act Windows for Visual Correspondence via Minimum Ratio
- Slides: 20
act Windows for Visual Correspondence via Minimum Ratio Cycle Algorithm Olga Veksler NEC Labs America
Global Approach • Look at the whole image • Solve one large problem • Slower, more accurate Local Approach • Look at one image patch at at time • Solve many small problems independently • Fast, sufficient for some problems
Local Approach • Sufficient for some problems • Central problem: window shape selection • Efficiently solved using Minimum Ratio Cycle algorithm for graphs
Visual Correspondence left image (x 1, y) disparity = x 1 -x 2 right image (x 2, y) stereo vertical motion first image (x 1, y 1) second image (x 2, y 2) motion horizontal motion
Local Approach [Levine’ 73] left image right image 3 p 2 1 = i which gives best 2 Common C = + 2 + 2
need different window shapes Fixed Window Shape Problems left image fixed small window true disparities fixed large window
Variable Window: Previous Work • Two inefficient methods proposed previously 1. Local greedy search [Levine CGIP’ 73, Kanade’PAMI 94] 2. Direct search [Intille ECCV 94, Geiger IJCV 95] ……. • Need efficient optimization algorithm over sizes and shapes
Minimum Ratio Cycle image pixels • G(V, E) and w(e), t(e): E R • Find cycle C which minimizes: W = t
From Area to Cycle 1 1 1 blue edge 1 red edge + 5 sum up terms inside using weights of edges -2
Window Cost OK for any graphs 2 C(W) = +…+ size of W 2 = not OK for any graph positive negative
Compact Windows we construct graph s. t. p only clockwise cycles simple graph cycles C one-to-one correspondence compact windows W
Cycle which is not Simple cycle C in this case: m (C ) = m (C )
Solving MRC find smallest s. t. åw(e) åt (e ) åw(e) - l åt (e ) £ for some cycle 0 • search for smallest s. t. there is negative cycle on graph with edge weights: w (e ) - l t (e ) • negative cycle detection takes time due to the special structure of our graphs
examples of compact windows (small perimeter ) area • there are compact windows, if the largest allowed window is n by n • Contains all possible rectangles but much more general than just rectangles Find optimal window in in theory, linear ( ) in practice Search over in time • •
Sample Compact Windows
Speedup for pixel p, the algorithm extends windows over pixels which are likely to have the same disparity as p use the optimal window computed for p to approximate for pixels inside that window
Comparison to Fixed Window true disparities fixed small window: 33% errors Compact windows: 16% errors fixed large window: 30% errors
motion
Results all global Algorithm Tsukuba Venus Sawtooth Map Layered 1. 58 1. 52 0. 34 0. 37 Graph cuts 1. 94 1. 79 1. 30 0. 31 Belief prop 1. 15 1. 00 0. 98 0. 84 GC+occl. 1. 27 2. 79 0. 36 1. 79 Graph cuts 1. 86 1. 69 0. 42 2. 39 Multiw. Cut 8. 08 0. 53 0. 61 0. 26 Comp. win. 3. 36 1. 67 1. 61 0. 33 13 other algorithms, local and global Running time: 8 to 22 seconds
Future Work • Generalize the window class • Generalize objective function – mean? – variance?
- Local max
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