An Elasticity Approach to Principal Modes of Shape Variation

Abstract. Concepts from elasticity are applied to analyze modes of variation on shapes in two and three dimensions. This approach represents a physically motivated alternative to shape statistics on a Riemannian shape space, and it robustly treats strong nonlinear geometric variations of the input shapes. To compute a shape average, all input shapes are elastically deformed into the same configuration. That configuration which minimizes the total elastic deformation energy is defined as the average shape. Each of the deformations from one of the shapes onto the shape average induces a boundary stress. Small amplitude stimulation of these stresses leads to displacements which reflect the impact of every single input shape on the average. To extract the dominant modes of variation, a PCA is performed on this set of displacements. To make the approach computationally tractable, a relaxed formulation is proposed, and sharp contours are approximated via phase fields. For the spatial di...

• Type: Conference
• Year: 2009
• Where: SCALESPACE
• Authors: Martin Rumpf, Benedikt Wirth
• Keywords: Computer Vision, Input Shape, Riemannian Shape Space, SCALESPACE 2009, Shape Average