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 I1, I2,
I1
I2
Registration Principle
• If correct correspondences (pi,qi ), 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 alignment
• Converges if starting position (T0) is “close
enough“
Getting T0 (Crude Registration)
• It can be obtained in manual form.
Getting T0 (Crude Registration)
• In automatic form :
– Intrinsic Properties Matching .
– Generating transformation T for each set of
correspondences
– Discarding false transformations
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 (2D histograms) generated from dense
sampling (only distances are considered)
- Spin-images matching.
Related Works
•RANSAC based DARCES
A structure is determined in image I1 and exhaustively
searched in image I2. Complete (dense) sampling is used.
Related Works
• 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 discard the false matches efficiently ?
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.
• 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.
Quadric error of a point v is given by sum of squared
distances to adjacent faces.
The substitute point of the edge contraction is
determined by quadric error minimization process –
optimal contraction.
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.
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.
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)
- 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
Images with same characteristics that those used by Planitz
et.al.
Curvature variation low
Edges and apexes
Curvature variation high (reasonable)
Symmetry
Results- Efficiency in data reduction
Data Reduction Percentage  99,5%
Results – Efficiency in Correspondences
reduction
Angel
Dragon
Hub
Club
Banana
Dino
machine
Correspondences Reduction  90,4%
Results – Efficiency in falses local matches
reduction
Angel
Dragon
Hub
Club
Banana
Dino
machine
Falses matches reduction 89,9%
Results
Results
Results – ICP Convergence
Angel
Dragon
Hub
Club
Banana
Dino
machine
ICP Convergence (in average) 6