MEASURING 3-D SHAPE SIMILARITY USING PROGRESSIVE TRANSFORMATIONS

We present a quantitative approach to the measurement of shape similar ity among 3-D (three-dimensional) objects. Using voxels, an object is mapped to a representation invariant under translation and rotation. T he different objects to be compared are normalized to have the same am ount of information (equal number of voxels) and this is termed invari ance under volume. When the different objects to be compared are norma lized under translation, rotation and volume, a quantity of work (from a physics point of view) is performed that transforms an object O-1 i nto object O-2 (the transformation of an object into another is perfor med moving voxels, as if they were bricks). Voxels to move are selecte d so as to minimize the work involved. The work done by transforming O -1 into O-2 is the measure of dissimilarity between them. Dissimilar o bjects will have a large quantity of work done to transform one into o ther, while analogous objects will have a small quantity of work done. When two objects are identical, the quantity of work done is zero. Th us, the distance or shape dissimilarity between two objects can be def ined as the amount of work needed to convert one into another. Informa lly, if two objects to be compared consist of bricks, their shape diff erence could be ascertained by counting how many bricks we have to mov e and how far to change one object into another. Copyright (C) 1996 Pa ttern Recognition Society.