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Image-Based Visual Hulls

Image-Based Visual Hulls. Wojciech Matusik Chris Buehler Ramesh Raskar Steven Gortler Leonard McMillan. Presentation by: Kenton McHenry. Visual Hull.

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Image-Based Visual Hulls

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  1. Image-Based Visual Hulls Wojciech Matusik Chris Buehler Ramesh Raskar Steven Gortler Leonard McMillan Presentation by: Kenton McHenry

  2. Visual Hull • Project rays through silhouette of various views to carve out regions containing the object. The intersection of all such cones is the visual hull. • Not the true object shape, concavities can not be captured.

  3. Visual Hull

  4. Previous Work • CSG (Constructive Solid Geometry) • Boolean operators over polygonal silohuettes • 3D intersections • Volume Carving • Large memory requirements • Aliasing

  5. Contribution • Real time rendering • Perform intersection tests in 2D image space • No explicit hull

  6. Epipolar Geometry • Epipole: projection of 2nd cameras optical center in our view • Baseline: line connecting optical centers • Epipolar line: Projection of ray in our view, can restrict search to this line. • Epipolar plane: formed by the baseline and the epipolar lines in both images.

  7. Epipolar Geometry

  8. Elminiate Polyhedra Intersections … is equivelent to …

  9. Elminiate Polyhedron-Line Intersections • Absolute cross-section (defined by the silouhette) remains fixed (scaled). • Can project our 3D ray into any plane along the cone, find intersections, and unproject.

  10. Visual Hull Computation • Given a desired view • For each of the n2 pixels create a ray from the optical center through the pixel and project it into each of the reference views (epipolar lines) • Calculate intervals with silouhette • Lift the intervals back into 3D space

  11. Sampling the hull

  12. Speed up Search over Edges • Observation: The pixels of a scanline in the desired image scan out a pencil of line segments in the reference image whose slope varies monotonically.

  13. Incremental Computation

  14. Binning

  15. Scanning

  16. Complexity • n = width/height of images • k = number of reference images • l = average number of intersections • O(lkn2)

  17. Partial Results

  18. Shading • Use reference images as textures • View Dependent Texturing • Assign pixel color based on reference view whose angle is most simular to desired view.

  19. Visibility • We need to watch out for reference views that have an occluded view of the point. • All visibility interactions occur within epipolar planes.

  20. 2D Visibility O(nl)

  21. Discrete 3D Visibility • Due to discretization the pixels of an epipolar line in one image may be on different lines in the other image. O(lkn2)

  22. Results

  23. Results

  24. Silhouettes • Fixed cameras => Background substraction • 2D version of marching cubes to recover edges of silhouette

  25. The Fundamental Matrix • xrefT F xdes = 0 • 8-point algorithm • Epipolar line corresponding to xdes in reference image = F xdes = (a b c)T such that ax + by + c = 0

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