Using simplified meshes for crude registration of two partially overlapping range images Mercedes R.G.Márquez Wu Shin-Ting State University of Matogrosso do Sul State University of Campinas- Brazil

Topics 1.Registration Problem 2.Related Works 3.Our Proposal 4.1 QSLIM Method 4.2. Structures for Matching 4.3. Local Matching 4.4. Filtering matches 5. Results

Problem Find the rigid transformation T which aligns two partially overlapped range images I 1, I 2,Find the rigid transformation T which aligns two partially overlapped range images I 1, I 2, I1I1I1I1 I2I2I2I2

Registration Principle If correct correspondences (p i, q i ), are known, then the solution of equations system, by least squares method is the transformation T.If correct correspondences (p i, q i ), are known, then the solution of equations system, by least squares method is the transformation T.

Traditional ICP (Iterative Closest Point) Assume closest points correspond to each other, compute the best transform and iterate to find alignmentAssume closest points correspond to each other, compute the best transform and iterate to find alignment Converges if starting position (T 0 ) is “close enough“Converges if starting position (T 0 ) is “close enough“

Getting T 0 (Crude Registration) It can be obtained in manual form. It can be obtained in manual form.

In automatic form : In automatic form : – Intrinsic Properties Matching. – Generating transformation T for each set of correspondences – Discarding false transformations Getting T 0 (Crude Registration)

Topics 1.Registration Problem 2.Related Works 3.Our Proposal 4.1 QSLIM Method 4.2. Structures for Matching 4.3. Local Matching 4.4. Filtering matches 5. Results

Related Works Spin Images Matching (SIM)Spin Images Matching (SIM) - Spin-images (2D histograms) generated from dense sampling (only distances are considered) - Spin-images matching.

RANSAC based DARCESRANSAC based DARCES A structure is determined in image I 1 and exhaustively searched in image I 2. Complete (dense) sampling is used. Related Works

Intrinsic Curve Matching (ICM) Intrinsic Curve Matching (ICM) - Curves with zero mean gaussian curvature. - Smallest distance between each curve pair is compared for matching Related Works

Methods use complete sampling for extracting correspondences. Questions : How can we select more efficiently the correspondences ? How can we select more efficiently the correspondences ? How can we discard the false matches efficiently ? How can we discard the false matches efficiently ? Related Works

Topics 1.Registration Problem 2.Related Works 3.Our Proposal 4.1 QSLIM Method 4.2. Structures for Matching 4.3. Local Matching 4.4. Filtering matches 5. Results

Our Proposal We propose to reduce the size of data sets by simplifying the range images into meshes with fewer elements.We propose to reduce the size of data sets by simplifying the range images into meshes with fewer elements. Conjecture  A simplified mesh that preserves the global geometric characteristic of the original data suffices for a coarse registration.Conjecture  A simplified mesh that preserves the global geometric characteristic of the original data suffices for a coarse registration.

Topics 1.Registration Problem 2.Related Works 3.Our Proposal 4.1 QSLIM Method 4.2. Structures for Matching 4.3. Local Matching 4.4. Filtering matches 5. Results

QSLIM Method It is a method based in edge contraction and quadric error concept.It is a method based in edge contraction and quadric error concept. The substitute point of the edge contraction is determined by quadric error minimization process – optimal contraction. The substitute point of the edge contraction is determined by quadric error minimization process – optimal contraction. Quadric error of a point v is given by sum of squared distances to adjacent faces.

Topics 1.Registration Problem 2.Related Works 3.Our Proposal 4.1 QSLIM Method 4.2. Structures for Matching 4.3. Local Matching 4.4. Filtering matches 5. Results

Structures for matching We construct a spatial structure for matching. It is from simplified mesh and consists of a vertex and three adjacent vertices. It is more discriminative than planar structure !!! It possesses two intrinsic properties : distance and curvature (given by angles between edges and approximate normal vector in V)

Topics 1.Registration Problem 2.Related Works 3.Our Proposal 4.1 QSLIM Method 4.2. Structures for Matching 4.3. Local Matching 4.4. Filtering matches 5. Results

Local Matching QSLIM guarantees than geometric characteristics are similarly represented but does not ensure the existence of a corresponding vertex in corresponding mesh. QSLIM guarantees than geometric characteristics are similarly represented but does not ensure the existence of a corresponding vertex in corresponding mesh. For ensuring success in matching we add in mesh M2 the 4-neighbors of each vertex. For ensuring success in matching we add in mesh M2 the 4-neighbors of each vertex.

Local Matching The search procedure is similar to DARCES. The search procedure is similar to DARCES. When distances are similar, we still compare solid angle of spatial structure (curvature) !!!. When distances are similar, we still compare solid angle of spatial structure (curvature) !!!.

Topics 1.Registration Problem 2.Related Works 3.Our Proposal 4.1 QSLIM Method 4.2. Structures for Matching 4.3. Local Matching 4.4. Filtering matches 5. Results

Filtering Matches - Neighborhood Test: We evaluate the errors in the neighborhood of vertex V (generator of structure) We evaluate the errors in the neighborhood of vertex V (generator of structure) - Visibility Test: – If 50% of faces of 1-neighborhood of V (transformed by T) are not visible from view direction of image I2, T is discarded.

Topics 1.Registration Problem 2.Related Works 3.Our Proposal 4.1 QSLIM Method 4.2. Structures for Matching 4.3. Local Matching 4.4. Filtering matches 5. Results

Results Curvature variation low Edges and apexes Curvature variation low Edges and apexes Images with same characteristics that those used by Planitz et.al. Images with same characteristics that those used by Planitz et.al. Curvature variation high (reasonable) Symmetry

Results- Efficiency in data reduction Data Reduction Percentage  99,5%

Results – Efficiency in Correspondences reduction Correspondences Reduction  90,4% AngelDragonHubClubBananaDinomachine

Results – Efficiency in falses local matches reduction Falses matches reduction  89,9% AngelDragonHubClubBananaDinomachine

Results

Results

Results – ICP Convergence ICP Convergence (in average)  6 AngelDragonHubClubBananaDinomachine