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Lecture 06 geometric transformations and image registration
1.
LinĀ ZHANG,Ā SSE,Ā 2013 LectureĀ 6 GeometricĀ TransformationsĀ and ImageĀ Registration LinĀ ZHANG,Ā PhD SchoolĀ ofĀ SoftwareĀ EngineeringĀ TongjiĀ University SpringĀ 2013
2.
LinĀ ZHANG,Ā SSE,Ā 2013 Contents ā¢ TransformingĀ points ā¢ HierarchyĀ ofĀ geometricĀ transformations ā¢
ApplyingĀ geometricĀ transformationsĀ toĀ images ā¢ ImageĀ registration
3.
LinĀ ZHANG,Ā SSE,Ā 2013 ā¢ GeometricĀ transformationsĀ modifyĀ theĀ spatialĀ relationshipĀ betweenĀ pixelsĀ inĀ anĀ image ā¢ TheĀ imagesĀ canĀ beĀ shifted,Ā rotated,Ā orĀ stretchedĀ inĀ aĀ varietyĀ ofĀ ways ā¢
GeometricĀ transformationsĀ canĀ beĀ usedĀ toĀ ā¢ createĀ thumbnailĀ views ā¢ changeĀ digitalĀ videoĀ resolution ā¢ correctĀ distortionsĀ causedĀ byĀ viewingĀ geometry ā¢ alignĀ multipleĀ imagesĀ ofĀ theĀ sameĀ scene TransformingĀ Points
4.
LinĀ ZHANG,Ā SSE,Ā 2013 TransformingĀ Points SupposeĀ (w, z) andĀ (x,
y) areĀ twoĀ spatialĀ coordinateĀ systems inputĀ space outputĀ space AĀ geometricĀ transformationĀ T thatĀ mapsĀ theĀ inputĀ spaceĀ toĀ outputĀ spaceĀ ļ ļ( , ) ( , )x y T w zļ½ T isĀ calledĀ aĀ forwardĀ transformation orĀ forwardĀ mapping ļ ļ1 ( , ) ( , )w z T x yļ ļ½ T-1 isĀ calledĀ aĀ inverseĀ transformation orĀ inverseĀ mapping
5.
LinĀ ZHANG,Ā SSE,Ā 2013 TransformingĀ Points w z y x ļ ļ(
, ) ( , )x y T w zļ½ ļ ļ1 ( , ) ( , )w z T x yļ ļ½
6.
LinĀ ZHANG,Ā SSE,Ā 2013 TransformingĀ Points AnĀ example ļ ļ( ,
) ( , ) ( / 2, / 2)x y T w z w zļ½ ļ½ ļ ļ1 ( , ) ( , ) (2 ,2 )w z T x y x yļ ļ½ ļ½
7.
LinĀ ZHANG,Ā SSE,Ā 2013 Contents ā¢ TransformingĀ points ā¢ HierarchyĀ ofĀ geometricĀ transformations ā¢
ApplyingĀ geometricĀ transformationsĀ toĀ images ā¢ ImageĀ Registration
8.
LinĀ ZHANG,Ā SSE,Ā 2013 HierarchyĀ ofĀ GeometricĀ Transformations ā¢ ClassĀ I:Ā Isometry transformation IfĀ onlyĀ rotationĀ andĀ translationĀ areĀ considered ' 1 ' 2 cos
sin sin cos tx x y ty ļ± ļ± ļ± ļ± ļ¦ ļ¶ ļ ļ¦ ļ¶ļ© ļ¹ļ¦ ļ¶ ļ½ ļ«ļ§ ļ· ļ§ ļ·ļ§ ļ·ļŖ ļŗļ§ ļ· ļ« ļ»ļØ ļø ļØ ļøļØ ļø ' 1 ' 2 cos sin sin cos 1 10 0 1 x t x y t y ļ± ļ± ļ± ļ± ļ¦ ļ¶ ļļ© ļ¹ļ¦ ļ¶ ļ§ ļ· ļ§ ļ·ļŖ ļŗļ½ļ§ ļ· ļ§ ļ·ļŖ ļŗ ļ§ ļ·ļ§ ļ· ļŖ ļŗļØ ļøļ« ļ»ļØ ļø InĀ homogeneousĀ coordinates (MoreĀ concise!)
9.
LinĀ ZHANG,Ā SSE,Ā 2013 HierarchyĀ ofĀ GeometricĀ Transformations ā¢ ClassĀ I:Ā Isometry transformation ' ' cos
sin sin cos 1 10 0 1 x y x t x y t y ļ± ļ± ļ± ļ± ļ¦ ļ¶ ļ© ļ¹ļ ļ¦ ļ¶ ļ§ ļ· ļŖ ļŗļ§ ļ· ļ½ļ§ ļ· ļŖ ļŗļ§ ļ· ļ§ ļ·ļ§ ļ· ļŖ ļŗļØ ļøļ« ļ»ļØ ļø ' 1T ļ© ļ¹ ļ½ ļŖ ļŗ ļ« ļ» R t x x 0 Properties ā¢ R isĀ anĀ orthogonalĀ matrix ā¢ EuclideanĀ distanceĀ isĀ preserved ā¢ HasĀ threeĀ degreesĀ ofĀ freedom;Ā twoĀ forĀ translation,Ā andĀ oneĀ forĀ rotation
10.
LinĀ ZHANG,Ā SSE,Ā 2013 HierarchyĀ ofĀ GeometricĀ Transformations ā¢ ClassĀ II:Ā SimilarityĀ transformation ' 1 ' 2 cos sin sin
cos 1 10 0 1 x s s t x y s s t y ļ± ļ± ļ± ļ± ļ¦ ļ¶ ļļ© ļ¹ļ¦ ļ¶ ļ§ ļ· ļ§ ļ·ļŖ ļŗļ½ļ§ ļ· ļ§ ļ·ļŖ ļŗ ļ§ ļ·ļ§ ļ· ļŖ ļŗļØ ļøļ« ļ»ļØ ļø ' 1T sļ© ļ¹ ļ½ ļŖ ļŗ ļ« ļ» R t x x 0
11.
LinĀ ZHANG,Ā SSE,Ā 2013 HierarchyĀ ofĀ GeometricĀ Transformations ā¢ ClassĀ II:Ā SimilarityĀ transformation ' 1 ' 2 cos sin sin
cos 1 10 0 1 x s s t x y s s t y ļ± ļ± ļ± ļ± ļ¦ ļ¶ ļļ© ļ¹ļ¦ ļ¶ ļ§ ļ· ļ§ ļ·ļŖ ļŗļ½ļ§ ļ· ļ§ ļ·ļŖ ļŗ ļ§ ļ·ļ§ ļ· ļŖ ļŗļØ ļøļ« ļ»ļØ ļø ' 1T sļ© ļ¹ ļ½ ļŖ ļŗ ļ« ļ» R t x x 0 Properties ā¢ R isĀ anĀ orthogonalĀ matrix ā¢ SimilarityĀ ratioĀ (theĀ ratioĀ ofĀ twoĀ lengths)Ā isĀ preserved ā¢ HasĀ fourĀ degreesĀ ofĀ freedom;Ā twoĀ forĀ translation,Ā oneĀ forĀ rotation,Ā andĀ oneĀ forĀ scaling
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LinĀ ZHANG,Ā SSE,Ā 2013 HierarchyĀ ofĀ GeometricĀ Transformations ā¢ ClassĀ III:Ā AffineĀ transformation ' 11 12 ' 21
22 1 10 0 1 x y x a a t x y a a t y ļ¦ ļ¶ ļ© ļ¹ļ¦ ļ¶ ļ§ ļ· ļŖ ļŗļ§ ļ· ļ½ļ§ ļ· ļŖ ļŗļ§ ļ· ļ§ ļ·ļ§ ļ· ļŖ ļŗļØ ļøļ« ļ»ļØ ļø ' A 1T ļ© ļ¹ ļ½ ļŖ ļŗ ļ« ļ» t x x 0
13.
LinĀ ZHANG,Ā SSE,Ā 2013 HierarchyĀ ofĀ GeometricĀ Transformations ā¢ ClassĀ III:Ā AffineĀ transformation ' 11 12 ' 21
22 1 10 0 1 x y x a a t x y a a t y ļ¦ ļ¶ ļ© ļ¹ļ¦ ļ¶ ļ§ ļ· ļŖ ļŗļ§ ļ· ļ½ļ§ ļ· ļŖ ļŗļ§ ļ· ļ§ ļ·ļ§ ļ· ļŖ ļŗļØ ļøļ« ļ»ļØ ļø ' A 1T ļ© ļ¹ ļ½ ļŖ ļŗ ļ« ļ» t x x 0 Properties ā¢ A isĀ aĀ nonāsingularĀ matrix ā¢ RatioĀ ofĀ lengthsĀ ofĀ parallelĀ lineĀ segmentsĀ isĀ preserved ā¢ HasĀ sixĀ degreesĀ ofĀ freedom;Ā twoĀ forĀ translation,Ā oneĀ forĀ rotation,Ā oneĀ forĀ scaling,Ā oneĀ forĀ scalingĀ direction,Ā andĀ oneĀ forĀ scalingĀ ratio
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LinĀ ZHANG,Ā SSE,Ā 2013 HierarchyĀ ofĀ GeometricĀ Transformations ā¢ ClassĀ IV:Ā ProjectiveĀ transformation ' 11 12
13 ' 21 22 23 ' 31 32 33 x a a a x c y a a a y za a az ļ¦ ļ¶ ļ© ļ¹ļ¦ ļ¶ ļ§ ļ· ļ§ ļ·ļŖ ļŗļ½ļ§ ļ· ļ§ ļ·ļŖ ļŗ ļ§ ļ·ļ§ ļ· ļŖ ļŗļØ ļøļ« ļ»ļØ ļø
15.
LinĀ ZHANG,Ā SSE,Ā 2013 HierarchyĀ ofĀ GeometricĀ Transformations ā¢ ClassĀ IV:Ā ProjectiveĀ transformation ' 11 12
13 ' 21 22 23 ' 31 32 33 x a a a x c y a a a y za a az ļ¦ ļ¶ ļ© ļ¹ļ¦ ļ¶ ļ§ ļ· ļ§ ļ·ļŖ ļŗļ½ļ§ ļ· ļ§ ļ·ļŖ ļŗ ļ§ ļ·ļ§ ļ· ļŖ ļŗļØ ļøļ« ļ»ļØ ļø Properties ā¢ CrossĀ ratioĀ preserved ā¢ ThoughĀ itĀ hasĀ 9Ā parameters,Ā itĀ hasĀ 8 degreesĀ ofĀ freedom,Ā sinceĀ onlyĀ theĀ ratioĀ isĀ importantĀ inĀ theĀ homogeneousĀ coordinates AlsoĀ referredĀ toĀ asĀ homography matrix
16.
LinĀ ZHANG,Ā SSE,Ā 2013 Contents ā¢ TransformingĀ points ā¢ HierarchyĀ ofĀ geometricĀ transformations ā¢
ApplyingĀ geometricĀ transformationsĀ toĀ images ā¢ ImageĀ Registration
17.
LinĀ ZHANG,Ā SSE,Ā 2013 ApplyingĀ GeometricĀ TransformationsĀ toĀ Images GivenĀ theĀ imageĀ f,Ā applyĀ T toĀ f toĀ getĀ g,Ā howĀ toĀ getĀ g? TheĀ procedureĀ forĀ computingĀ theĀ outputĀ pixelĀ atĀ locationĀ (xk,
yk) is ā¢ EvaluateĀ ā¢ Evaluate ā¢ ļØ ļ© ļ ļ1 , ( , )k k k kw z T x yļ ļ½ ļØ ļ©,k kf w z ļØ ļ© ļØ ļ©, ,k k k kg x y f w zļ½
18.
LinĀ ZHANG,Ā SSE,Ā 2013 ApplyingĀ GeometricĀ TransformationsĀ toĀ Images ( , )k
kx y ( , )k kw z ā¢ NotesĀ onĀ interpolation ā¢ EvenĀ ifĀ Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā areĀ integers,Ā inĀ mostĀ casesĀ Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā areĀ not ā¢ ForĀ digitalĀ images,Ā theĀ valuesĀ ofĀ f areĀ knownĀ onlyĀ atĀ integerā valuedĀ locations ā¢ UsingĀ theseĀ knownĀ valuesĀ toĀ evaluateĀ f atĀ nonāintegerĀ valuedĀ locationsĀ isĀ calledĀ asĀ interpolation w z y x ( , )f w z ( , )g x y ( , )k kx y ( , )k kw z 1 T ļ
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LinĀ ZHANG,Ā SSE,Ā 2013 ā¢ NotesĀ onĀ interpolation ā¢ InĀ Matlab,Ā threeĀ commonlyĀ usedĀ interpolationĀ schemesĀ areĀ builtāin,Ā includingĀ nearestĀ neighborhood,Ā bilinear,Ā andĀ bicubic ā¢
ForĀ mostĀ Matlab routinesĀ whereĀ interpolationĀ isĀ required,Ā ābilinearā isĀ theĀ defaultĀ Ā ApplyingĀ GeometricĀ TransformationsĀ toĀ Images
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LinĀ ZHANG,Ā SSE,Ā 2013 ApplyingĀ GeometricĀ TransformationsĀ toĀ Images ā¢ Matlab implementation ā¢
āMaketformā isĀ usedĀ toĀ constructĀ aĀ geometricĀ transformationĀ structure ā¢ āimtransformā transformsĀ theĀ imageĀ accordingĀ toĀ theĀ 2āDĀ spatialĀ transformationĀ definedĀ byĀ tform Note:Ā inĀ Matlab,Ā geometricĀ transformationsĀ areĀ expressedĀ as ļØ ļ© ļØ ļ©' ' 1 1x y x yļ½ A whereĀ A isĀ aĀ 3Ā byĀ 3Ā transformationĀ matrix
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LinĀ ZHANG,Ā SSE,Ā 2013 ApplyingĀ GeometricĀ TransformationsĀ toĀ Images ā¢ Matlab implementation AnĀ example im
= imread('tongji.bmp'); theta = pi/6; rotationMatrix = [cos(theta) sin(theta) 0;-sin(theta) cos(theta) 0;0 0 1]; tformRotation = maketform('affine',rotationMatrix); rotatedIm = imtransform(im, tformRotation,'FillValues',255); figure; subplot(1,2,1); imshow(rotatedIm,[]); rotatedIm = imtransform(im, tformRotation,'FillValues',0); subplot(1,2,2); imshow(rotatedIm,[]);
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LinĀ ZHANG,Ā SSE,Ā 2013 ApplyingĀ GeometricĀ TransformationsĀ toĀ Images ā¢ Matlab implementation AnĀ example originalĀ image rotatedĀ images
23.
LinĀ ZHANG,Ā SSE,Ā 2013 ApplyingĀ GeometricĀ TransformationsĀ toĀ Images ā¢ Matlab implementation AnotherĀ example originalĀ image affineĀ transformedĀ images
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LinĀ ZHANG,Ā SSE,Ā 2013 ApplyingĀ GeometricĀ TransformationsĀ toĀ Images ā¢ OutputĀ imageĀ withĀ locationĀ specified ā¢ ThisĀ isĀ usefulĀ whenĀ weĀ wantĀ toĀ displayĀ theĀ originalĀ imageĀ andĀ theĀ transformedĀ imageĀ onĀ theĀ sameĀ figure InĀ Matlab,Ā thisĀ isĀ accomplishedĀ by imshow(image,Ā āXDataā,Ā xVector,Ā āYDataā,Ā yVector) āXDataā
andĀ āYDataā canĀ beĀ obtainedĀ byĀ imtransform
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LinĀ ZHANG,Ā SSE,Ā 2013 ApplyingĀ GeometricĀ TransformationsĀ toĀ Images ā¢ OutputĀ imageĀ withĀ locationĀ specified AnĀ example im =
imread('tongji.bmp'); theta = pi/4; affineMatrix = [cos(theta) sin(theta) 0;-sin(theta) cos(theta) 0;-300 0 1]; tformAffine = maketform('affine',affineMatrix); [affineIm, XData, YData] = imtransform(im, tformAffine,'FillValues',255); figure; imshow(im,[]); hold on imshow(affineIm,[],'XData',XData,'YData',YData); axis auto axis on
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LinĀ ZHANG,Ā SSE,Ā 2013 ApplyingĀ GeometricĀ TransformationsĀ toĀ Images ā¢ OutputĀ imageĀ withĀ locationĀ specified AnĀ example -600 -400
-200 0 200 400 600 0 100 200 300 400 500 600 700 DisplayĀ theĀ originalĀ imageĀ andĀ theĀ transformedĀ imageĀ inĀ theĀ same coordinateĀ system
27.
LinĀ ZHANG,Ā SSE,Ā 2013 Contents ā¢ TransformingĀ points ā¢ HierarchyĀ ofĀ geometricĀ transformations ā¢
ApplyingĀ geometricĀ transformationsĀ toĀ images ā¢ ImageĀ Registration ā¢Background ā¢AĀ manualĀ method
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LinĀ ZHANG,Ā SSE,Ā 2013 Background ā¢ OneĀ ofĀ theĀ mostĀ importantĀ applicationsĀ ofĀ geometricĀ transformationsĀ isĀ imageĀ registration ā¢ ImageĀ registrationĀ seeksĀ toĀ alignĀ imagesĀ takenĀ inĀ differentĀ times,Ā orĀ takenĀ fromĀ differentĀ modalities ā¢
ImageĀ registrationĀ hasĀ applicationsĀ especiallyĀ in ā¢Medicine ā¢RemoteĀ sensing ā¢Entertainment
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LinĀ ZHANG,Ā SSE,Ā 2013 BackgroundāExample,Ā CTĀ andĀ MRIĀ Registration TopĀ row:Ā unregisteredĀ MRĀ (left)Ā andĀ CTĀ (right)Ā imagesĀ BottomĀ row:Ā MRĀ imagesĀ inĀ sagittal,Ā coronalĀ andĀ axialĀ planesĀ withĀ theĀ outlineĀ ofĀ bone,Ā thresholded fromĀ theĀ registeredĀ CTĀ scan,Ā overlaid
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LinĀ ZHANG,Ā SSE,Ā 2013 BackgroundāExample,Ā PanoramaĀ Stitching TwoĀ images,Ā sharingĀ someĀ objects imageĀ 1 imageĀ 2
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LinĀ ZHANG,Ā SSE,Ā 2013 BackgroundāExample,Ā PanoramaĀ Stitching TransformĀ imageĀ 1Ā intoĀ theĀ sameĀ coordinateĀ systemĀ ofĀ imageĀ 2
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LinĀ ZHANG,Ā SSE,Ā 2013 BackgroundāExample,Ā PanoramaĀ Stitching Finally,Ā stitchĀ theĀ transformedĀ imageĀ 1Ā withĀ imageĀ 2Ā toĀ getĀ theĀ panorama
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LinĀ ZHANG,Ā SSE,Ā 2013 Background ā¢ TheĀ basicĀ registrationĀ process ā¢ DetectĀ features ā¢
MatchĀ correspondingĀ features ā¢ InferĀ geometricĀ transformation ā¢ UseĀ theĀ geometricĀ transformationĀ toĀ alignĀ oneĀ imageĀ withĀ theĀ other ā¢ ImageĀ registrationĀ canĀ beĀ manualĀ orĀ automaticĀ dependingĀ onĀ whetherĀ featureĀ detectionĀ andĀ matchingĀ isĀ humanāassistedĀ orĀ performedĀ usingĀ anĀ automaticĀ algorithm
34.
LinĀ ZHANG,Ā SSE,Ā 2013 Contents ā¢ TransformingĀ points ā¢ HierarchyĀ ofĀ geometricĀ transformations ā¢
ApplyingĀ geometricĀ transformationsĀ toĀ images ā¢ ImageĀ Registration ā¢Background ā¢AĀ manualĀ method ā¢OtherĀ methods
35.
LinĀ ZHANG,Ā SSE,Ā 2013 AĀ ManualĀ Method WeĀ illustrateĀ thisĀ methodĀ byĀ usingĀ anĀ example,Ā whichĀ registersĀ theĀ followingĀ twoĀ images BaseĀ image inputĀ imageĀ whichĀ needsĀ toĀ beĀ registeredĀ toĀ theĀ baseĀ image
36.
LinĀ ZHANG,Ā SSE,Ā 2013 AĀ ManualĀ Method ā¢ StepĀ 1:Ā ManualĀ featureĀ selectionĀ andĀ matchingĀ usingĀ ācpselectā (controlĀ pointsĀ selection) ā¢
ācpselectā isĀ aĀ GUIĀ toolĀ forĀ manuallyĀ selectingĀ andĀ matchingĀ correspondingĀ controlĀ pointsĀ inĀ aĀ pairĀ ofĀ imagesĀ toĀ beĀ registered
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LinĀ ZHANG,Ā SSE,Ā 2013 AĀ ManualĀ Method ā¢ StepĀ 1:Ā ManualĀ featureĀ selectionĀ andĀ matchingĀ usingĀ ācpselectā (controlĀ pointsĀ selection)
38.
LinĀ ZHANG,Ā SSE,Ā 2013 AĀ ManualĀ Method ā¢ StepĀ 2:Ā InferringĀ transformationĀ parametersĀ usingĀ ācp2tformā ā¢ ācp2tformā
canĀ inferĀ geometricĀ transformationĀ parametersĀ fromĀ setĀ ofĀ featureĀ pairs tform =Ā cp2tform(input_points,Ā base_points,Ā transformtype) TheĀ argumentsĀ input_points andĀ base_points areĀ bothĀ Ā Ā Ā Ā Ā Ā matricesĀ containingĀ correponding featureĀ locations 2P ļ“
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LinĀ ZHANG,Ā SSE,Ā 2013 AĀ ManualĀ Method ā¢ StepĀ 3:Ā UseĀ theĀ geometricĀ transformationĀ toĀ alignĀ oneĀ imageĀ withĀ theĀ other ā¢ InĀ Matlab,Ā thisĀ isĀ achievedĀ byĀ āimtransformā TwoĀ imagesĀ areĀ registered
40.
LinĀ ZHANG,Ā SSE,Ā 2013 Contents ā¢ TransformingĀ points ā¢ HierarchyĀ ofĀ geometricĀ transformations ā¢
ApplyingĀ geometricĀ transformationsĀ toĀ images ā¢ ImageĀ Registration ā¢Background ā¢AĀ manualĀ method ā¢OtherĀ methods
41.
LinĀ ZHANG,Ā SSE,Ā 2013 AreaābasedĀ Registration ā¢ AreaābasedĀ registration ā¢ AĀ ātemplateĀ imageā
isĀ shiftedĀ toĀ coverĀ eachĀ locationĀ inĀ theĀ baseĀ image ā¢ AtĀ eachĀ location,Ā anĀ areaābasedĀ similarityĀ isĀ computed ā¢ TheĀ templateĀ isĀ saidĀ toĀ beĀ aĀ matchĀ atĀ aĀ particularĀ positionĀ inĀ theĀ baseĀ imageĀ ifĀ aĀ distinctĀ peakĀ inĀ theĀ similarityĀ metricĀ isĀ foundĀ atĀ thatĀ position
42.
LinĀ ZHANG,Ā SSE,Ā 2013 AreaābasedĀ Registration ā¢ AreaābasedĀ registration AĀ commonlyĀ usedĀ areaābasedĀ similarityĀ metricĀ isĀ theĀ correlationĀ coefficient , 2 2 ,
, ( , ) ( , ) ( , ) ( , ) ( , ) xys t xys t s t w s t w f x s y t f x y w s t w f x s y t f ļ§ ļ© ļ¹ ļ© ļ¹ļ ļ« ļ« ļļ« ļ» ļ« ļ»ļ½ ļ© ļ¹ ļ© ļ¹ļ ļ« ļ« ļļ« ļ» ļ« ļ» ļ„ ļ„ ļ„ whereĀ w isĀ theĀ templateĀ image,Ā Ā Ā Ā Ā Ā isĀ theĀ averageĀ valueĀ ofĀ theĀ template,Ā f isĀ theĀ baseĀ image,Ā andĀ Ā Ā Ā Ā Ā Ā Ā Ā isĀ theĀ averageĀ valueĀ ofĀ theĀ basedĀ imageĀ inĀ theĀ regionĀ whereĀ f andĀ w overlapĀ w xyf InĀ Matlab,Ā suchĀ aĀ 2DĀ correlationĀ coefficientĀ canĀ beĀ realizedĀ byĀ ānormxcorr2ā
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LinĀ ZHANG,Ā SSE,Ā 2013 AreaābasedĀ Registration ā¢ LimitationsĀ ofĀ areaābasedĀ registration ā¢ ClassicalĀ areaābasedĀ registrationĀ methodĀ canĀ onlyĀ dealĀ withĀ translationĀ transformationĀ betweenĀ twoĀ images; ā¢
ItĀ willĀ failĀ ifĀ rotation,Ā scaling,Ā orĀ affineĀ transformationsĀ existĀ betweenĀ theĀ twoĀ images
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LinĀ ZHANG,Ā SSE,Ā 2013 AutomaticĀ FeatureābasedĀ Registration ā¢ FeatureĀ pointsĀ (sometimesĀ referredĀ asĀ keyĀ pointsĀ orĀ interestĀ points)Ā canĀ beĀ detectedĀ automaticallyĀ ā¢ HarrisĀ cornerĀ detector ā¢
Extrema ofĀ LoG ā¢ FeatureĀ pointsĀ descriptorsĀ canĀ beĀ performedĀ automaticallyĀ ā¢ SIFTĀ (scaleĀ invariantĀ featureĀ transform) ā¢ FeatureĀ matchingĀ canĀ beĀ performedĀ automatically ToĀ knowĀ more,Ā comeĀ toĀ ourĀ anotherĀ courseĀ āComputerĀ Visionā!
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LinĀ ZHANG,Ā SSE,Ā 2013 ThanksĀ forĀ yourĀ attention
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