Recognition of 3-D Objects from Partial View Data

We consider a problem that occurs in machine vision research, namely, how to determine the class membership of an object when only partial view data about it is available. For example, suppose that a machine vision system must determine whether a physical (i.e., a three-dimensional) object belongs to class A or class B and only 90 degree view data is available. How should the data be organized into a useful feature vector? What rule should be used to determine class—membership? One way to proceed is via image recovery i.e., the restoration of missing view data using any of the several extrapolation algorithms known to the image recovery community. However if only class membership is desired, is image recovery really needed? First we note that if the partial view data is insufficient i.e, it contains no information that is not common to both classes, then image recovery will not work (now for that matter will anything else!). Second, assuming that the data is sufficient i.e., that it contains at least some data characteristic of only one class, image recovery may not be the answer for two reasons: 1) the recovery process is most-often ill-posed, thereby introducing possibly too much noise for subsequent discrimination; and 2) regularization may induce sufficient smoothing to destroy what little class-differentiability may exist in the partial data. Thus we concentrate on information recovery rather than image recovery. We are therefore led to the following problem statement: given partial view data of a 3-D object known to belong to one of M well-defined classes, what operation (linear or non-linear) will enhance the discriminating value of the data? The algorithm we have derived is based on the ful1-view algorithm described below.