Moving least squares (MLS) is a very attractive tool to design effective meshless surface representations. However, as long as approximations are performed in a least square sense, the resulting definitions remain sensitive to outliers, and smooth-out small or sharp features. In this paper, we address these major issues, and present a novel point based surface definition combining the simplicity of implicit MLS surfaces [SOS04, Kol05] with the strength of robust statistics. To reach this new definition, we review MLS surfaces in terms of local kernel regression, opening the doors to a vast and well established literature from which we utilize robust kernel regression. Our novel representation can handle sparse sampling, generates a continuous surface better preserving fine details, and can naturally handle any kind of sharp features with controllable sharpness. Finally, it combines ease of implementation with performance competing with other non-robust approaches.

Analyzing and synthesizing point distributions are of central importance for a wide range of problems in computer graphics. Existing synthesis algorithms can only generate white or blue-noise distributions with characteristics dictated by the underlying processes used, and analysis tools have not been focused on exploring relations among distributions. We propose a unified analysis and general synthesis algorithms for point distributions. We employ the pair correlation function as the basis of our methods and design synthesis algorithms that can generate distributions with given target characteristics, possibly extracted from an example point set, and introduce a unified characterization of distributions by mapping them to a space implied by pair correlations. The algorithms accept example and output point sets of different sizes and dimensions, are applicable to multi-class distributions and non-Euclidean domains, simple to implement and run in O ( n ) time. We illustrate applications of our method to real world distributions.

We propose a perceptually based method for downscaling images that provides a better apparent depiction of the input image. We formulate image downscaling as an optimization problem where the difference between the input and output images is measured using a widely adopted perceptual image quality metric. The downscaled images retain perceptually important features and details, resulting in an accurate and spatio-temporally consistent representation of the high resolution input. We derive the solution of the optimization problem in closed-form, which leads to a simple, efficient and parallelizable implementation with sums and convolutions. The algorithm has running times similar to linear filtering and is orders of magnitude faster than the state-of-the-art for image downscaling. We validate the effectiveness of the technique with extensive tests on many images, video, and by performing a user study, which indicates a clear preference for the results of the new algorithm.

In this work, we present a method to vectorize raster images of line art. Inverting the rasterization procedure is inherently ill‐conditioned, as there exist many possible vector images that could yield the same raster image. However, not all of these vector images are equally useful to the user, especially if performing further edits is desired. We therefore define the problem of computing an instance segmentation of the most likely set of paths that could have created the raster image. Once the segmentation is computed, we use existing vectorization approaches to vectorize each path, and then combine all paths into the final output vector image. To determine which set of paths is most likely, we train a pair of neural networks to provide semantic clues that help resolve ambiguities at intersection and overlap regions. These predictions are made considering the full context of the image, and are then globally combined by solving a Markov Random Field (MRF). We demonstrate the flexibility of our method by generating results on character datasets, a synthetic random line dataset, and a dataset composed of human drawn sketches. For all cases, our system accurately recovers paths that adhere to the semantics of the drawings.

With the widespread use of 3D acquisition devices, there is an increasing need of consolidating captured noisy and sparse point cloud data for accurate representation of the underlying structures. There are numerous algorithms that rely on a variety of assumptions such as local smoothness to tackle this ill‐posed problem. However, such priors lead to loss of important features and geometric detail. Instead, we propose a novel data‐driven approach for point cloud consolidation via a convolutional neural network based technique. Our method takes a sparse and noisy point cloud as input, and produces a dense point cloud accurately representing the underlying surface by resolving ambiguities in geometry. The resulting point set can then be used to reconstruct accurate manifold surfaces and estimate surface properties. To achieve this, we propose a generative neural network architecture that can input and output point clouds, unlocking a powerful set of tools from the deep learning literature. We use this architecture to apply convolutional neural networks to local patches of geometry for high quality and efficient point cloud consolidation. This results in significantly more accurate surfaces, as we illustrate with a diversity of examples and comparisons to the state‐of‐the‐art.