Shape from Silhouettes II
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1 Shape from Silhouettes II Guido Gerig CS 6320, S2013 (slides modified from Marc Pollefeys UNC Chapel Hill, some of the figures and slides are adapted from M. Pollefeys, J.S. Franco, J. Matusik s presentations, and referenced papers)
2 Shape from silhouettes Slides from Lazebnik, Matusik Yerex and others Automatic 3D Model Construction for Turn-Table Sequences, A.W. Fitzgibbon, G. Cross, and A. Zisserman, SMILE 1998
3 Outline Silhouettes basic concepts extract silhouettes fundamentals about using silhouettes reconstruct shapes from silhouettes use uncertain silhouettes calibrate from silhouettes Perspectives and interesting ideas
4 Algorithms Standard voxel based method Exact polyhedral methods Image-based visual hulls
5 IBVH: Image based visual hulls VH without constructing auxiliary geometric/volumetric representation All steps of rendering are in computed in 2D image space coordinates (eliminates resampling/quantization artifacts) Reference images used as textures for shading the VH Image-based objects in real-time Wojciech Matusik, Image Based Visual Hulls
6 Image based visual hulls This algorithm will only produce renderings of a visual hull from any view. Every pixel in the desired output image is backprojected to form a 3D ray. Each of those rays is intersected with each of the input silhouettes in the same way as the rays in the marching intersections method. Then a pixel in the output image is inside the new rendering of the visual hull if its ray has any segments left in it that are intersecting the visual hull. The depth of these pixels is known from the depth of the nearest entry point on the ray Wojciech Matusik, Image Based Visual Hulls
7 Image based - example
8 Image-Based Computation 1. Project 3D viewing ray (blue) into reference image 2. Intersection of projected ray with 2D silhouettes list of intervals along ray interior to cone s cross section 3. Intervals lifted back to 3D, intersected with results of other reference images
9 Image-Based Computation Reference 1 Desired Reference 2
10 Image-Based Computation Naïve Algorithm Efficiency for desired view: n: #pixels per scanline O(n 2 ): #pixels in image k: #images l: average #times ray intersects silhouette O(lk): #silhouette edges (search along epip lines) O(lkn 3 ): Efficiency
11 Image-Based Computation Remember Epipolar Geometry: Epipolar planes: Set of planes that share line OO Epipolar planes project to lines in each image: epipolar lines All epipolar lines intersect in common point: epipole
12 Image-Based Computation Improved Algorithm: Take advantage of incremental computations enabled by epipolar geometry relating reference and desired images Efficiency: O(lkn 2 ) Traverse scan line of desired view Each ray project to line through epipole in reference image Set of rays in desired image: pencil of epipolar lines in reference image Monotonic change of slope Compute silhouette intersections for whole scan line incrementally (trick: presorted silhouette edges relative to epipole)
13 Observation Incremental computation along scanlines
14 Shading Algorithm A view-dependent strategy
15 Shading Algorithm A view-dependent strategy Use reference images as textures Rank reference-image textures as best to worst based on angle between desired viewing ray and rays of each reference image Consider visibility (avoid textures of points that are blocked): Take advantage of epipolar geometry for incremental procedure
16 Visibility Algorithm
17 Visibility in 2D Reference view Desired view
18 Visibility in 2D Front-most Points Reference view Desired view
19 Visibility in 2D Visible Reference view Desired view
20 Visibility in 2D Coverage Mask Reference view Desired view
21 Visibility in 2D Visible Coverage Mask Reference view Desired view
22 Visibility in 2D Visible Coverage Mask Reference view Desired view
23 Visibility in 2D Not Visible Coverage Mask Reference view Desired view
24 Visibility in 2D Coverage Mask Reference view Desired view
25 Visibility in 2D Visible Coverage Mask Reference view Desired view
26 Visibility in 2D Coverage Mask Reference view Desired view
27 Visibility in 2D Not Visible Coverage Mask Reference view Desired view
28 System Server (4x 500 Mhz)
29 System Trigger Signal Server (4x 500 Mhz)
30 System Server (4x 500 Mhz)
31 System Compressed video Server (4x 500 Mhz)
32 System Server (4x 500 Mhz) Intersection
33 System Server (4x 500 Mhz) Visibility
34 System Server (4x 500 Mhz) Shading
35 IBVH Results Approximately constant computation per pixel per camera Parallelizes Consistent with input silhouettes
36 IBVH Results
37 Image Based Visual Hulls See also:
38 Outline Silhouettes basic concepts extract silhouettes fundamentals about using silhouettes reconstruct shapes from silhouettes use uncertain silhouettes calibrate from silhouettes Perspectives and cool ideas
39 Next Lecture Visual Hulls using uncalibrated camera views (Forbes et al.) Wrap-up
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