Recognition by prototypes A scheme for recognizing 3D objects from single 2D images under orthographic projection is introduced. The scheme proceeds in two stages. In the first stage, the categorization stage, the image is compared to prototype objects. For each prototype, the view that most resembles the image is recovered, and, if the view is found to be similar to the image, the class identity of the object is determined. In the second stage, the identification stage, the observed object is compared to the individual models of its class, where classes are expected to contain objects with relatively similar shapes. For each model, a view that matches the image is sought. If such a view is found, the objectu0027s specific identity is determined. The advantage of categorizing the object before it is identified is twofold. First, the image is compared to a smaller number of models, since only models that belong to the objectu0027s class need to be considered. Second, the cost of comparing the image to each model in a class is very low, because correspondence is computed once for the whole class. More specifically, the correspondence and object pose computed in the categorization stage to align the prototype with the image are reused in the identification stage to align the individual models with the image. As a result, identification is reduced to a series of simple template comparisons. The paper concludes with an algorithm for constructing optimal prototypes for classes of objects.

Mathematical aspects of shape analysis for object recognition In this paper we survey some of the mathematical techniques that have led to useful new results in shape analysis and their application to a variety of object recognition tasks. In particular, we will show how these techniques allow one to solve a number of fundamental problems related to object recognition for configurations of point features under a generalized weak perspective model of image formation. Our approach makes use of progress in shape theory and includes the development of objectimage equations for shape matching and the exploitation of shape space metrices (especially objectimage metrics) to measure matching up to certain transformations. This theory is built on advanced mathematical techniques from algebraic and differential geometry which are used to construct generalized shape spaces for various projection and sensor models. That construction in turn is used to find natural metrics that express the distance (geometric difference) between two configurations of object features, two configurations of image features, or an object and an image pair. Such metrics are believed to produce the most robust tests for object identification; at least as far as the objectu0027s geometry is concerned. Moreover, these metrics provide a basis for efficient hashing schemes to do identification quickly, and they provide a rigorous foundation for error and statistical analysis in any recognition system. The most important feature of a shape theoretic approach is that all of the matching tests and metrics are independent of the choice of coordinates used to express the feature locations on the object or in the image. In addition, the approach is independent of the camerasensor position and any camerasensor parameters. Finally, the method is also independent of object pose or image orientation. This is what makes the results so powerful.