Scale-Based Description and Recognition of Planar Curves and Two-Dimensional Shapes

The problem of finding a description for planar curves and two-dimensional shapes at varying levels of detail and matching two such descriptions is posed and solved in this paper. A number of necessary criteria are imposed on any candidate solution method. Path-based Gaussian smoothing techniques are applied to the curve to find zeroes of curvature at varying levels of detail. The result is the 'generalized scale space' image of a planar curve which is invariant under rotation, uniform scaling and translation of the curve. These properties make the scale space image suitable for matching. The matching algorithm is a modification of the uniform cost algorithm and finds the lowest cost match of contours in the scale space images. It is argued that this is preferable to matching in a stable scale of the curve because no such scale may exist for a given curve. This technique is applied to register a Landsat aerial image of the Strait of Georgia, B.C. (manually corrected for skew) to a map containing the shorelines of an overlapping area.