This paper presents a brief overview and focuses on two key aspects of a technology for representing and recognizing complicated 2D and 3D shapes subject to partial occlusion and missing data, based on implicit polynomials. The two key aspects are new concepts and results for fast, robust, repeatable fitting of implicit polynomials to data, and new approaches to representing and recognizing complicated shapes based on these polynomials. This representation is built around signature curves of vector valued algebraic invariants which permit a recognition machine to start anywhere in a shape data set, choose a data patch of appropriate length, fit an implicit polynomial to the patch, and recognize the shape or index into a database by comparing algebraic invariants of the polynomial with those stored in the signature curves. Fitting and recognition or indexing can be multiscale. This technology can also be applied to curves obtained from shape data, such as Kimia's shocks and time to shock-formation, and our set-of-curves representation for generalized cylinders.
@InProceedings{Lei:1997:IPB,
author = {Z. Lei and David B. Cooper},
title = {Implicit Polynomial Based Geometric Shape Modeling and Recognition},
booktitle = {Proceedings of International Workshop on Visual Form},
year = {1997},
address = {Capri, Italy},
month = {May},
publisher = "Plenum Press, New York",
}