
1.3 Why the Hough Transform? 5
1.4 RepresentingShapeSymbolically............................. 5
2 TransformsWithoutTears
2.1 Beginningto See 20
2.2 WhataboutShape? 25
2.3 Tacklingthe Maths 31
2.4 Beginningto Compute 35
3 Preprocessing
3.1 The Real World 39
3.2 Spotthe Difference 40
3.3 Convolution, a NecessaryTool 42
3.4 Edge Detection 47
3.5 Which Parametrisation? 55
3.6 GettingStarted 57
3.7 Quantization 60
3.8 TestImages.......................................................... 63
4 Postprocessing
4.1 Results ofthe Transformation 66
4.2 The ButterflyFilter 70
4.3 DesignerButterflies ,'...................................... 74
4.4 PuttingThings to Work 75
4.5 Reconstruction 77
4.6 Summary 79
5 Representing Shape
5.1 From Lines to Circles 84
5.2 Double Houghing 85
5.3 Towards a Representation ofShape 88
5.3.1 Decomposition 88
5.3.2 Geometricand Spatial Relations 94
5.3.3 Saliency 98
5.3.4 Invariance 102
5.3.5 Stability 107
5.3.6 Accessibility 111
5.4 Summary 111
6 Which Hough?
6.1 Background 115
6.1.1 Historical - 115
6.1.2 Whole Shape Detection 116
6.2 Refinements 118
6.2.1 Preprocessing Considerations 118
6.2.2 Postprocessing Considerations 119
6.3 Software Solutions 121
6.3.1 Computer Friendly Algorithms........................ 121
6.3.2 Dynamically Quantised Accumulators 122
6.3.3 Constraints on ParameterCalculation 122
6.3.4 ParameterSpace Decomposition 123
6.3.5 Segmentingthe Image 124
6.4 Parallel Processing 124
6.4.1 SIMD Implementations 125
6.4.2 MIMD Implementations 126
6.5 Dedicated Hardware 126
6.6 The Probabilistic Houghs: A Review 126
7 A Case Study: Circles and Ellipses
7.1 Preprocessing the Image Data 138
7.2 The Dynamic Generalized HoughTransform 142
7.2.1 Connectivity Detection................................... 142
7.2.2 Segmentation 144
7.2.3 Sampling ofData Points................................. 148
7.2.4 Calculating the Parameters 148
7.2.5 Accumulation ofthe Parameters 151
7.2.6 Statistical Informationand a RobustStopping
Criterion 152
7.2.7 Removal ofFeatures from the Image 159
viii
7.3 A Case Study 160
7.3.1 Edge IntensityThreshold and Connectivity
Detection 160
7.3.2 Segmentation 160
7.3.3 Automatic StoppingCriterion 160
7.3.4 Results 163
7.3.5 Coping with the Unexpected 163
7.4 Discussion 170
7.5 Conclusions 172
Appendix1 173
1.1 The Radon Transform 174
1.2 Generalized Function Concentrated on a Line_ 174
1.3 The General Case : 175
1.4 Application to an Ellipse 179
Appendix 2 181
Appendix 3 183
Appendix4 184
References 187
Index 199
LIST OF FIGURES
1.1 Writing on the wall ofcomputervision 4
1.2 Faulty vision 6
1.3 Clearvision . 7
1.4 Japanese -;............ 8
1.5 Hebrew 10
1.6 Chain coding approximation ofa curve 11
1.7 Comparingdissimilar shapes 13
1.8 The medial <!Xis transform 14
2.1 Blackboxes withinblackboxes 21
2.2 Digital image 22
2.3 Counting 'ON' pixels columnby column 23
2.4 Countingonly pixels on theboundary 24
2.5 Making the pixel size smaller 25
2.6 Going into two dimensions 26
2.7 Reconstruction from tangents 27
2.8 Birth ofabutterfly! 28
2.9 Transforming straightlines 30
2.10 illustration ofdevelopmentofa b-function 32
2.11 Putting the b-function to use 33
2.12 p,OParametrization ofthe probe line 34
2.13 Relating points to curves andbackagain 36
2.14 Flow diagramofHoughalgorithm 38
3.1 Real image ofwooden block 41
3.2 Operatorcorrespondingto notional point 42
3.3 One dimensionalimage ofa pointobject 43
3.4 Results ofmatchingoperator to image points 44
3.5 Furtherresults ofmatchingoperatorto image points 45
3.6 illustration ofresponse to point detection operation 46
3.7 ConvolvingSobel operatorwith uniformintensity
pattern 48
3.8 Convolving Sobel operatorwithedge point 50
3.9 Convolving wholeimage with Sobeloperator.............. 51
3.10 Result ofSobel edge detection on real image 52
3.11 Result ofthresholding Sobel image 53
3.12 Thinned image with noise pointsremoved 54
3.13 Slope intercept parameterisation 55
3.14 Normal parametrization :.............................. 56
3.15 Muffparametrization :. 57
3.16 Flow diagram ofbasicHough algorithm 58
3.17 Topology oftransform plane 59
3.18 Length ofintersection ofprobe line 60
7)
3.19 Value ofthe integral for of};;:?; tan-1( 61
7)
3.20 Single maximum obtained for of};;:?; tan-1( 62
7)
3.21 Spread ofvalues obtained for of}< tan-1( 62
3.22 Testimages 64
4.1 Intensity oftransform plane 67
4.2 Digital line splitting 68
4.3 Search for localmaxima and threshold 69
4.4 Production ofthe boundarycurves ofbutterfly 70
4.5 illustration oflimits ofdisplayed slope 71
4.6 illustration ofconstraints on movementofboundaries .. 73
4.7 illustration ofchangein symmetry ofbutterfly shape... 73
4.8 Decomposition ofdigitalline segment........................ 76
4.9 Result of applying butterfly filter with a threshold of 20 78
4.10 Reconstruction superimposed onoriginal edge image 80
4.11 Modular shape detection system 81
5.1 Image ofcirclewithfirst and second transform planes.. 87
5.2 Iterative transformation ofcircle................................ 89
5.3 Algorithm for decompositionofimage 90
5.4 Image (1) Hexagonal nut.............................. 91
5.5 First transform plane ofimage(l) 92
5.6 Secondtransform plane ofimage(l) 93
5.7 Image(2) Circularwasher 95
5.8 Firsttransform plane ofimage(2) 96
5.9 Second transform plane ofimage(2) 97
5.10 Image(3) Hexagonal nut rotated and shifted 99
5.11 First transform plane ofimage(3) 100
5.12 Second transform plane ofimage(3) 101
5.13 Image(4) Circularwasher shifted 103
5.14 First transform plane ofimage (4) 104
5.15 Second transform plane ofimage(4) 105
5.16 Labelling of parameters associated with salient features 106
xii