Many geometry processing applications are sensitive to noise and sharp features. Although there are a number of works on detecting noise and sharp features in the literature, they are heuristic. On one hand, traditional denoising methods use filtering operators to remove noise, however, they may blur sharp features and shrink the object. On the other hand, noise makes detection of features, which relies on computation of differential properties, unreliable and unstable. Therefore, detecting noise and features on discrete surfaces still remains challenging. In this article, we present an approach for decoupling noise and features on 3D shapes. Our approach consists of two phases. In the first phase, a base mesh is estimated from the input noisy data by a global Laplacian regularization denoising scheme. The estimated base mesh is guaranteed to asymptotically converge to the true underlying surface with probability one as the sample size goes to infinity. In the second phase, an ℓ1-analysis compressed sensing optimization is proposed to recover sharp features from the residual between base mesh and input mesh. This is based on our discovery that sharp features can be sparsely represented in some coherent dictionary which is constructed by the pseudo-inverse matrix of the Laplacian of the shape. The features are recovered from the residual in a progressive way. Theoretical analysis and experimental results show that our approach can reliably and robustly remove noise and extract sharp features on 3D shapes.

3D printers have become popular in recent years and enable fabrication of custom objects for home users. However, the cost of the material used in printing remains high. In this paper, we present an automatic solution to design a skin-frame structure for the purpose of reducing the material cost in printing a given 3D object. The frame structure is designed by an optimization scheme which significantly reduces material volume and is guaranteed to be physically stable, geometrically approximate, and printable. Furthermore, the number of struts is minimized by solving an l0 sparsity optimization. We formulate it as a multi-objective programming problem and an iterative extension of the preemptive algorithm is developed to find a compromise solution. We demonstrate the applicability and practicability of our solution by printing various objects using both powder-type and extrusion-type 3D printers. Our method is shown to be more cost-effective than previous works.

We present a complete system to semantically decompose and reconstruct 3D models from point clouds. Different than previous urban modeling approaches, our system is designed for residential scenes, which consist of mainly low-rise buildings that do not exhibit the regularity and repetitiveness as high-rise buildings in downtown areas. Our system first automatically labels the input into distinctive categories using supervised learning techniques. Based on the semantic labels, objects in different categories are reconstructed with domain-specific knowledge. In particular, we present a novel building modeling scheme that aims to decompose and fit the building point cloud into basic blocks that are block-wise symmetric and convex. This building representation and its reconstruction algorithm are flexible, efficient, and robust to missing data. We demonstrate the effectiveness of our system on various datasets and compare our building modeling scheme with other state-of-the-art reconstruction algorithms to show its advantage in terms of both quality and speed.

We present an algorithm for multi-scale partial intrinsic symmetry detection over 2D and 3D shapes, where the scale of a symmetric region is defined by intrinsic distances between symmetric points over the region. To identify prominent symmetric regions which overlap and vary in form and scale, we decouple scale extraction and symmetry extraction by performing two levels of clustering. First, significant symmetry scales are identified by clustering sample point pairs from an input shape. Since different point pairs can share a common point, shape regions covered by points in different scale clusters can overlap. We introduce the symmetry scale matrix (SSM), where each entry estimates the likelihood two point pairs belong to symmetries at the same scale. The pair-to-pair symmetry affinity is computed based on a pair signature which encodes scales. We perform spectral clustering using the SSM to obtain the scale clusters. Then for all points belonging to the same scale cluster, we perform the second-level spectral clustering, based on a novel point-to-point symmetry affinity measure, to extract partial symmetries at that scale. We demonstrate our algorithm on complex shapes possessing rich symmetries at multiple scales.

We present an easy-to-use image retouching technique for realistic reshaping of human bodies in a single image. A model-based approach is taken by integrating a 3D whole-body morphable model into the reshaping process to achieve globally consistent editing effects. A novel body-aware image warping approach is introduced to reliably transfer the reshaping effects from the model to the image, even under moderate fitting errors. Thanks to the parametric nature of the model, our technique parameterizes the degree of reshaping by a small set of semantic attributes, such as weight and height. It allows easy creation of desired reshaping effects by changing the full-body attributes, while producing visually pleasing results even for loosely-dressed humans in casual photographs with a variety of poses and shapes.

Aesthetic images evoke an emotional response that transcends mere visual appreciation. In this work we develop a novel computational means for evaluating the composition aesthetics of a given image based on measuring several well‐grounded composition guidelines. A compound operator of crop‐and‐retarget is employed to change the relative position of salient regions in the image and thus to modify the composition aesthetics of the image. We propose an optimization method for automatically producing a maximally‐aesthetic version of the input image. We validate the performance of the method and show its effectiveness in a variety of experiments.

We present a novel approach to localization of sensors in a network given a subset of noisy inter-sensor distances. The algorithm is based on “stitching” together local structures by solving an optimization problem requiring the structures to fit together in an “As-Rigid-As-Possible” manner, hence the name ARAP. The local structures consist of reference “patches” and reference triangles, both obtained from inter-sensor distances. We elaborate on the relationship between the ARAP algorithm and other state-of-the-art algorithms, and provide experimental results demonstrating that ARAP is significantly less sensitive to sparse connectivity and measurement noise. We also show how ARAP may be distributed.

The Delaunay triangulation of a planar point set is a fundamental construct in computational geometry. A simple algorithm to generate it is based on flips of diagonal edges in convex quads. We characterize the effect of a single edge flip in a triangulation on the geometric Laplacian of the triangulation, which leads to a simpler and shorter proof of a theorem of Rippa that the Dirichlet energy of any piecewise-linear scalar function on a triangulation obtains its minimum on the Delaunay triangulation. Using Rippa's theorem, we provide a spectral characterization of the Delaunay triangulation, namely that the spectrum of the geometric Laplacian is minimized on this triangulation. This spectral theorem then leads to a simpler proof of a theorem of Musin that the harmonic index also obtains its minimum on the Delaunay triangulation.

This paper presents a new approach, called cubic clipping, for computing all the roots of a given polynomial within an interval. In every iterative computation step, two cubic polynomials are generated to enclose the graph of the polynomial within the interval of interest. A sequence of intervals is then obtained by intersecting the sequence of strips with the abscissa axis. The sequence of these intervals converges to the corresponding root with the convergence rate 4 for the single roots, 2 for the double roots and super-linear for the triple roots. Numerical examples show that cubic clipping has many expected advantages over Bézier clipping and quadratic clipping. We also extend our approach by enclosing the graph of the polynomial using two lower degree polynomials by degree reduction. The sequence of intervals converges to the corresponding root of multiplicity s with convergence rate .

The essence of a 3D shape can often be well captured by its salient feature curves. In this paper, we explore the use of salient curves in synthesizing intuitive, shape-revealing textures on surfaces. Our texture synthesis is guided by two principles: matching the direction of the texture patterns to those of the salient curves, and aligning the prominent feature lines in the texture to the salient curves exactly. We have observed that textures synthesized by these principles not only fit naturally to the surface geometry, but also visually reveal, even reinforce, the shape's essential characteristics. We call these feature-aligned shape texturing. Our technique is fully automatic, and introduces two novel technical components in vector-field-guided texture synthesis: an algorithm that orients the salient curves on a surface for constrained vector field generation, and a feature-to-feature texture optimization.