Centroidal Voronoi tessellation (CVT) is a particular type of Voronoi tessellation that has many applications in computational sciences and engineering, including computer graphics. The prevailing method for computing CVT is Lloyd's method, which has linear convergence and is inefficient in practice. We develop new efficient methods for CVT computation and demonstrate the fast convergence of these methods. Specifically, we show that the CVT energy function has 2nd order smoothness for convex domains with smooth density, as well as in most situations encountered in optimization. Due to the 2nd order smoothness, it is possible to minimize the CVT energy functions using Newton-like optimization methods and expect fast convergence. We propose a quasi-Newton method to compute CVT and demonstrate its faster convergence than Lloyd's method with various numerical examples. It is also significantly faster and more robust than the Lloyd-Newton method, a previous attempt to accelerate CVT. We also demonstrate surface remeshing as a possible application.

Image inpainting has made remarkable progress with recent advances in deep learning. Popular networks mainly follow an encoder-decoder architecture (sometimes with skip connections) and possess sufficiently large receptive field, i.e. , larger than the image resolution. The receptive field refers to the set of input pixels that are path-connected to a neuron. For image inpainting task, however, the size of surrounding areas needed to repair different kinds of missing regions are different, and the very large receptive field is not always optimal, especially for the local structures and textures. In addition, a large receptive field tends to involve more undesired completion results, which will disturb the inpainting process. Based on these insights, we rethink the process of image inpainting from a different perspective of receptive field, and propose a novel three-stage inpainting framework with local and global refinement. Specifically, we first utilize an encoder-decoder network with skip connection to achieve coarse initial results. Then, we introduce a shallow deep model with small receptive field to conduct the local refinement, which can also weaken the influence of distant undesired completion results. Finally, we propose an attention-based encoder-decoder network with large receptive field to conduct the global refinement. Experimental results demonstrate that our method outperforms the state of the arts on three popular publicly available datasets for image inpainting. Our local and global refinement network can be directly inserted into the end of any existing networks to further improve their inpainting performance. Code is available at https://github.com/weizequan/LGNet.git .

Large-scale acquisition of exterior urban environments is by now a well-established technology, supporting many applications in search, navigation, and commerce. The same is, however, not the case for indoor environments, where access is often restricted and the spaces are cluttered. Further, such environments typically contain a high density of repeated objects (e.g., tables, chairs, monitors, etc.) in regular or non-regular arrangements with significant pose variations and articulations. In this paper, we exploit the special structure of indoor environments to accelerate their 3D acquisition and recognition with a low-end handheld scanner. Our approach runs in two phases: (i) a learning phase wherein we acquire 3D models of frequently occurring objects and capture their variability modes from only a few scans, and (ii) a recognition phase wherein from a single scan of a new area, we identify previously seen objects but in different poses and locations at an average recognition time of 200ms/model. We evaluate the robustness and limits of the proposed recognition system using a range of synthetic and real world scans under challenging settings.

Distinguishing between natural images (NIs) and computer-generated (CG) images by naked human eyes is difficult. In this paper, we propose an effective method based on a convolutional neural network (CNN) for this fundamental image forensic problem. Having observed the rather limited performance of training existing CCNs from scratch or fine-tuning pre-trained network, we design and implement a new and appropriate network with two cascaded convolutional layers at the bottom of a CNN. Our network can be easily adjusted to accommodate different sizes of input image patches while maintaining a fixed depth, a stable structure of CNN, and a good forensic performance. Considering the complexity of training CNNs and the specific requirement of image forensics, we introduce the so-called local-to-global strategy in our proposed network. Our CNN derives a forensic decision on local patches, and a global decision on a full-sized image can be easily obtained via simple majority voting. This strategy can also be used to improve the performance of existing methods that are based on hand-crafted features. Experimental results show that our method outperforms existing methods, especially in a challenging forensic scenario with NIs and CG images of heterogeneous origins. Our method also has good robustness against typical post-processing operations, such as resizing and JPEG compression. Unlike previous attempts to use CNNs for image forensics, we try to understand what our CNN has learned about the differences between NIs and CG images with the aid of adequate and advanced visualization tools.