The Alignment Between 3-D Data and Articulated Shapes with Bending Surfaces

In this paper we address the problem of aligning 3-D data with articulated shapes. This problem resides at the core of many motion tracking methods with applications in human motion capture, action recognition, medical-image analysis, etc. We describe an articulated and bending surface representation well suited for this task as well as a method which aligns (or registers) such a surface to 3-D data. Articulated objects, e.g., humans and animals, are covered with clothes and skin which may be seen as textured surfaces. These surfaces are both articulated and deformable and one realistic way to model them is to assume that they bend in the neighborhood of the shape’s joints. We will introduce a surface-bending model as a function of the articulated-motion parameters. This combined articulated-motion and surface-bending model better predicts the observed phenomena in the data and therefore is well suited for surface registration. Given a set of sparse 3-D data (gathered with a stereo camera pair) and a textured, articulated, and bending surface, we describe a register-and-fit method that proceeds as follows. First, the data-to-surface registration problem is formalized as a classifier and is carried out using an EM algorithm. Second, the data-to-surface fitting problem is carried out by minimizing the distance from the registered data points to the surface over the joint variables. In order to illustrate the method we applied it to the problem of hand tracking. A hand model with 27 degrees of freedom is successfully registered and fitted to a sequence of 3-D data points gathered with a stereo camera pair.