PIMs and invariant parts for shape recognition

We present completely new very powerful solutions t o 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 20 data along a curve (or 30 data along a surface), decompose the data into patches such that new data taken along affine transformation-s or Eucladean transformations of the curve (or surface) can be decomposed into corresponding 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.