A Method for Registration of 3-D Shapes
IEEE Transactions on Pattern Analysis and Machine Intelligence - Special issue on interpretation of 3-D scenes—part II
Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Proceedings of the conference on Visualization '01
The Softassign Procrustes Matching Algorithm
IPMI '97 Proceedings of the 15th International Conference on Information Processing in Medical Imaging
A new point matching algorithm for non-rigid registration
Computer Vision and Image Understanding - Special issue on nonrigid image registration
SMI '04 Proceedings of the Shape Modeling International 2004
Variational shape approximation
ACM SIGGRAPH 2004 Papers
A Statistical Method for Robust 3D Surface Reconstruction from Sparse Data
3DPVT '04 Proceedings of the 3D Data Processing, Visualization, and Transmission, 2nd International Symposium
Statistical Shape Analysis: Clustering, Learning, and Testing
IEEE Transactions on Pattern Analysis and Machine Intelligence
Spectral surface reconstruction from noisy point clouds
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
A Theoretical and Computational Framework for Isometry Invariant Recognition of Point Cloud Data
Foundations of Computational Mathematics
3D Building Detection and Modeling from Aerial LIDAR Data
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 2
Surface reconstruction from noisy point clouds
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Looking for Shapes in Two-Dimensional Cluttered Point Clouds
IEEE Transactions on Pattern Analysis and Machine Intelligence
Provable surface reconstruction from noisy samples
Computational Geometry: Theory and Applications
Single spin image-ICP matching for efficient 3D object recognition
Proceedings of the ACM workshop on 3D object retrieval
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The problems of detecting, classifying, and estimating shapes in point cloud data are important due to their general applicability in image analysis, computer vision, and graphics. They are challenging because the data is typically noisy, cluttered, and unordered. We study these problems using a fully statistical model where the data is modeled using a Poisson process on the object's boundary (curves or surfaces), corrupted by additive noise and a clutter process. Using likelihood functions dictated by the model, we develop a generalized likelihood ratio test for detecting a shape in a point cloud. This ratio test is based on optimizing over some unknown parameters, including the pose and scale associated with hypothesized objects, and an empirical evaluation of the log-likelihood ratio distribution. Additionally, we develop a procedure for estimating most likely shapes in observed point clouds under given shape hypotheses. We demonstrate this framework using examples of 2D and 3D shape detection and estimation in both real and simulated data, and a usage of this framework in shape retrieval from a 3D shape database.