Multiscale representations of planar boundaries
A. Rattarangsi · 1991
Multiscale representations of planar curves are investigated. The objective is to describe an object at various scales for noise cleaning, boundary detection, and object description. First, the development of a multiscale corner detection is presented. It is based on the construction of a scale space map which consists of curvature maxima as a function of scale. Properties of this scale space map have been analyzed using a number of isolated corner models. The analysis has shown that the resulting scale space converges, that is, it contains line patterns that either persist, terminate, or merge with a neighboring line. The developed corner detector uses the scale space map and a stability criterion to search for stable corners. The searching strategy is based on the argument that if the same curvature maximum is present in a large range of scales, it represents the presence of an image signal due to a single physical corner. This detector requires no input parameter. Experiments were performed to show that the scale space corner detector is reliable for objects with multiple-size features and compares favorably with other corner detectors tested. We further investigate a multiscale boundary representation for the purpose of detecting object boundaries from their noisy observations. This representation is based on the fact that the degree of invariance of the boundary due to changing scales is directly related to the stability of the boundary. The composite of a set of Gaussian smoothed boundaries is used to measure a boundary's invariance in the form of probability of occurrence. Based on the probability, an uncertainty measure of the boundary due to smoothing have been defined from which a reliable boundary and its discontinuities (corners) can be detected. The developed algorithm does not rely on prior assumptions of the signal and of the noise, and is able to detect boundaries without blurring their corners. In addition, its detection is reliable even with nonstationary noise and changing feature size. A comparison with the $GCV$ smoothing cubic spline have been made and shown to compare favorably.