The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
Analysis of planar shapes using geodesic paths on shape spaces
Abstract
For analyzing shapes of planar, closed curves, we propose differential geometric representations of curves using their direction functions and curvature functions. Shapes are represented as elements of infinite-dimensional spaces and their pairwise differences are quantified using the lengths of geodesics connecting them on these spaces. We use a Fourier basis to represent tangents to the shape spaces and then use a gradient-based shooting method to solve for the tangent that connects any two shapes via a geodesic. Using the Surrey fish database, we demonstrate some applications of this approach: 1) interpolation and extrapolations of shape changes, 2) clustering of objects according to their shapes, 3) statistics on shape spaces, and 4) Bayesian extraction of shapes in low-quality images.
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Cites
Riemannian center of mass and mollifier smoothing
Karcher, H. (1977) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.3160300502 · Cited by 995
Probability, Convexity, and Harmonic Maps with Small Image I: Uniqueness and Fine Existence
Kendall, W. S. (1990) · Proceedings of the London Mathematical Society · doi:10.1112/plms/s3-61.2.371 · Cited by 281
Cited by
Geometric modeling in shape space
Kilian, M., Mitra, N. J., & Pottmann, H. (2007) · ACM SIGGRAPH 2007 papers · doi:10.1145/1275808.1276457 · Cited by 224
Expression recognition from 3D dynamic faces using robust spatio-temporal shape features
Le, V., Tang, H., & Huang, T. S. (2011) · Face and Gesture 2011 · doi:10.1109/fg.2011.5771435 · Cited by 67
MORPHING OF TRIANGULAR MESHES IN SHAPE SPACE
WUHRER, S., BOSE, P., CHANG, S., O'ROURKE, J., & BRUNTON, A. (2010) · International Journal of Shape Modeling · doi:10.1142/s0218654310001341 · Cited by 1
Metadata
- Authors
- Klassen, E., Srivastava, A., Mio, W., & Joshi, S. H.
- Venue
- IEEE Transactions on Pattern Analysis and Machine Intelligence
- Published
- 2004-03
- Volume
- 26
- Issue
- 3
- Pages
- 372-383
- ISSN
- 0162-8828 (ISSN-L)
- OpenAlex
- W2140798815
- Cited by
- 479
- References
- 2
- FWCI
- 37.41
- Type
- journal article
- Language
- en
- Open access
- closed
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- Klassen, E., Srivastava, A., Mio, W., & Joshi, S. H. (2004). Analysis of planar shapes using geodesic paths on shape spaces. IEEE Transactions on Pattern Analysis and Machine Intelligence. https://doi.org/10.1109/tpami.2004.1262333
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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