3D Point Correspondence by Minimum Description Length in Feature Space
Open accessAbstract
Finding point correspondences plays an important role in automatically building statistical shape models from a training set of 3D surfaces. For the point correspondence problem, Davies et al. [1] proposed a minimum-description-length-based objective function to balance the training errors and generalization ability. A recent evaluation study [2] that compares several well-known 3D point correspondence methods for modeling purposes shows that the MDL-based approach [1] is the best method. We adapt the MDL-based objective function for a feature space that can exploit nonlinear properties in point correspondences, and propose an efficient optimization method to minimize the objective function directly in the feature space, given that the inner product of any vector pair can be computed in the feature space. We further employ a Mercer kernel [3] to define the feature space implicitly. A key aspect of our proposed framework is the generalization of the MDL-based objective function to kernel principal component analysis (KPCA) [4] spaces and the design of a gradient-descent approach to minimize such an objective function. We compare the generalized MDL objective function on KPCA spaces with the original one and evaluate their abilities in terms of reconstruction errors and specificity. From our experimental results on different sets of 3D shapes of human body organs, the proposed method performs significantly better than the original method.
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The minimum description length criterion is well-known for determining the best model from data; it has been used in image registration [119], face (texture and depth) registration [120] and medical data registration [121] in computer vision, but is relatively little used in computer graphics and shape analysis.
“In information theory, the minimum description length criterion is well-known for determining the best model from data; it has been used in image registration [119], face (texture and depth) registration [120] and medical data registration [121] in computer vision, but is relatively little used in computer graphics and shape analysis.”
From Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid (2013) · cites this paper as [121]
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- Authors
- Chen, J.-H., Zheng, K. C., & Shapiro, L. G.
- Affiliations
- University of Washington (US)
- Microsoft (United States) (US)
- Venue
- Lecture Notes in Computer Science
- Publisher
- Springer Berlin Heidelberg
- Published
- 2010
- Volume
- 6313
- Pages
- 621-634
- ISSN
- 0302-9743 (ISSN-L)
- 1611-3349
- PMC
- PMC4201652
- OpenAlex
- W1880722738
- Cited by
- 12
- References
- 17
- Citations by year
- 2020: 1 · 2018: 1 · 2016: 3 · 2015: 1 · 2014: 2 · 2013: 2 · 2012: 1
- FWCI
- 2.53
- Type
- conference paper
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Lecture notes in computer science (publishedVersion)
- PubMed (publishedVersion)
- PubMed Central (acceptedVersion)
- Funders
- National Institute of Dental and Craniofacial Research (U01DE020050)
- Topics
- Physical Sciences › Engineering › Computational Mechanics › 3D Shape Modeling and Analysis
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Medical Image Segmentation Techniques
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Image Processing and 3D Reconstruction
- Keywords
- minimum description length, statistical shape models, feature space, kernel principal component analysis, Mercer kernels, gradient descent, 3D shape reconstruction, human organs
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