Graph matching with a dual-step EM algorithm

This paper describes a new approach to matching geometric structure in 2D point-sets. The novel feature is to unify the tasks of estimating transformation geometry and identifying point-correspondence matches. Unification is realized by constructing a mixture model over the bipartite graph representing the correspondence match and by affecting optimization using the EM algorithm. According to our EM framework, the probabilities of structural correspondence gate contributions to the expected likelihood function used to estimate maximum likelihood transformation parameters. These gating probabilities measure the consistency of the matched neighborhoods in the graphs. The recovery of transformational geometry and hard correspondence matches are interleaved and are realized by applying coupled update operations to the expected log-likelihood function. In this way, the two processes bootstrap one another. This provides a means of rejecting structural outliers. We evaluate the technique on two real-world problems. The first involves the matching of different perspective views of 3.5-inch floppy discs. The second example is furnished by the matching of a digital map against aerial images that are subject to severe barrel distortion due to a line-scan sampling process. We complement these experiments with a sensitivity study based on synthetic data

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

International audienceIn 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