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## EFFICIENT VARIANTS OF THE ICP ALGORITHM Introduction ICP Initial alignment Constraints

Dickerson, John, General Assignment Reporter has reference to this Academic Journal, PHwiki organized this Journal EFFICIENT VARIANTS OF THE ICP ALGORITHM Szymon Rusinkiewicz Marc Levoy Introduction Problem of aligning 3D models, based on geometry or color of meshes ICP is the chief algorithm used Used to register output of 3D scanners [1] ICP Starting point: Two meshes in addition to an initial guess as long as a relative rigid-body trans as long as m Iteratively refines the trans as long as m Generates pairs of corresponding points on the mesh Minimizes an error metric Repeats

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Initial alignment Tracking scanner position Indexing surface features Spin image signatures Exhaustive search User Input [2] Constraints Assume a rough initial alignment is available Focus only on a single of meshes Global registration problem not addressed Stages of the ICP Selection of the set of points Matching the points to the samples Weighting corresponding pairs Rejecting pairs to eliminate outliers Assigning an error metric Minimizing the error metric

Focus Speed Accuracy Per as long as mance in tough scenes Introducing test scenes Discuss combinations Normal-space directed sampling Convergence per as long as mance Optimal combination Comparison Methodology Baseline Algorithm: [Pulli 99] R in addition to om sampling on both meshes Matching to a point where the normal is < 45 degrees from the source Uni as long as m weighting Rejection of edge vertices pairs Point-to-plane error metric Select-match-minimize iteration Assumptions 2000 source points in addition to 100,000 samples Simple perspective range images Surface normal is based on the four nearest neighbors Only geometry (color, intensity excluded) Test Scenes a) Wave Scene Fractal L in addition to scape Incised Plane Shamelessly stolen from [3] Sample scanning application Representative of different kinds of surfaces Low frequency All frequency High Frequency Smooth statues Unfinished statues Fragments More shameless lifts from [3] Comparison Stages Selection of the set of points Matching the points to the samples Weighting corresponding pairs Rejecting pairs to eliminate outliers Assigning an error metric Minimizing the error metric Selection of point pairs Use all available points Uni as long as m sub-sampling R in addition to om sampling Pick points with high intensity gradient Pick from one or both meshes Select points where the distribution of the normal between these points is as large as possible Normal Sampling Small features may play a critical role Distribute the spread of the points across the position of the normals Simple Low-cost Low robustness Comparison of per as long as mance Uni as long as m sub-sampling R in addition to om sampling normal-space sampling Comparison of per as long as mance Incised Plane: Only the normal-space sampling converges Why Samples outside the grooves: 1 translation, 2 rotations Inside the grooves: 2 translations, 1 rotation Fewer samples + noise + distortion = bad results Sampling Direction Points from one mesh vs. points from both meshes Difference is minimal, as algorithm is symmetric Sampling direction Asymmetric algorithm Two meshes is better If overlap is small, two meshes is better Comparison Stages Selection of the set of points Matching the points to the samples Weighting corresponding pairs Rejecting pairs to eliminate outliers Assigning an error metric Minimizing the error metric Matching Points Match a sample point with the closest in the other mesh Normal shooting Reverse calibration Project source point onto destination mesh; search in destination range image Match points compatible with source points Variants compared Closest point Closest compatible point Normal shooting Normal shooting to a compatible point Projection Projection followed by a search : uses steepest-descent neighbor-neighbor walk k-d tree Fractal Scene Best: normal shooting Worst: closest-point

Incised Plane Closest point converges: most robust Error Error as a function of running time Applications that need quick running of the ICP should choose algorithms with the fastest per as long as mance Best: Projection algorithm Comparison Stages Selection of the set of points Matching the points to the samples Weighting corresponding pairs Rejecting pairs to eliminate outliers Assigning an error metric Minimizing the error metric

Algorithms Constant weight Lower weights as long as points with higher point-point distances Weight = 1 [Dist(p1, p2)/Dist max] Weight based on normal compatibility Weight = n1 n2 Weight based on the effect of noise on uncertainty Wave Scene Incised Plane

Conclusion Compared ICP variants Introduced a new sampling method Optimized ICP algorithm Future Work Focus on stability in addition to robustness Effects of noise in addition to distortion Algorithms that switch between variants would increase robustness References [1] http://foto.hut.fi/opetus/ 260/luennot/9/9.html [2] http://www.sztaki.hu/news/2001-07/maszk-allthree.jpg [3] http://graphics.stan as long as d.edu/projects/mich/ [4] http://www.cs.unc.edu/~sud/courses/comp258/final-pres.ppt 257,2,Problem Statement

## Dickerson, John General Assignment Reporter

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