Watermarking algorithms provide a way of hiding or embedding some bits of information in a watermark. In the case of watermarking a 3D model, many algorithms employ a so-called indexed localization scheme. In this paper, we propose an optimization framework with two new steps for such watermarking algorithms to improve their capacity and invisibility. The first step is to find an optimal layout of invariant units to improve capacity. The second step is to rearrange the correspondence between the watermark units and the invariant units to improve invisibility. Experimental tests show that by using this framework, the capacity and invisibility of watermarking algorithms can be greatly improved.

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We present an automatic reconstruction pipeline for large scale urban scenes from aerial images captured by a camera mounted on an unmanned aerial vehicle. Using state-of-the-art Structure from Motion and Multi-View Stereo algorithms, we first generate a dense point cloud from the aerial images. Based on the statistical analysis of the footprint grid of the buildings, the point cloud is classified into different categories (i.e., buildings, ground, trees, and others). Roof structures are extracted for each individual building using Markov random field optimization. Then, a contour refinement algorithm based on pivot point detection is utilized to refine the contour of patches. Finally, polygonal mesh models are extracted from the refined contours. Experiments on various scenes as well as comparisons with state-of-the-art reconstruction methods demonstrate the effectiveness and robustness of the proposed method.

The alternating direction multiplier method (ADMM) is widely used in computer graphics for solving optimization problems that can be nonsmooth and nonconvex. It converges quickly to an approximate solution, but can take a long time to converge to a solution of high‐accuracy. Previously, Anderson acceleration has been applied to ADMM, by treating it as a fixed‐point iteration for the concatenation of the dual variables and a subset of the primal variables. In this paper, we note that the equivalence between ADMM and Douglas‐Rachford splitting reveals that ADMM is in fact a fixed‐point iteration in a lower‐dimensional space. By applying Anderson acceleration to such lower‐dimensional fixed‐point iteration, we obtain a more effective approach for accelerating ADMM. We analyze the convergence of the proposed acceleration method on nonconvex problems, and verify its effectiveness on a variety of computer graphics including geometry processing and physical simulation.

NURBS surfaces are among the most commonly used parametric surfaces in CAGD and Computer Graphics. This paper investigates shape modification of NURBS surfaces with geometric constraints, such as point, normal vector, and curve constraints. Two new methods are presented by constrained optimization and energy minimization. The former is based on minimizing changes in control net of surfaces, whereas the latter is based on strain energy minimization. By these two methods, we change control points and weights of an original surface, such that the modified surface satisfies the given constraints. Comparison results and practical examples are also given.