To improve the catastrophic forgetting that existed in the high-resolution range profile (HRRP) target recognition model of offline training, this paper proposed a continuous learning method of radar HRRP based on conditional variational auto-encoding and generative adversarial network (CVAE-GAN). Firstly, this method generates data through CVAE to simulate the real training data, and replays it in the series of subsequent tasks. By using generators, the proposed method does not need to save the original HRRP data and can ensure the privacy of the training dataset. Secondly, the proposed method takes the categorical data label as a generating condition, solves the unbalanced categories of the generated data samples, and improves the accuracy of the radar HRRP target recognition. Finally, by combining the attention mechanism and GAN network of the transformer, the generative capacity of the CVAE generator is enhanced effectively. In this paper, the continuous learning method is verified by a validation framework with three task settings. The experimental results show that the proposed method has a better continuous learning ability and better engineering practicality in various tasks compared with the previous regularization methods which can guarantee the privacy of the training dataset.

We propose a novel method to generate sparse integer-constrained cone singularities with low distortion constraints for conformal parameterizations. Inspired by [Fang et al. 2021; Soliman et al. 2018], the cone computation is formulated as a constrained optimization problem, where the objective is the number of cones measured by the ℓ 0 -norm of Gaussian curvature of vertices, and the constraint is to restrict the cone angles to be multiples of π /2 and control the distortion while ensuring that the Yamabe equation holds. Besides, the holonomy angles for the non-contractible homology loops are additionally required to be multiples of π /2 for achieving rotationally seamless conformal parameterizations. The Douglas-Rachford (DR) splitting algorithm is used to solve this challenging optimization problem, and our success relies on two key components. First, replacing each integer constraint with the intersection of a box set and a sphere enables us to manage the subproblems in DR splitting update steps in the continuous domain. Second, a novel solver is developed to optimize the ℓ 0 -norm without any approximation. We demonstrate the effectiveness and feasibility of our algorithm on a data set containing 3885 models. Compared to state-of-the-art methods, our method achieves a better tradeoff between the number of cones and the parameterization distortion.

We propose a novel method to compute a piecewise mesh with a few developable patches and a small approximation error for an input triangular mesh. Our key observation is that a deformed mesh after enforcing discrete developability is easily partitioned into nearly developable patches. To obtain the nearly developable mesh, we present a new edge-oriented notion of discrete developability to define a developability-encouraged deformation energy, which is further optimized by the block nonlinear Gauss-Seidel method. The key to successfully applying this optimizer is three types of auxiliary variables. Then, a coarse-to-fine segmentation technique is developed to partition the deformed mesh into a small set of nearly discrete developable patches. Finally, we refine the segmented mesh to reduce the discrete Gaussian curvature while keeping the patches smooth and the approximation error small. In practice, our algorithm achieves a favorable tradeoff between the number of developable patches and the approximation error. We demonstrate the feasibility and practicability of our method over various examples, including seventeen physical manufacturing models with paper.

The emerging 4D printing techniques open new horizons for fabricating self-actuated deformable objects by combing strength of 3D printing and stimuli-responsive shape memory materials. This article focuses on designing self-actuated deformable solids for 4D printing such that a solid can be programmed into a temporary shape and later recovers to its original shape after heating. To avoid a high material cost, we choose a dual-material strategy that mixes an expensive thermo-responsive shape memory polymer (SMP) material with a common elastic material, which however leads to undesired deformation at the shape programming stage. We model this shape programming process as two elastic models with different parameters linked by a median shape based on customizing a constitutive model of thermo-responsive SMPs. Taking this material modeling as a foundation, we formulate our design problem as a nonconvex optimization to find the distribution of SMP materials over the whole object as well as the median shape, and develop an efficient and parallelizable method to solve it. We show that our proposed approach is able to design self-actuated deformable objects that cannot be achieved by state of the art approaches, and demonstrate their usefulness with three example applications.

We propose a novel method to generate sparse cone singularities with bounded distortion constraints for conformal parameterizations. It is formulated as minimizing the ℓ 0 -norm of Gaussian curvature of vertices with hard constraints of bounding the distortion that is measured by the ℓ 2 -norm of the log conformal factor. We use the reweighted ℓ 1 -norm to approximate the ℓ 0 -norm and solve each convex weighted ℓ 1 minimization subproblem by the Douglas-Rachford (DR) splitting scheme. To quickly generate sparse cones, we modify DR splitting by weighting the ℓ 2 -norm of the proximal mapping to force the small Gaussian curvature to quickly approach zero. Accordingly, compared with the conventional DR splitting, the modified method performs one to two orders of magnitude faster. Besides, we perform variable substitution of log conformal factors to simplify the computation process for acceleration. Our algorithm is able to bound distortion to compute sparse cone singularities, so that the resulting conformal parameterizations achieve a favorable tradeoff between the area distortion and the number of cones. We demonstrate its effectiveness and feasibility on a large number of models.

Abstract 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.

The alternating direction method of multipliers (ADMM) is a popular approach for solving optimization problems that are potentially non-smooth and with hard constraints. It has been applied to various computer graphics applications, including physical simulation, geometry processing, and image processing. However, ADMM can take a long time to converge to a solution of high accuracy. Moreover, many computer graphics tasks involve non-convex optimization, and there is often no convergence guarantee for ADMM on such problems since it was originally designed for convex optimization. In this paper, we propose a method to speed up ADMM using Anderson acceleration, an established technique for accelerating fixed-point iterations. We show that in the general case, ADMM is a fixed-point iteration of the second primal variable and the dual variable, and Anderson acceleration can be directly applied. Additionally, when the problem has a separable target function and satisfies certain conditions, ADMM becomes a fixed-point iteration of only one variable, which further reduces the computational overhead of Anderson acceleration. Moreover, we analyze a particular non-convex problem structure that is common in computer graphics, and prove the convergence of ADMM on such problems under mild assumptions. We apply our acceleration technique on a variety of optimization problems in computer graphics, with notable improvement on their convergence speed.