A typical NURBS surface model has a large percentage of superfluous control points that significantly interfere with the design process. This paper presents an algorithm for eliminating such superfluous control points, producing a T-spline. The algorithm can remove substantially more control points than competing methods such as B-spline wavelet decomposition. The paper also presents a new T-spline local refinement algorithm and answers two fundamental open questions on T-spline theory.

With the powerfulness of convolution neural networks (CNN), CNN based face reconstruction has recently shown promising performance in reconstructing detailed face shape from 2D face images. The success of CNN-based methods relies on a large number of labeled data. The state-of-the-art synthesizes such data using a coarse morphable face model, which however has difficulty to generate detailed photo-realistic images of faces (with wrinkles). This paper presents a novel face data generation method. Specifically, we render a large number of photo-realistic face images with different attributes based on inverse rendering. Furthermore, we construct a fine-detailed face image dataset by transferring different scales of details from one image to another. We also construct a large number of video-type adjacent frame pairs by simulating the distribution of real video data. With these nicely constructed datasets, we propose a coarse-to-fine learning framework consisting of three convolutional networks. The networks are trained for real-time detailed 3D face reconstruction from monocular video as well as from a single image. Extensive experimental results demonstrate that our framework can produce high-quality reconstruction but with much less computation time compared to the state-of-the-art. Moreover, our method is robust to pose, expression and lighting due to the diversity of data.

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One weakness in the existing interactive image segmentation algorithms is the lack of more intelligent ways to understand the intention of user inputs. In this paper, we advocate the use of multiple intuitive user inputs to better reflect a user's intention. In particular, we propose a constrained random walks algorithm that facilitates the use of three types of user inputs: 1) foreground and background seed input, 2) soft constraint input, and 3) hard constraint input, as well as their combinations. The foreground and background seed input allows a user to draw strokes to specify foreground and background seeds. The soft constraint input allows a user to draw strokes to indicate the region that the boundary should pass through. The hard constraint input allows a user to specify the pixels that the boundary must align with. Our proposed method supports all three types of user inputs in one coherent computational framework consisting of a constrained random walks and a local editing algorithm, which allows more precise contour refinement. Experimental results on two benchmark data sets show that the proposed framework is highly effective and can quickly and accurately segment a wide variety of natural images with ease.

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The problem of decomposing a 3D mesh into meaningful segments (or parts) is of great practical importance in computer graphics. This article presents a variational mesh decomposition algorithm that can efficiently partition a mesh into a prescribed number of segments. The algorithm extends the Mumford-Shah model to 3D meshes that contains a data term measuring the variation within a segment using eigenvectors of a dual Laplacian matrix whose weights are related to the dihedral angle between adjacent triangles and a regularization term measuring the length of the boundary between segments. Such a formulation simultaneously handles segmentation and boundary smoothing, which are usually two separate processes in most previous work. The efficiency is achieved by solving the Mumford-Shah model through a saddle-point problem that is solved by a fast primal-dual method. A preprocess step is also proposed to determine the number of segments that the mesh should be decomposed into. By incorporating this preprocessing step, the proposed algorithm can automatically segment a mesh into meaningful parts. Furthermore, user interaction is allowed by incorporating the user's inputs into the variational model to reflect the user's special intention. Experimental results show that the proposed algorithm outperforms competitive segmentation methods when evaluated on the Princeton Segmentation Benchmark.