Global-to-local, shape-based, real and virtual landmarks for shape modeling by recursive boundary subdivision

Abstract

Landmark based statistical object modeling techniques, such as Active Shape Model (ASM), have proven useful in medical image analysis. Identification of the same homologous set of points in a training set of object shapes is the most crucial step in ASM, which has encountered challenges such as (C1) defining and characterizing landmarks; (C2) ensuring homology; (C3) generalizing to <i>n</i> &gt; 2 dimensions; (C4) achieving practical computations. In this paper, we propose a novel global-to-local strategy that attempts to address C3 and C4 directly and works in <i>R</i>ⁿ. The 2D version starts from two initial corresponding points determined in all training shapes via a method &alpha;, and subsequently by subdividing the shapes into connected boundary segments by a line determined by these points. A shape analysis method &beta; is applied on each segment to determine a landmark on the segment. This point introduces more pairs of points, the lines defined by which are used to further subdivide the boundary segments. This recursive boundary subdivision (RBS) process continues simultaneously on all training shapes, maintaining synchrony of the level of recursion, and thereby keeping correspondence among generated points automatically by the correspondence of the homologous shape segments in all training shapes. The process terminates when no subdividing lines are left to be considered that indicate (as per method &beta;) that a point can be selected on the associated segment. Examples of &alpha; and &beta; are presented based on (a) distance; (b) Principal Component Analysis (PCA); and (c) the novel concept of virtual landmarks.