Conclusions

Abstract

The principal objective of our research was to extend the analysis of shape to grey-scale images. This goal was accomplished by designing and implementing a new structural shape description called the intensity axis of symmetry (IAS) and an associated curvature—based description called vertex curves. Both of these descriptions focus on properties of individual level curves of the image and combine this information across intensities to obtain representations which capture both spatial and intensity properties of shape in an image. To demonstrate the effectiveness of this image shape description, an interactive image segmentation program was implemented which identifies and displays image regions associated with individual components of the IAS. These regions often correspond to sensible anatomical structures in medical images. An analysis of the multiresolution behavior of the IAS reveals that it is possible to impose a quasi-hierarchy on IAS sheets by focusing on the multiresolution properties of much simpler geometric structures: vertex curves approximated by watershed boundaries. The next four sections expand on these accomplishments.