lecture8 - EECS 442 Computer vision Volumetric stereo...

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EECS 442 – Computer vision Volumetric stereo Definition Shape from Contours Shape from Shadows Voxel coloring Today’s lecture is a special topic
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“Traditional” Stereo Goal: estimate the position of P given the observation of P from two view points Assumptions : known camera parameters and position (K, R, T) p’ P p O 1 O 2
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Subgoals: 1. Solve the correspondence problem 2. Use corresponding observations to triangulate p’ P p O 1 O 2 “Traditional” Stereo
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Volumetric stereo 1. Hypothesis: pick up a point within the volume O 1 O 2 Scene volume 2. Project this point into 2 (or more) images Assumptions : known camera parameters and position (K, R, T) 3. Validation: are the observations consistent?
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Consistency based on cues such as: - Contours/silhouettes - Shadows - Colors
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Contours are a rich source of geometric information
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Apparent contour Image Camera DEFINITION: projection of the locus of points on the surface which separate the visible and occluded parts on the surface apparent contour projection of the locus of points on the surface which separate the visible projection of the [sato & cipolla]
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Silhouettes Image Camera silhouette
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± Provide information in absence of other visual cues No shading No texture Why contours are interesting visual cues?
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Image Camera ± Relatively easy to detect Object Easy contour segmentation Why contours are interesting visual cues?
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Image Camera Object How can we use contours? Object apparent contour Visual cone
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Image Camera Image object’s contour Object in 2D: Camera Image Object Visual cone Image object’s contour How can we use contours?
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View point 1 Object View point 2 Object Object estimate (visual hull) The views are calibrated
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± decompose visual cone in polygonal surfaces (among others: Reed and Allen ‘99) how to perform visual cones intersection?
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Using contours/silhouettes in volumetric stereo also called Space carving [ Martin and Aggarwal (1983) ] voxel
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Computing visual hull in 2D
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Computing visual hull in 2D
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Computing visual hull in 2D
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Computing visual hull in 2D Consistency: A voxel must be projected into a silhouette in each image Visual hull: an upper bound estimate
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Space Carving has complexity … ± Octrees (Szeliski ‘93) N N N O(N 3 )
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Complexity reduction: octrees 1 1 1
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2 2 2 Complexity reduction: octrees Subdiving volume in voxels of progressive smaller size
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4 4 4 Complexity reduction: octrees
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Complexity reduction: 2D example 4 voxels analyzed
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16 voxels analyzed Complexity reduction: 2D example
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52 voxels analyzed Complexity reduction: 2D example
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This note was uploaded on 10/26/2010 for the course EECS 442 taught by Professor Savarese during the Fall '09 term at University of Michigan.

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lecture8 - EECS 442 Computer vision Volumetric stereo...

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