Scale-based description and recognition of planar curves and two-dimensional shapes

Area of Science:

• Computer Vision
• Image Processing
• Computational Geometry

Background:

• Describing and matching planar curves at varying levels of detail is a fundamental challenge in computer vision and pattern recognition.
• Existing methods often rely on finding a 'stable scale' for curve matching, which may not always exist for all curves.

Purpose of the Study:

• To develop a robust method for generating detailed descriptions of planar curves.
• To solve the problem of matching two such curve descriptions effectively.
• To create a curve representation invariant to common transformations like rotation, scaling, and translation.

Main Methods:

• Application of path-based Gaussian smoothing to planar curves to identify curvature zeros at multiple scales.
• Generation of a 'generalized scale space' image for each curve, ensuring invariance to rotation, uniform scaling, and translation.
• Modification of the uniform cost algorithm to perform contour matching within the generated scale space images.

Main Results:

• The generalized scale space image provides a suitable representation for curve matching due to its invariance properties.
• The modified uniform cost algorithm successfully finds the lowest cost match between contours in scale space images.
• The method is demonstrated to be preferable to matching at a stable scale, as such scales are not guaranteed to exist.

Conclusions:

• The proposed generalized scale space representation and matching algorithm offer a robust solution for planar curve description and matching.
• The technique effectively handles curves without a distinct stable scale.
• Successful application to registering a Landsat satellite image with a map demonstrates practical utility in geospatial applications.