The Euler Elastica (EE) model with surface curvature can generate artifact-free results compared with the traditional total variation regularization model in image processing. However, strong nonlinearity and singularity due to the curvature term in the EE model pose a great challenge for one to design fast and stable algorithms for the EE model. In this paper, we propose a new, fast, hybrid alternating minimization (HALM) algorithm for the EE model based on a bilinear decomposition of the gradient of the underlying image and prove the global convergence of the minimizing sequence generated by the algorithm under mild conditions. The HALM algorithm comprises three sub-minimization problems and each is either solved in the closed form or approximated by fast solvers making the new algorithm highly accurate and efficient. We also discuss the extension of the HALM strategy to deal with general curvature-based variational models, especially with a Lipschitz smooth functional of the curvature. A host of numerical experiments are conducted to show that the new algorithm produces good results with much-improved efficiency compared to other state-of-the-art algorithms for the EE model. As one of the benchmarks, we show that the average running time of the HALM algorithm is at most one-quarter of that of the fast operator-splitting-based Deng-Glowinski-Tai algorithm.
Style transfer of 3D faces has gained more and more attention. However, previous methods mainly use images of artistic faces for style transfer while ignoring arbitrary style images such as abstract paintings. To solve this problem, we propose a novel method, namely Face-guided Dual Style Transfer (FDST). To begin with, FDST employs a 3D decoupling module to separate facial geometry and texture. Then we propose a style fusion strategy for facial geometry. Subsequently, we design an optimization-based DDSG mechanism for textures that can guide the style transfer by two style images. Besides the normal style image input, DDSG can utilize the original face input as another style input as the face prior. By this means, high-quality face arbitrary style transfer results can be obtained. Furthermore, FDST can be applied in many downstream tasks, including region-controllable style transfer, high-fidelity face texture reconstruction, large-pose face reconstruction, and artistic face reconstruction. Comprehensive quantitative and qualitative results show that our method can achieve comparable performance. All source codes and pre-trained weights will be released to the public.