Optimized statistical deformable surface models with manifold embedding P. Horkaew * , G.Z. Yang Department of Computing, Royal Society/Wolfson Foundation MIC Laboratory, Imperial College of Science, Technology and Medicine, 180 Queen’s Gate, London SW7 2BZ, United Kingdom Received 13 March 2003; received in revised form 13 March 2003; accepted 20 March 2003 Abstract A key challenge for statistical shape modeling is the definition of a set of dense correspondence points across a group of segmented shapes. This paper describes a novel method for building an optimal statistical deformable model from a set of surfaces whose topological realization is homeomorphic to a compact 2D manifold with boundary. The optimal parameterization of each shape is recursively refined by using hierarchical piecewise bilinear maps (PBMs) and tensor product B-spline representation of the surface. A criterion based on minimum description length (MDL) is used to define the internal correspondence of the training data. The strength of the proposed technique is demonstrated by deriving a concise statistical model of the human left ventricle which has principal modes of variation that correspond to intrinsic cardiac motions. The extension of the technique to shapes with complex topology is also discussed. D 2003 Published by Elsevier Science B.V. Keywords: Minimum description length; Statistical shape models 1. Introduction In cardiac imaging, accurate delineation of anatomical boundaries is essential for quantification of cardiac mass, volume and function. Image segmentation based on deformable models [1] recovers the underlying shape by exploiting a priori knowledge about the geometry of anatomical structures. The active shape model (ASM) [2–5] represents a robust parametric deformable structure, which captures plausible variability of structures over time as well as across different individuals. A key challenge for statistical 0531-5131/03 D 2003 Published by Elsevier Science B.V. doi:10.1016/S0531-5131(03)00420-5 * Corresponding author. Tel.: +44-207-5948370. E-mail address: phorkaew@doc.ic.ac.uk (P. Horkaew). International Congress Series 1256 (2003) 253 – 258