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

TLDR

The paper addresses how to generate multi‑level descriptions of planar curves and match two such descriptions. It introduces criteria, applies path‑based Gaussian smoothing to locate curvature zeros, constructs a generalized scale‑space image invariant to rotation, scaling and translation, and uses a modified uniform‑cost algorithm to match contours in this space, demonstrated on registering a Landsat image to a shoreline map. The resulting scale‑space representation is invariant and effective for matching, and the proposed algorithm is argued to be preferable to matching in a stable scale, successfully registering the satellite image to the map.

Abstract

The problem of finding a description, at varying levels of detail, for planar curves 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 zeros 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 so-called stable scale of the curve because no such scale may exist for a given curve. This technique is applied to register a Landsat satellite image of the Strait of Georgia, B.C. (manually corrected for skew) to a map containing the shorelines of an overlapping area.