On Interactive Object Shape Modeling Using Algebraic Curves
Journal of VLSI Signal Processing Systems - special issue on multimedia signal processing
The 3L Algorithm for Fitting Implicit Polynomial Curves and Surfaces to Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Covariant-Conics Decomposition of Quartics for 2D Shape Recognition and Alignment
Journal of Mathematical Imaging and Vision
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Recognition of computationally constructed loci
ADG'06 Proceedings of the 6th international conference on Automated deduction in geometry
Efficient detection of symmetries of polynomially parametrized curves
Journal of Computational and Applied Mathematics
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We present completely new very powerful solutions to two fundamental problems central to computer vision. 1. Given data sets representing C objects to be stored in a database, and given a new data set for an object, determine the object in the database that is most like the object measured. We solve this problem through use of PIMs ("Polynomial Interpolated Measures"), which is a new representation integrating implicit polynomial curves and surfaces, explicit polynomials, and discrete data sets which may be sparse. The method provides high accuracy at low computational cost. 2. Given noisy 2D data along a curve (or 3D data along a surface), decompose the data into patches such that new data taken along affine transformations or Euclidean transformations of the curve (or surface) can be decomposed into correponding patches. Then recognition of complex or partially occluded objects can be done in terms of invariantly determined patches. We briefly outline a low computational cost image-database indexing-system based on this representation for objects having complex shape-geometry.