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Unformatted text preview: Iterative Closest Point Ronen Gvili The Problem Align two partially overlapping meshes given initial guess for relative transform Data Types Point sets Line segment sets (polylines) Implicit curves : f(x,y,z) = 0 Parametric curves : (x(u),y(u),z(u)) Triangle sets (meshes) Implicit surfaces : s(x,y,z) = 0 Parametric surfaces (x(u,v),y(u,v),z(u,v))) Motivation Shape inspection Motion estimation Appearance analysis Texture Mapping Tracking Motivation Range images registration Motivation Range images registration Range Scanners Aligning 3D Data Corresponding Point Set Alignment Let M be a model point set. Let S be a scene point set. We assume : 1. N M = N S . 2. Each point S i correspond to M i . Corresponding Point Set Alignment The MSE objective function : The alignment is : = = = = S S N i T i R i S N i i i S q s q R m N q f Trans s Rot m N T R f 1 2 1 2 ) ( 1 ) ( ) ( 1 ) , ( ) , ( ) , , ( S M d trans rot mse = Aligning 3D Data If correct correspondences are known, can find correct relative rotation/translation Aligning 3D Data How to find correspondences: User input? Feature detection? Signatures? Alternative: assume closest points correspond Aligning 3D Data How to find correspondences: User input? Feature detection? Signatures? Alternative: assume closest points correspond Aligning 3D Data Converges if starting position close enough Closest Point Given 2 points r 1 and r 2 , the Euclidean distance is: Given a point r 1 and set of points A , the Euclidean distance is: 2 2 1 2 2 1 2 2 1 2 1 2 1 ) ( ) ( ) ( ) , ( z z y y x x r r r r d + + = = ) , ( min ) , ( 1 .. 1 1 i n i a r d A r d = Finding Matches The scene shape S is aligned to be in the best alignment with the model shape M. The distance of each point s of the scene from the model is : s m d M s d M m = min ) , ( Finding Matches M Y M S C Y M y y s d s m d M s d M m = = = ) , ( ) , ( min ) , ( C the closest point operator Y the set of closest points to S Finding Matches Finding each match is performed in O(N M ) worst case. Given Y we can calculate alignment S is updated to be : ) , ( ) , , ( Y S d trans rot = trans S rot S new + = ) ( The Algorithm Init the error to Calculate correspondence Calculate alignment Apply alignment Update error If error &gt; threshold Y = CP(M,S),e (rot,trans,d) S`= rot(S)+trans d` = d The Algorithm function ICP(Scene,Model) begin E` + ; (Rot,Trans) In InitializeAlignment(Scene,Model);...
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This note was uploaded on 02/21/2010 for the course SOE 12 taught by Professor Smith during the Spring '10 term at Aarhus Universitet.
 Spring '10
 SMITH

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