Approximate Geometric Pattern Matching Under Rigid Motions
IEEE Transactions on Pattern Analysis and Machine Intelligence
Comparing Images Using the Hausdorff Distance
IEEE Transactions on Pattern Analysis and Machine Intelligence
Adaptive thinning for bivariate scattered data
Journal of Computational and Applied Mathematics
Approximate congruence in nearly linear time
Computational Geometry: Theory and Applications - Fourth CGC workshop on computional geometry
Geometric modeling in shape space
ACM SIGGRAPH 2007 papers
Gromov-Hausdorff stable signatures for shapes using persistence
SGP '09 Proceedings of the Symposium on Geometry Processing
Improving shape retrieval by spectral matching and meta similarity
IEEE Transactions on Image Processing
ACM SIGGRAPH 2011 papers
Metric structures on datasets: stability and classification of algorithms
CAIP'11 Proceedings of the 14th international conference on Computer analysis of images and patterns - Volume Part II
Superposition and Alignment of Labeled Point Clouds
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Combining CPU and GPU architectures for fast similarity search
Distributed and Parallel Databases
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Point clouds are one of the most primitive and fundamental surface representations. A popular source of point clouds are three dimensional shape acquisition devices such as laser range scanners. Another important field where point clouds are found is in the representation of high-dimensional manifolds by samples. With the increasing popularity and very broad applications of this source of data, it is natural and important to work directly with this representation, without having to go to the intermediate and sometimes impossible and distorting steps of surface reconstruction. A geometric framework for comparing manifolds given by point clouds is presented in this paper. The underlying theory is based on Gromov-Hausdorff distances, leading to isometry invariant and completely geometric comparisons. This theory is embedded in a probabilistic setting as derived from random sampling of manifolds, and then combined with results on matrices of pairwise geodesic distances to lead to a computational implementation of the framework. The theoretical and computational results here presented are complemented with experiments for real three dimensional shapes.