Linear Filtering

Image Processing and Analysis (ImagePandA)

10 Shape and MotionChristoph Lampert / Chris Wojtan

Space23Distance functions

4Signed Distance functions

5Medial Axis

6Signed Distance functions7Normals

8Signed Distance functions9Curvature

10Signed Distance functions

11Surface Extraction12Surface Extraction

13Surface Extraction

14Surface Extraction

Time15Blending Images1617

t=0t=1

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t=0t=1t=0.520

t=0t=1t=0.5Morphing Images21

Distorting ImagesTypically break up image into triangle meshEach triangle has a piece of the image Moving vertices distorts the triangleApplies affine transformation to the triangleApplies affine transformation to the image

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Morphing ImagesFind corresponding features in both imagesInterpolate feature positionsBlend image colors

More sophisticated non-uniform distortions and blends are used in practice

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Distortion24Distortion25Take image data from a pixel locationAnd send it to some generic non-pixel location?26

Semi-Lagrangian AdvectionDisplacement Field27Displacement Field28Displacement Field2930Semi-Lagrangian AdvectionAdvection31Advection32Advection3334Semi-Lagrangian Advection35Semi-Lagrangian Advection36Signed Distance functionsThe level set methodhttps://www.youtube.com/watch?v=t7yOR882Et0https://www.youtube.com/watch?v=TeuLhhR7UxMhttps://www.youtube.com/watch?v=JaBBQDx2BBk#t=61https://www.youtube.com/watch?v=JaBBQDx2BBk#t=12837Level set method for segmentationVelocity is gradient of some energy functionAlways go downhillWhat is our energy function?We want it to penalize undesired segmentationsShould tightly wrap around objectAdd length and curvature to energyAttract towards edges in imageSubtract magnitude of image gradient from energy

38Level set method for segmentation39LEFT: the initial curve was at the boundary of the image.RIGHT: the initial curve was a closed contour around a point on the inside of the pollen grain. The boundary is identified in white.