Using simplified meshes Using simplified meshes for crude registration of for crude registration of two partially overlapping two partially overlapping

range imagesrange images

Mercedes R.G.Márquez Mercedes R.G.Márquez

Wu Shin-TingWu Shin-Ting

State University of Matogrosso State University of Matogrosso do Suldo Sul

State University of Campinas- State University of Campinas- BrazilBrazil

TopicsTopics

1.1. Registration ProblemRegistration Problem

2.2. Related WorksRelated Works

3.3. Our ProposalOur Proposal

4.1 QSLIM Method4.1 QSLIM Method

4.2. Structures for 4.2. Structures for MatchingMatching

4.3. Local Matching4.3. Local Matching

4.4. Filtering matches4.4. Filtering matches

5. Results5. Results

ProblemProblem

• Find the rigid Find the rigid transformation T transformation T which aligns two which aligns two partially partially overlapped range overlapped range images images II11, I, I2,2,

II11 II22

Registration PrincipleRegistration Principle

• If correct correspondences (If correct correspondences (ppi,i,qqi i ), ), are are

known,known,then the solution of equations system then the solution of equations system , by least squares method , by least squares method is the transformation is the transformation T.T.

Traditional ICP (Iterative Traditional ICP (Iterative Closest Point)Closest Point)

• Assume Assume closestclosest points correspond points correspond to each other, compute the best to each other, compute the best transform and iterate to find transform and iterate to find alignmentalignment

• Converges if starting position (TConverges if starting position (T00) )

is “close enough“is “close enough“

Getting TGetting T0 0 (Crude Registration)(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 .Intrinsic Properties Matching .

– Generating transformation T for each set of Generating transformation T for each set of correspondences correspondences

– Discarding false transformationsDiscarding false transformations

Getting TGetting T0 0 (Crude Registration)(Crude Registration)

TopicsTopics

1.1. Registration ProblemRegistration Problem

2.2. Related WorksRelated Works

3.3. Our ProposalOur Proposal

4.1 QSLIM Method4.1 QSLIM Method

4.2. Structures for 4.2. Structures for MatchingMatching

4.3. Local Matching4.3. Local Matching

4.4. Filtering matches4.4. Filtering matches

5. Results5. Results

Related WorksRelated Works

•Spin Images Matching (SIM) Spin Images Matching (SIM)

- Spin-images (2D histograms) generated from - Spin-images (2D histograms) generated from dense sampling (only distances are considered)dense sampling (only distances are considered)

- Spin-images matching.- Spin-images matching.

•RANSAC based DARCES RANSAC based DARCES

A structure is deA structure is determined termined in image Iin image I11 and and

exhaustively searched in image Iexhaustively searched in image I22. Complete . Complete

(dense) sampling is used.(dense) sampling is used.

Related WorksRelated Works

• Intrinsic Curve Matching (ICM)Intrinsic Curve Matching (ICM)

- Curves with zero mean gaussian curvature.- Curves with zero mean gaussian curvature.

- Smallest distance between each curve pair - Smallest distance between each curve pair is compared for matchingis compared for matching

Related WorksRelated Works

Methods use complete sampling for Methods use complete sampling for extracting correspondences. extracting correspondences.

Questions :Questions :

• How can we select more efficiently the How can we select more efficiently the correspondences ?correspondences ?

• How can we discard the false matches How can we discard the false matches efficiently ?efficiently ?

Related WorksRelated Works

TopicsTopics

1.1. Registration ProblemRegistration Problem

2.2. Related WorksRelated Works

3.3. Our ProposalOur Proposal

4.1 QSLIM Method4.1 QSLIM Method

4.2. Structures for 4.2. Structures for MatchingMatching

4.3. Local Matching4.3. Local Matching

4.4. Filtering matches4.4. Filtering matches

5. Results5. Results

Our ProposalOur Proposal

• We propose to reduce the size of data sets by simplifying the range images into meshes with fewer We propose to reduce the size of data sets by simplifying the range images into meshes with fewer elements. elements.

• Conjecture Conjecture A simplified mesh that preserves the global geometric characteristic of the original data A simplified mesh that preserves the global geometric characteristic of the original data suffices for a coarse registration.suffices for a coarse registration.

TopicsTopics

1.1. Registration ProblemRegistration Problem

2.2. Related WorksRelated Works

3.3. Our ProposalOur Proposal

4.1 QSLIM Method4.1 QSLIM Method

4.2. Structures for 4.2. Structures for MatchingMatching

4.3. Local Matching4.3. Local Matching

4.4. Filtering matches4.4. Filtering matches

5. Results5. Results

QSLIMQSLIM Method 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 The substitute point of the edge contraction is determined by quadric error contraction is determined by quadric error minimization process – optimal minimization process – optimal contraction.contraction.

Quadric error of a point v is given by sum Quadric error of a point v is given by sum of squared distances to adjacent faces.of squared distances to adjacent faces.

TopicsTopics

1.1. Registration ProblemRegistration Problem

2.2. Related WorksRelated Works

3.3. Our ProposalOur Proposal

4.1 QSLIM Method4.1 QSLIM Method

4.2. Structures for 4.2. Structures for MatchingMatching

4.3. Local Matching4.3. Local Matching

4.4. Filtering matches4.4. Filtering matches

5. Results5. Results

Structures for matchingStructures for matching

We construct a spatial structure for We construct a spatial structure for matching. It is from simplified mesh and matching. It is from simplified mesh and consists of a vertex and three adjacent consists of a vertex and three adjacent vertices.vertices.

It is more discriminative than planar It is more discriminative than planar structure !!!structure !!!It possesses two intrinsic properties : It possesses two intrinsic properties : distance and curvature (given by angles distance and curvature (given by angles between edges and approximate normal between edges and approximate normal vector in V)vector in V)

TopicsTopics

1.1. Registration ProblemRegistration Problem

2.2. Related WorksRelated Works

3.3. Our ProposalOur Proposal

4.1 QSLIM Method4.1 QSLIM Method

4.2. Structures for 4.2. Structures for MatchingMatching

4.3. Local Matching4.3. Local Matching

4.4. Filtering matches4.4. Filtering matches

5. Results5. Results

LLocalocal Matching Matching

QSLIM guarantees than geometric QSLIM guarantees than geometric characteristics are similarly represented characteristics are similarly represented but does not ensure the existence of a but does not ensure the existence of a corresponding vertex in corresponding corresponding vertex in corresponding mesh.mesh.

For ensuring success in matching we add in For ensuring success in matching we add in mesh M2 the 4-neighbors of each vertex.mesh M2 the 4-neighbors of each vertex.

LLocalocal Matching Matching

The search procedure is similar to DARCESThe search procedure is similar to DARCES..

When distances are similar, we still When distances are similar, we still compare solid angle of spatial structure compare solid angle of spatial structure (curvature) (curvature) !!!. !!!.

TopicsTopics

1.1. Registration ProblemRegistration Problem

2.2. Related WorksRelated Works

3.3. Our ProposalOur Proposal

4.1 QSLIM Method4.1 QSLIM Method

4.2. Structures for 4.2. Structures for MatchingMatching

4.3. Local Matching4.3. Local Matching

4.4. Filtering matches4.4. Filtering matches

5. Results5. Results

Filtering MatchesFiltering Matches

- Neighborhood Test:- Neighborhood Test: We evaluate the errors in the We evaluate the errors in the

neighborhood of vertex V (generator of neighborhood of vertex V (generator of structure)structure)

- Visibility Test:- Visibility Test:– If 50% of faces of 1-neighborhood of V If 50% of faces of 1-neighborhood of V

(transformed by T) are not visible from view (transformed by T) are not visible from view direction of image I2, T is discarded. direction of image I2, T is discarded.

TopicsTopics

1.1. Registration ProblemRegistration Problem

2.2. Related WorksRelated Works

3.3. Our ProposalOur Proposal

4.1 QSLIM Method4.1 QSLIM Method

4.2. Structures for 4.2. Structures for MatchingMatching

4.3. Local Matching4.3. Local Matching

4.4. Filtering matches4.4. Filtering matches

5. Results5. Results

ResultsResults

Curvature variation low Curvature variation low Edges Edges and apexesand apexes

Images Images with same characteristics that those used bywith same characteristics that those used by Planitz Planitz

et.al. et.al.

Curvature variation high (reasonable)Curvature variation high (reasonable)

SymmetrySymmetry

Results- Results- Efficiency in data Efficiency in data reductionreduction

Data Reduction Percentage Data Reduction Percentage 99,5% 99,5%

Results – Results – Efficiency Efficiency in in Correspondences reductionCorrespondences reduction

Correspondences Reduction Correspondences Reduction 90,4% 90,4%

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Results – EResults – Efffficiencyiciency in falses in falses local matches reductionlocal matches reduction

Falses matches reductionFalses matches reduction 89,9% 89,9%

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Results Results

ResultsResults

Results – ICPResults – ICP Convergence Convergence

ICP ICP Convergence (in average)Convergence (in average) 6 6

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