We present a method for modifying the topology of a 3D model with user control. The heart of our method is a guided topology editing algorithm. Given a source model and a user-provided target shape, the algorithm modifies the source so that the resulting model is topologically consistent with the target. Our algorithm permits removing or adding various topological features (e.g., handles, cavities and islands) in a common framework and ensures that each topological change is made by minimal modification to the source model. To create the target shape, we have also designed a convenient 2D sketching interface for drawing 3D line skeletons. As demonstrated in a suite of examples, the use of sketching allows more accurate removal of topological artifacts than previous methods, and enables creative designs with specific topological goals.

This paper presents a skeleton-based method for deforming meshes (the skeleton need not be the medial axis). The significant difference from previous skeleton-based methods is that the latter use the skeleton to control movement of vertices, whereas we use it to control the simplices defining the model. By doing so, errors that occur near joints in other methods can be spread over the whole mesh, via an optimization process, resulting in smooth transitions near joints of the skeleton. By controlling simplices, our method has the additional advantage that no vertex weights need be defined on the bones, which is a tedious requirement in previous skeleton-based methods. Furthermore, by incorporating the translation vector in our optimization, unlike other methods, we do not need to fix an arbitrary vertex, and the deformed mesh moves with the deformed skeleton. Our method can also easily be used to control deformation by moving a few chosen line segments, rather than a skeleton.

In this report, we propose a new semi-fragile watermarking algorithm for the authentication of 3D models based on integral invariants. To do so, we embed a watermark image by modifying the integral invariants of some of the vertices. Basically, we shift a vertex and its neighbors in order to change the integral invariants. To extract the watermark, test all the vertices for the embedded information, and combine them to recover the watermark image. How many parts can the watermark image be recovered would help us to make the authentication decision. Experimental test shows that this method is robust against rigid transform and noise attack, and useful to test purposely attack besides transferring noise and geometrical transforming noise. An additional contribution of this paper is a new algorithm for computing two kinds of integral invariants.

A time domain blind source separation algorithm of convolutive sound mixtures is studied based on a compact partial inversion formula in closed form. An L1-constrained minimization problem is formulated to find demixing filter coefficients for source separation while capturing scaling invariance and sparseness of solutions. The minimization aims to reduce (lagged) cross correlations of the mixture signals, which are modeled stochastically. The problem is non-convex, however it is put in a nonlinear least squares form where the robust and convergent Levenberg-Marquardt iterative method is applicable to compute local minimizers. Efficiency is achieved in recovering lower dimensional demixing filter solutions than the physical ones. Computations on recorded and synthetic mixtures show satisfactory performance, and are compared with other iterative methods.

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