Representation for Shape based on Peaks and Ridges in the Difference of Low-pass Transform

Abstract

This papcr defines a multiple resolution representation for the two-dimensional gray-scale shapes in an image. This representation is constructed by detecting peaks and ridges in the Difference of Low Pass (DOLP) transform. Descriptions of shapes which are encoded in this representation may be matched efficiently despite changes in size, orientation or position. Motivations for a multiple resolution representation are presented first, followed by the definition of the DOLP Transform. Techniques are then presented for encoding a symbolic structural description of forms from the DOLP transform. This proccss involves detecting local peaks and ridges in each band-pass image and in the entire three-dimensional space defined by the DOLP transform. Linking adjacent peaks in different band-pass images gives a multiple resolution tree which describes shape. Peaks which are local maxima in this tree provide landmarks for aligning, manipulating, and matching shapes. Detecting and linking the ridges in each DOLP band-pass irnage provides a graph which links peaks within a shape in a band-pass image and describes the positions of the boundaries of the shape at multiple resolutions. Dctccting and linking the ridges in the DOLP three space describes elongated forms and links the Iargest peaks in the tree. The principles for determining the correspondence between symbols in pairs of such descriptions are then described. Such correspondence matching is shown to be simplified by using the correspondence at lower resolutions to constrain thc possible correspondence at higher resolutions.