Binary Shape Analysis
Although binary images contain much less information than their gray-scale counterparts, they embody shape and size information that is highly relevant for object recognition. However, this information resides in a digital lattice of pixels, and this results in intricacies appearing in the geometry. This chapter resolves these problems and explores a number of important algorithms for processing shapes.
• the connectedness paradox and how it is resolved.
• object labeling and how labeling conflicts are resolved.
• problems related to measurement in binary images.
• the convex hull as a means of characterizing shape, and methods for determining it.
• distance functions and how they are obtained using parallel and sequential algorithms.
• the skeleton and how it is found by thinning: the crucial role played by the crossing number, both in determining the skeleton and in analyzing it.
• simple measures for shape recognition, including circularity and aspect ratio.
• more rigorous measures of shape, including moments and boundary descriptors.
In reality, this chapter almost exclusively covers area-based methods of shape analysis, leaving boundary-based procedures to Chapter 7–though circularity measures and boundary tracking are both covered. However, chapter boundaries cannot be completely exclusive, as any new concept requires “hooks” that have been laid down in a variety of places. Indeed, it is often valuable to meet an idea before finding out in detail how to put flesh on it.
Returning briefly to the present chapter, it is interesting to note how intricate some of the algorithmic processes are: connectedness, in particular, pervades the whole subject of digital shape analysis and comes with a serious health warning.