Abstract

For shapes represented as closed planar contours, we introduce a class of functionals which are invariant with respect to the Euclidean group and which are obtained by performing integral operations. While such integral invariants enjoy some of the desirable properties of their differential counterparts, such as locality of computation (which allows matching under occlusions) and uniqueness of representation (asymptotically), they do not exhibit the noise sensitivity associated with differential quantities and, therefore, do not require presmoothing of the input shape. Our formulation allows the analysis of shapes at multiple scales. Based on integral invariants, we define a notion of distance between shapes. The proposed distance measure can be computed efficiently and allows warping the shape boundaries onto each other; its computation results in optimal point correspondence as an intermediate step. Numerical results on shape matching demonstrate that this framework can match shapes despite the deformation of subparts, missing parts and noise. As a quantitative analysis, we report matching scores for shape retrieval from a database.

Keywords

ComputationInvariant (physics)Shape analysis (program analysis)Computer scienceMatching (statistics)LocalityImage warpingNoise (video)MathematicsDynamic time warpingEuclidean geometryAlgorithmArtificial intelligenceGeometryImage (mathematics)

Affiliated Institutions

Related Publications

Publication Info

Year
2006
Type
article
Volume
28
Issue
10
Pages
1602-1618
Citations
227
Access
Closed

External Links

Social Impact

Altmetric

Social media, news, blog, policy document mentions

Citation Metrics

227
OpenAlex

Cite This

Siddharth Manay, Daniel Cremers, Byung‐Woo Hong et al. (2006). Integral Invariants for Shape Matching. IEEE Transactions on Pattern Analysis and Machine Intelligence , 28 (10) , 1602-1618. https://doi.org/10.1109/tpami.2006.208

Identifiers

DOI
10.1109/tpami.2006.208