PIMs and Invariant Parts for Shape Recognition

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 Mea-sures"), which is a new representation integrating implicit polynomial curves and surfaces, explicit polyno-mials, 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 aane 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 brieey outline a low computational cost image-database indexing-system based on this representation for objects having complex shape-geometry.