Stability of Corner Points in Scale Space: The Effects of Small Nonrigid Deformations

摘要

To provide a good basis for the registration of medical images we search for reliable feature points using a scale-space approach. Our main concern is with 2D images: we analyze corner points, defined by differential invariants, at increasing scales. The number and position of corner points change in the scale-extended space, which define moving paths or orbits. To extract them we use a fast and reliable algorithm, based on iso-surface techniques, which automatically finds the corresponding singularities in scale space. We then get a representation of orbits that is very convenient both for detection at a coarse scale and localization at a fine scale. We find that the significance of corner points depends not only on their scale-space lifetime but also on how they are related to curvature inflection points. We investigate some topological changes of orbits which can be observed following image transformations. Afterward we examine whether features, stable at multiple scales, are stable as well with respect to various types of transformations. Thus we can compare the usefulness of different stability criteria for registration. We then go to present statistical results showing the dependency on the type of transformation and on the scale parameters.