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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.