Displacement estimation
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1 Displacemet estimatio Displacemet estimatio by block matchig l Search strategies l Subpixel estimatio Digital Image Processig: Berd Girod, Gordo Wetzstei Staford Uiversity -- Displacemet Estimatio 1
2 Where is the defect? Image g[x,y] (o defect) Image f [x,y] (w/ defect) Digital Image Processig: Berd Girod, Gordo Wetzstei Staford Uiversity -- Displacemet Estimatio 2
3 Absolute differece betwee two images f-g w/o aligmet f-g w/ aligmet Digital Image Processig: Berd Girod, Gordo Wetzstei Staford Uiversity -- Displacemet Estimatio 3
4 Displacemet estimatio by block matchig Measuremet widow is compared with a shifted array of pixels i the other image, to determie the best match Rectagular array of pixels is selected as a measuremet widow Image g[x,y] Image f [x,y] Digital Image Processig: Berd Girod, Gordo Wetzstei Staford Uiversity -- Displacemet Estimatio 4
5 Displacemet estimatio by block matchig Image g[x,y] Image f [x,y]... process repeated for aother measuremet widow positio. Digital Image Processig: Berd Girod, Gordo Wetzstei Staford Uiversity -- Displacemet Estimatio 5
6 Iteger pixel shifts Measuremet widow is compared with a shifted array of pixels i the other image, to determie the best match Rectagular array of pixels is selected as a measuremet widow Image g[x,y] Image f [x,y] Digital Image Processig: Berd Girod, Gordo Wetzstei Staford Uiversity -- Displacemet Estimatio 6
7 Iteger pixel shifts Rectagular array of pixels is selected as a measuremet widow Measuremet widow is compared with a shifted array of pixels i the other image, to determie the best match Digital Image Processig: Berd Girod, Gordo Wetzstei Staford Uiversity -- Displacemet Estimatio 7
8 Error metric Sum of Squared Differeces Sum all values i measuremet widow SSD Δ x,δ y = f x, y g x + Δ x, y + Δ y x,y msmt widow ( ) 2 Horizotal displacemet Vertical displacemet Alteratives: SAD (Sum of Absolute Differeces), cross correlatio, mutual iformatio... Robustess agaist outliers: sum of saturated squared differeces, media of squared differeces... Digital Image Processig: Berd Girod, Gordo Wetzstei Staford Uiversity -- Displacemet Estimatio 8
9 SSD values resultig from block matchig SSD Estimated displacemet 0.2 Iteger-pixel accuracy Vertical shift Δ y Horizotal shift Δ x Digital Image Processig: Berd Girod, Gordo Wetzstei Staford Uiversity -- Displacemet Estimatio 9
10 Block matchig: search strategies Full search Δd x All possible displacemets withi the search rage are compared. Computatioally expesive Highly regular, parallelizable Δd y Digital Image Processig: Berd Girod, Gordo Wetzstei Staford Uiversity -- Displacemet Estimatio 10
11 Block matchig: search strategies Cojugate directio search Δd x Alterate search i x ad y directios Stop whe there is o further improvemet Δd y Digital Image Processig: Berd Girod, Gordo Wetzstei Staford Uiversity -- Displacemet Estimatio 11
12 Block matchig: search strategies Coarse-to-fie Δd x Start with coarsely spaced cadidate displacemets Smaller patter whe best match is i the middle Stop whe desired displacemet accuracy is reached Δd y Digital Image Processig: Berd Girod, Gordo Wetzstei Staford Uiversity -- Displacemet Estimatio 12
13 Block matchig: search strategies Diamod search [Li, Zeg, Liou, 1994] [Zhu, Ma, 1997] Δd y Δd x Start with large diamod patter at [0,0] If best match lies i the ceter of large diamod, proceed with small diamod If best match does ot lie i the ceter of large diamod, ceter large diamod patter at ew best match Digital Image Processig: Berd Girod, Gordo Wetzstei Staford Uiversity -- Displacemet Estimatio 13
14 Absolute differece betwee images w/ iteger-pixel aligmet w/o aligmet Digital Image Processig: Berd Girod, Gordo Wetzstei Staford Uiversity -- Displacemet Estimatio 14
15 Iterpolatio of the SSD Miimum SSD Sub-pixel Accurate Miimum Fit parabola through 3 > 3 poits exactly approximately Horizotal shift Δ x Digital Image Processig: Berd Girod, Gordo Wetzstei Staford Uiversity -- Displacemet Estimatio 15
16 2-d Iterpolatio of SSD Miimum SSD Paraboloid Perfect fit through 6 poits Approximate fit through > 6 poits Digital Image Processig: Berd Girod, Gordo Wetzstei Staford Uiversity -- Displacemet Estimatio 16
E X P E R I M E N T 13
E X P E R I M E N T 13 Stadig Waves o a Strig Produced by the Physics Staff at Colli College Copyright Colli College Physics Departmet. All Rights Reserved. Uiversity Physics, Exp 13: Stadig Waves o a
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