A new concept for examining shapes as vectors in a shape space is described. The shape space is defined in terms of its properties and the importance of the independence of the size variable to the shape vectors. Also, two theorems essential to the process of comparing partial shapes to the complete shape are stated and proved. A new method for detecting the points on a shape that appear to dominate visual perception is described. This method, called the adaptive line of sight method, detects the dominant points on a shape even though they do not always occur on points of high curvature. The critical points determined by this method are based on a set of axes that are dependent on the shape itself. Therefore, the points determined are independent of size, rotation, or relative displacement. The line of sight of a point concept is also introduced and subsequently utilized to extract features from a shape. These features are then compared to the features of other shape by a syntactic procedure for the purpose of recognizing whether a shape is a partial shape or a shape in its own right.

A new concept for examining shapes as vectors in a shape space is described. The shape space is defined in terms of its properties and the importance of the independence of the size variable to the shape vectors defined on this shape space is stressed. Also, two theorems essential to the process of comparing partial shapes to the complete shape are given. A new method for detecting the points on a shape which appear to dominate visual perception is described. This method, called the Adaptive Line of Sight Method detects the dominant points of high curvature. The critical points, or the dominant points of the shape, which are determined by this method are based on a set of axes that are dependent on the shape itself. Therefore, the points determined are independent of size, rotation, or relative displacement. This concept is utilized to extract features from a shape. It is demonstrated that the feature vectors determined by this procedure are independent of size rotation, and displacement.

In this correspondence it is demonstrated that the derivative of the angle with respect to an arbitrary independent parameter cannot in general be used to find peaks and valleys of a shape. It is then shown, using concepts from differential geometry, that curvature corresponds to the derivative of the angle with respect to an independent variable if and only if the angle is deflned as a single variable. It is further shown that peaks and valleys detected using curvature as a criterion are insufficient to completely describe a shape.