Shape Matching / Object Recognition

Transcription

1 Image Pocessing - Lesson 4 Poduction Line object classification Object Recognition Shape Repesentation Coelation Methods Nomalized Coelation Local Methods Featue Matching Coespondence Poblem Alignment Geometic Hashing Secuit Face Recognition Shape Matching / Object Recognition/ Patten Recognition Model # Model # Model #3 Model #4 Shape Matching / Object Recognition Geneal Algoithm: ) Repesent the Model(s) ) Find Measuement in image (e.g. segmentation) 3) Repesent Measuement 4) Compae Repesentations of Model and Measuement???? Eample: Model Rep. # Piels = 00 Which Model matches the Measuement? Which Model What is the tansfomation fom Model to Measuement (tanslation, otation, scale, ) Image Segment Rep. Measuement # Piels = 7 Compae: 7 00

2 Shape Repesentation Shape epesentation must be GOOD: Shape Repesentation Must be GOOD: Sufficient: Diffeent shapes Diffeent Codes Location Invaiant Rotation Invaiant Scale Invaiant Convenient Stable Sufficient enough? Depends on the application. Sufficient? Wide Domain 3 E.g. numbes fo elements in a queue Unique Invaiance Eve distinct object has a single distinct epesentation Invaiance to Tanslation Invaiance to Rotation Not unique: dog dog dog unique : pitbull collie cocke-spaniel Invaiance to Scale Unambiguous No two distinct objects ma have a common epesentation. 3 Thee III Two II Diffeent shapes Diffeent codes

3 Stable Convenient Small petubations and Noise do not change the Repesentation dasticall. Geneative Capable of diectl geneating (ecoveing) the epesented object. 8 Chain-code : Shape Repesentation Moments Region Based Repesentation Aea Cicumfeence Width Eule Numbe Moments Quad Tees Edge Based Repesentation Chain Code Fouie Descipto Inteio Based Repesentation MAT / Skeleton Hieachical Repesentations I(,) = ij Moment: Aea: Cente of Mass M If piel (,) is IN object 0 othewise i j ij I(, ) M 00 Aveage -coodinate: Aveage -coodinate: = = M = M M = M I(,) ( M 0 M (,) =, M M )

4 Moments Quad Tee Repesentation Cental Moment: i j µ ij = ( ) ( ) I(, ) Moment epessions that ae invaiant to tanslation, otation and/o scale: wide domain, unique, unambiguous, geneative up to eo toleance patiall stable Not invaiant to tanslation, otation scale. Inefficient fo compaison wide domain, not unique, not unambiguous, not geneative, not stable invaiant to tanslation, otation. Ve convenient. Edge Based Repesentation Fouie Descipte Chain Code Bounda Repesentation wide domain unique unambiguous geneative - D onl Not ve stable Invaiant to tanslation. Rotation (90 deg) Fouie Tansfom

5 Tanslation Bounda Repesentation Fouie Tansfom Fouie Descipte wide domain unique unambiguous geneative stable - depends upon toleance Invaiant to tanslation, otation, scale Rotation (spectum) Scale Inteio Based Repesentation Hieachical Gaphical Repesentation MAT / Skeleton wide domain unique unambiguous geneative not stable - small changes affect damaticall

6 Genealized Clindes A 3D shape-desciption Finding a Patten in an Image: Staight Fowad methods image patten Binfod 97 Global vs Featue Based Appoaches to Object Detection Finding a Patten in an Image image patten Look fo minimum of: d ( u,v ) = [ I( u+,v + ) P(, ) ] e, N D e (u,v)=0

7 = =, N, N Finding a Patten in an Image d ( u,v ) = [ I( u+,v + ) P(, ) ] e, N I( u+,v + ) + P(,) I ( u+,v + ) P(,) I( u+,v + ) + P(,) I( u+,v + ) P(,) Sum of squaes of the window, N Sum of squaes of the patten CONSTANT, N Coelation Finding a Patten in an Image Coelation image patten Look fo minimum of:, N [ I( u+,v + ) P(,) ] Coelation Real Image Coelation Eample I * P image patten I co P Coelation Coelation value is dependant on the local ga value of the patten and the image window.

8 Nomalized Coelation Eample Nomalized Coelation - Eample, N, N [ I( u+,v + ) I ] P(,) uv [ P] [ I( u+,v + ) I ] P(,) uv, N [ P] / image patten Coelation value is in (-..) Coelation value is independant of the local ga value of the patten and the image window. Coelation Nomalized Coelation Featue Based Object Detection Coespondence Poblem match? model compleit = O(n ) measuements

9 Solving the Coespondence Poblem Model Matching tee Measuement Given the matching calculate tansfomation Matching tee Given the tansfomation calculate matching,,,, Using a Matching tee - Eample Matching tee Model Measuement Matching tee??

10 Matching tee Matching tee? Alignment Method Shape Recognition using Alignment Geometic encoding: Models: model Model encoded: (0,0) (0,) (,) Measuements: Alignment: votes:,3,3,,,,,,3,5

11 Model: Geometic Hashing a: (0,0) (0.5,0.5) b: (0,0) (0,-) c: (0,0) (,-) encoding a : b: c: d: (0,0) (0.5,-0.5) e: (0,0) (,) f: (0,0) (0,) d: e: f:.5 f e a: (0,0) (0.5,0.5) b: (0,0) (0,-) c: (0,0) (,-) a,b...f a d a,b...f d: (0,0) (0.5,-0.5) e: (0,0) (,) f: (0,0) (0,) - c b Models: Geometic Hashing - Matching Measuements: M M M3 M M3 M M o a single mati: M4 eample cell M-a M-f M-c M4-d Choose andom coodinates: look in hash table at locations: (0,0) (0,) (,) (,) and vote fo Model and coodinate sstem: M-a M-b M-c M-a M-b M3-a M3-b... (0,0) (0,) (,) (,) + + total Maimum votes

12 Conclusion Image Enhancement Edge detection Segmentation Shape Repesentation Object Detection Object Recognition Object Motion Object Distance