Practical data mining rarely falls exactly into the supervised learning scenario. Rather, the growing amount of unlabeled data poses a big challenge to large-scale semi-supervised learning (SSL). We note that the computational intensiveness of graph-based SSL arises largely from the manifold or graph regularization, which in turn lead to large models that are difficult to handle. To alleviate this, we proposed the prototype vector machine (PVM), a highly scalable, graph-based algorithm for large-scale SSL. Our key innovation is the use of "prototypes vectors" for efficient approximation on both the graphbased regularizer and model representation. The choice of prototypes are grounded upon two important criteria: they not only perform effective low-rank approximation of the kernel matrix, but also span a model suffering the minimum information loss compared with the complete model. We demonstrate encouraging performance and appealing scaling properties of the PVM on a number of machine learning benchmark data sets.

We present a method to produce an integrated description of an object given multiple range views without registration. Our multiple view representation is in the form of B-rep (boundary representation), which has not been done so far by the computer vision community. We describe each view of the object as an attributed graph whose nodes are surface patches and links are the relations between surfaces. Any two attributed graphs, each corresponding to a given view, are matched and the rigid motion transformation between them is computed. The basic strategy for multiple view integration is composed of two aspects: We first build a composite graph, which contains the bounding surfaces, and their corresponding attributes, and then intersect these surfaces so that the edges and vertices corresponding to the B-rep description are identified. We present results on objects with polyhedral as well as quadratic curved surfaces.

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Most problems in ima e understanding involve ambiguities at different levels of a computational hierarchy. We suggest that a dynamic system model provides an attractive mechanism for resolving ambi uities. As a case example, we concentrate on the problem o f object description and correspondence in range images, and show how these problems can be modeled with a dynamic system, i.e. a system of differential equations. Our model exploits geometric features to satisfy strong and weak constraints for boundary extraction. To ensure the closure property on the contours, a dynamic network with feedback is formulated to perform boundary completion from local surface features. The underlying principle for this network is geometric cohesion and weak smoothness constraints, and is modeled as the interaction between long and short term variables. The correspondence problem involves matching visible surfaces and vertices from their attributed graph representation. This is a two step process, where each step is formulated as a dynamic system. At each step, we specify a set of local, adjacency and global constraints, and define an appropriate energy function to be minimized.