Shape retrieval with eigen-CSS search

Shape retrieval programs are comprised of two components: shape representation and matching algorithm. Building the representation on scale space filtering and the curvature function of a closed boundary curve, curvature scale space (CSS) has been demonstrated to be a robust 2D shape representation. The adoption of the CSS image as the default in the MPEG-7 standard, using a matching algorithm utilizing maxima of the CSS image contours, makes this feature of interest perforce. In this paper, we propose a framework in two stages for a novel approach to both representing and matching the CSS feature. Our contribution consists of three steps, each of which effects a profound speedup on CSS image matching. Each step is a well-known technique in other domains, but the proposed concatenation of steps leads to a novel approach to this subject which captures shape information more efficiently and decreases distracting noise. First, using experience derived from medical imaging, we define a set of marginal-sum features summarizing the CSS image. Second, the standard algorithm using CSS maxima involves a complicated and time-consuming search, since the zero of arc length is not known in any new contour. Here, we obviate this search via a phase normalization transform in the spatial dimension of the reduced marginal-CSS feature. Remarkably, this step also makes the method rotation- and reflection-invariant. Finally, the resulting feature space is amenable to dimension reduction via subspace projection methods, with a dramatic speedup in time, and as well orders of magnitude reduction in space. The first stage of the resultant program, using a general-purpose eigenspace, has class-categorization accuracy compatible with the original contour maxima program. In a second stage, we generate specialized eigenspaces for each shape category, with little extra runtime complexity because search can still be carried out in reduced dimensionality. In a leave-one-out categorization using the MPEG-7 contour database, a classification success rate of 94.1% over 1400 objects in 70 classes is achieved with very fast matching, and 98.6% in the top-2 classes. A leave-all-in test achieves 99.8% correct categorization. The method is rotation invariant, and is simple, fast, and effective.