Iterative Closest Point Algorithm Profiling Conclusion
Fast Image Registration Ugo Jardonnet EPITA Research and Development Laboratory
Seminar CSI, June 2008 The Olena Project
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Iterative Closest Point Algorithm Profiling Conclusion
Bootstrap
Image registration is to align objects from multimodal images.
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Rigid transformation An alignment or a rigid transform is the application of a translation and a rotation.
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Iterative Closest Point Algorithm Profiling Conclusion
Outline 1
Iterative Closest Point Algorithm Key Points Algorithm Final Transform
2
Profiling Gprof Analysis Lazy Closest Point Evaluation Multi-Scale Registration
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Conclusion
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Iterative Closest Point Algorithm Profiling Conclusion
Key Points Algorithm Final Transform
Outline 1
Iterative Closest Point Algorithm Key Points Algorithm Final Transform
2
Profiling Gprof Analysis Lazy Closest Point Evaluation Multi-Scale Registration
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Conclusion
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Iterative Closest Point Algorithm Profiling Conclusion
Key Points Algorithm Final Transform
Iterative Closest Point Algorithm (ICP)
Closest Point (CP) in X Given to shape C and X . The closest point of a point pc in C is the point px in X that minimizes the distance d(pc , px ). Projection [2] The projection of C over X is the set of every closest points.
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Iterative Closest Point Algorithm Profiling Conclusion
Key Points Algorithm Final Transform
Outline 1
Iterative Closest Point Algorithm Key Points Algorithm Final Transform
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Profiling Gprof Analysis Lazy Closest Point Evaluation Multi-Scale Registration
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Conclusion
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Key Points Algorithm Final Transform
Iterative Closest Point Algorithm
We want to align the green object over the black object
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Iterative Closest Point Algorithm Profiling Conclusion
Key Points Algorithm Final Transform
Iterative Closest Point Algorithm
1. Projection Step
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Key Points Algorithm Final Transform
Iterative Closest Point Algorithm
2. Compute Registration
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Iterative Closest Point Algorithm Profiling Conclusion
Key Points Algorithm Final Transform
Iterative Closest Point Algorithm
3. Apply Registration
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Iterative Closest Point Algorithm Profiling Conclusion
Key Points Algorithm Final Transform
Iterative Closest Point Algorithm
. . . and so on . . .
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Iterative Closest Point Algorithm Profiling Conclusion
Key Points Algorithm Final Transform
Iterative Closest Point Algorithm
. . . and so on . . .
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Iterative Closest Point Algorithm Profiling Conclusion
Key Points Algorithm Final Transform
Iterative Closest Point Algorithm
. . . and so on . . .
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Iterative Closest Point Algorithm Profiling Conclusion
Key Points Algorithm Final Transform
Iterative Closest Point Algorithm
. . . and so on . . .
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Iterative Closest Point Algorithm Profiling Conclusion
Key Points Algorithm Final Transform
Iterative Closest Point Algorithm
. . . and so on . . .
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Iterative Closest Point Algorithm Profiling Conclusion
Key Points Algorithm Final Transform
Iterative Closest Point Algorithm
. . . and so on . . .
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Iterative Closest Point Algorithm Profiling Conclusion
Key Points Algorithm Final Transform
Iterative Closest Point Algorithm
. . . and so on . . .
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Iterative Closest Point Algorithm Profiling Conclusion
Key Points Algorithm Final Transform
Iterative Closest Point Algorithm
. . . and so on . . .
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Iterative Closest Point Algorithm Profiling Conclusion
Key Points Algorithm Final Transform
Iterative Closest Point Algorithm
Until stability of < kpc − px k >.
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Iterative Closest Point Algorithm Profiling Conclusion
Key Points Algorithm Final Transform
Outline 1
Iterative Closest Point Algorithm Key Points Algorithm Final Transform
2
Profiling Gprof Analysis Lazy Closest Point Evaluation Multi-Scale Registration
3
Conclusion
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Key Points Algorithm Final Transform
Final Transform
Results of ICP can be disappointing. The Olena Project
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Key Points Algorithm Final Transform
Final Transform
One point of noise can heavily modify the center of mass or the orientation.
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Key Points Algorithm Final Transform
Final Transform
As a consequence registration is distorted.
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Key Points Algorithm Final Transform
Final Transform
Let’s mark point in P according to their distance with their closest points. The Olena Project
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Iterative Closest Point Algorithm Profiling Conclusion
Key Points Algorithm Final Transform
Final Transform 1
Remove points farther than 1 time the standard deviation [4].
2
Compute again a final rigid transform.
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Iterative Closest Point Algorithm Profiling Conclusion
Gprof Analysis Lazy Closest Point Evaluation Multi-Scale Registration
Outline 1
Iterative Closest Point Algorithm Key Points Algorithm Final Transform
2
Profiling Gprof Analysis Lazy Closest Point Evaluation Multi-Scale Registration
3
Conclusion
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Iterative Closest Point Algorithm Profiling Conclusion
Gprof Analysis Lazy Closest Point Evaluation Multi-Scale Registration
Gprof Analysis The most expensive part of the iterative closest point algorithm is the projection step.
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Iterative Closest Point Algorithm Profiling Conclusion
Gprof Analysis Lazy Closest Point Evaluation Multi-Scale Registration
Outline 1
Iterative Closest Point Algorithm Key Points Algorithm Final Transform
2
Profiling Gprof Analysis Lazy Closest Point Evaluation Multi-Scale Registration
3
Conclusion
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Iterative Closest Point Algorithm Profiling Conclusion
Gprof Analysis Lazy Closest Point Evaluation Multi-Scale Registration
Lazy Closest Point Evaluation
During the registration of C, the object X does not move. Hence, for a given coordinate c, the closest points of c is always the same. Closest point for a given coordinate is computed only one time, the first time it is requested.
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Iterative Closest Point Algorithm Profiling Conclusion
Gprof Analysis Lazy Closest Point Evaluation Multi-Scale Registration
Lazy Closest Point Evaluation
CP computed / CP requested: 42.48%, median: 39.04%. The Olena Project
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Iterative Closest Point Algorithm Profiling Conclusion
Gprof Analysis Lazy Closest Point Evaluation Multi-Scale Registration
Lazy Closest Point Evaluation
Gain: 4.7, median: 3.92 [Sempron 2Ghz, Ram 1Go] The Olena Project
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Iterative Closest Point Algorithm Profiling Conclusion
Gprof Analysis Lazy Closest Point Evaluation Multi-Scale Registration
Outline 1
Iterative Closest Point Algorithm Key Points Algorithm Final Transform
2
Profiling Gprof Analysis Lazy Closest Point Evaluation Multi-Scale Registration
3
Conclusion
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Iterative Closest Point Algorithm Profiling Conclusion
Gprof Analysis Lazy Closest Point Evaluation Multi-Scale Registration
Multi-Scale Registration
e is the number of scales used q is a quotient chosen by users Let N be the number of point in C. We perform e registrations of a subset of N/q i points from C, i varying from e − 1 to 0.
The subset must be representative of C!
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Iterative Closest Point Algorithm Profiling Conclusion
Gprof Analysis Lazy Closest Point Evaluation Multi-Scale Registration
Multi-Scale Registration
e is the number of scales used q is a quotient chosen by users Let N be the number of point in C. We perform e registrations of a subset of N/q i points from C, i varying from e − 1 to 0.
The subset must be representative of C!
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Iterative Closest Point Algorithm Profiling Conclusion
Gprof Analysis Lazy Closest Point Evaluation Multi-Scale Registration
Multi-Scale Registration We could build a subset taking 1 point out of 2.
Selection is wrong. We have to select point randomly [5]. The Olena Project
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Iterative Closest Point Algorithm Profiling Conclusion
Gprof Analysis Lazy Closest Point Evaluation Multi-Scale Registration
Multi-Scale Registration
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Gprof Analysis Lazy Closest Point Evaluation Multi-Scale Registration
Multi-Scale Registration
Gain: 3.12, median: 2.33 [Sempron 2Ghz, Ram 1Go] The Olena Project
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Iterative Closest Point Algorithm Profiling Conclusion
Conclusion We propose three improvements to the classical iterative closest point algorithm. One quality improvement: Final transform using standard deviation. Quality is enhanced for every test in our set. Two Speed Improvements: Lazy evaluation of closest point. Multi-scale registration. Execution time is improved by a factor 18.9.
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Conclusion
Gain: 18.9, median: 12.94 [Sempron 2Ghz, Ram 1Go] The Olena Project
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Future Works
Generalization This method is currently available for 2 and 3-D only. We can easily generalize to n-D [1] [3]. Speed Up Projection Step Use of k -d tree that segment space in order to speed up closest point research. Distance Map.
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Bibliography
Bibliography I K. S. Arun, T.S. Huang, and S. D. Blostein. Least squere fitting of two 3-d point sets. IEEE Trans. Pact. Anal. Machine Intell. vol. PAMI-9, 1987. Paul J. Besl and Neil D. McKay. A method for registration of 3-d shapes. IEEE transactions on paltern analysis and machine intelligence, Vol. 14, NO. 2, 1992. Ming Gu, James W. Demmel, and Inderjit Dhillon. Efficient computation of the singular value decomposition with applications to least squares problems. Technical Report CS-94-257, institut, Knoxville, TN, USA, 1994. The Olena Project
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Bibliography
Bibliography II
T. Masuda, K. Sakaue, and N. Yokoya. Registration and integration of multiple range images for 3-d model construction. Proc. CVPR, 1996. Graham McNeill and Sethu Vijayakumar. 2d shape classification and retrieval. Institute of Perception, Action and Behavior, 2001.
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