Neural-IMLS: Self-supervised Implicit Moving Least-Squares Network for Surface Reconstruction.

Surface reconstruction is a challenging task when input point clouds, especially real scans, are noisy and lack normals. Observing that the Multilayer Perceptron (MLP) and the implicit moving least-square function (IMLS) provide a dual representation of the underlying surface, we introduce Neural-IMLS, a novel approach that directly learns a noise-resistant signed distance function (SDF) from unoriented raw point clouds in a self-supervised manner. In particular, IMLS regularizes MLP by providing estimated SDFs near the surface and helps enhance its ability to represent geometric details and sharp features, while MLP regularizes IMLS by providing estimated normals. We prove that at convergence, our neural network produces a faithful SDF whose zero-level set approximates the underlying surface due to the mutual learning mechanism between the MLP and the IMLS. Extensive experiments on various benchmarks, including synthetic and real scans, show that Neural-IMLS can reconstruct faithful shapes even with noise and missing parts. The source code can be found at https://github.com/bearprin/Neural-IMLS.

Laplacian2Mesh: Laplacian-Based Mesh Understanding.

Geometric deep learning has sparked a rising interest in computer graphics to perform shape understanding tasks, such as shape classification and semantic segmentation. When the input is a polygonal surface, one has to suffer from the irregular mesh structure. Motivated by the geometric spectral theory, we introduce Laplacian2Mesh, a novel and flexible convolutional neural network (CNN) framework for coping with irregular triangle meshes (vertices may have any valence). By mapping the input mesh surface to the multi-dimensional Laplacian-Beltrami space, Laplacian2Mesh enables one to perform shape analysis tasks directly using the mature CNNs, without the need to deal with the irregular connectivity of the mesh structure. We further define a mesh pooling operation such that the receptive field of the network can be expanded while retaining the original vertex set as well as the connections between them. Besides, we introduce a channel-wise self-attention block to learn the individual importance of feature ingredients. Laplacian2Mesh not only decouples the geometry from the irregular connectivity of the mesh structure but also better captures the global features that are central to shape classification and segmentation. Extensive tests on various datasets demonstrate the effectiveness and efficiency of Laplacian2Mesh, particularly in terms of the capability of being vulnerable to noise to fulfill various learning tasks.

DO-Conv: Depthwise Over-Parameterized Convolutional Layer.

Convolutional layers are the core building blocks of Convolutional Neural Networks (CNNs). In this paper, we propose to augment a convolutional layer with an additional depthwise convolution, where each input channel is convolved with a different 2D kernel. The composition of the two convolutions constitutes an over-parameterization, since it adds learnable parameters, while the resulting linear operation can be expressed by a single convolution layer. We refer to this depthwise over-parameterized convolutional layer as DO-Conv, which is a novel way of over-parameterization. We show with extensive experiments that the mere replacement of conventional convolutional layers with DO-Conv layers boosts the performance of CNNs on many classical vision tasks, such as image classification, detection, and segmentation. Moreover, in the inference phase, the depthwise convolution is folded into the conventional convolution, reducing the computation to be exactly equivalent to that of a convolutional layer without over-parameterization. As DO-Conv introduces performance gains without incurring any computational complexity increase for inference, we advocate it as an alternative to the conventional convolutional layer. We open sourced an implementation of DO-Conv in Tensorflow, PyTorch and GluonCV at https://github.com/yangyanli/DO-Conv.

Data-Driven Colormap Adjustment for Exploring Spatial Variations in Scalar Fields.

Colormapping is an effective and popular visualization technique for analyzing patterns in scalar fields. Scientists usually adjust a default colormap to show hidden patterns by shifting the colors in a trial-and-error process. To improve efficiency, efforts have been made to automate the colormap adjustment process based on data properties (e.g., statistical data value or histogram distribution). However, as the data properties have no direct correlation to the spatial variations, previous methods may be insufficient to reveal the dynamic range of spatial variations hidden in the data. To address the above issues, we conduct a pilot analysis with domain experts and summarize three requirements for the colormap adjustment process. Based on the requirements, we formulate colormap adjustment as an objective function, composed of a boundary term and a fidelity term, which is flexible enough to support interactive functionalities. We compare our approach with alternative methods under a quantitative measure and a qualitative user study (25 participants), based on a set of data with broad distribution diversity. We further evaluate our approach via three case studies with six domain experts. Our method is not necessarily more optimal than alternative methods of revealing patterns, but rather is an additional color adjustment option for exploring data with a dynamic range of spatial variations.

Geodesic Tracks: Computing Discrete Geodesics With Track-Based Steiner Point Propagation.

This article presents a simple yet effective method for computing geodesic distances on triangle meshes. Unlike the popular window propagation methods that partition mesh edges into intervals of varying lengths, our method places evenly-spaced, source-independent Steiner points on edges. Given a source vertex, our method constructs a Steiner-point graph that partitions the surface into mutually exclusive tracks, called geodesic tracks. Inside each triangle, the tracks form sub-regions in which the change of distance field is approximately linear. Our method does not require any pre-computation, and can effectively balance speed and accuracy. Experimental results show that with 5 Steiner points on each edge, the mean relative error is less than 0.3 % for common 3D models used in the graphics community. We propose a set of effective filtering rules to eliminate a large amount of useless broadcast events. For a 1000K-face model, our method runs 10 times faster than the conventional Steiner point method that examines a complete graph of Steiner points in each triangle. We also observe that using more Steiner points increases the accuracy at only a small extra computational cost. Our method works well for meshes with poor triangulation and non-manifold configuration, which often poses challenges to the existing PDE methods. We show that geodesic tracks, as a new data structure that encodes rich information of discrete geodesics, support accurate geodesic path and isoline tracing, and efficient distance query. Our method can be easily extended to meshes with non-constant density functions and/or anisotropic metrics.

Top-Down Shape Abstraction Based on Greedy Pole Selection.

Motivated by the fact that the medial axis transform is able to encode the shape completely, we propose to use as few medial balls as possible to approximate the original enclosed volume by the boundary surface. We progressively select new medial balls, in a top-down style, to enlarge the region spanned by the existing medial balls. The key spirit of the selection strategy is to encourage large medial balls while imposing given geometric constraints. We further propose a speedup technique based on a provable observation that the intersection of medial balls implies the adjacency of power cells (in the sense of the power crust).We further elaborate the selection rules in combination with two closely related applications. One application is to develop an easy-to-use ball-stick modeling system that helps non-professional users to quickly build a shape with only balls and wires, but any penetration between two medial balls must be suppressed. The other application is to generate porous structures with convex, compact (with a high isoperimetric quotient) and shape-aware pores where two adjacent spherical pores may have penetration as long as the mechanical rigidity can be well preserved.

Super Diffusion for Salient Object Detection.

One major branch of saliency object detection methods are diffusion-based which construct a graph model on a given image and diffuse seed saliency values to the whole graph by a diffusion matrix. While their performance is sensitive to specific feature spaces and scales used for the diffusion matrix definition, little work has been published to systematically promote the robustness and accuracy of salient object detection under the generic mechanism of diffusion. In this work, we firstly present a novel view of the working mechanism of the diffusion process based on mathematical analysis, which reveals that the diffusion process is actually computing the similarity of nodes with respect to the seeds based on diffusion maps. Following this analysis, we propose super diffusion, a novel inclusive learning-based framework for salient object detection, which makes the optimum and robust performance by integrating a large pool of feature spaces, scales and even features originally computed for non-diffusion-based salient object detection. A closed-form solution of the optimal parameters for the integration is determined through supervised learning. At the local level, we propose to promote each individual diffusion before the integration. Our mathematical analysis reveals the close relationship between saliency diffusion and spectral clustering. Based on this, we propose to re-synthesize each individual diffusion matrix from the most discriminative eigenvectors and the constant eigenvector (for saliency normalization). The proposed framework is implemented and experimented on prevalently used benchmark datasets, consistently leading to state-of-the-art performance.

Is There a Robust Technique for Selecting Aspect Ratios in Line Charts?

The aspect ratio of a line chart heavily influences the perception of the underlying data. Different methods explore different criteria in choosing aspect ratios, but so far, it was still unclear how to select aspect ratios appropriately for any given data. This paper provides a guideline for the user to choose aspect ratios for any input 1D curves by conducting an in-depth analysis of aspect ratio selection methods both theoretically and experimentally. By formulating several existing methods as line integrals, we explain their parameterization invariance. Moreover, we derive a new and improved aspect ratio selection method, namely the -LOR (local orientation resolution), with a certain degree of parameterization invariance. Furthermore, we connect different methods, including AL (arc length based method), the banking to 45 principle, RV (resultant vector) and AS (average absolute slope), as well as -LOR and AO (average absolute orientation). We verify these connections by a comparative evaluation involving various data sets, and show that the selections by RV and -LOR are complementary to each other for most data. Accordingly, we propose the dual-scale banking technique that combines the strengths of RV and -LOR, and demonstrate its practicability using multiple real-world data sets.

Fast and robust shape diameter function.

The shape diameter function (SDF) is a scalar function defined on a closed manifold surface, measuring the neighborhood diameter of the object at each point. Due to its pose oblivious property, SDF is widely used in shape analysis, segmentation and retrieval. However, computing SDF is computationally expensive since one has to place an inverted cone at each point and then average the penetration distances for a number of rays inside the cone. Furthermore, the shape diameters are highly sensitive to local geometric features as well as the normal vectors, hence diminishing their applications to real-world meshes which often contain rich geometric details and/or various types of defects, such as noise and gaps. In order to increase the robustness of SDF and promote it to a wide range of 3D models, we define SDF by offsetting the input object a little bit. This seemingly minor change brings three significant benefits: First, it allows us to compute SDF in a robust manner since the offset surface is able to give reliable normal vectors. Second, it runs many times faster since at each point we only need to compute the penetration distance along a single direction, rather than tens of directions. Third, our method does not require watertight surfaces as the input-it supports both point clouds and meshes with noise and gaps. Extensive experimental results show that the offset-surface based SDF is robust to noise and insensitive to geometric details, and it also runs about 10 times faster than the existing method. We also exhibit its usefulness using two typical applications including shape retrieval and shape segmentation, and observe a significant improvement over the existing SDF.

Human Pose Estimation from Monocular Images: A Comprehensive Survey.

Human pose estimation refers to the estimation of the location of body parts and how they are connected in an image. Human pose estimation from monocular images has wide applications (e.g., image indexing). Several surveys on human pose estimation can be found in the literature, but they focus on a certain category; for example, model-based approaches or human motion analysis, etc. As far as we know, an overall review of this problem domain has yet to be provided. Furthermore, recent advancements based on deep learning have brought novel algorithms for this problem. In this paper, a comprehensive survey of human pose estimation from monocular images is carried out including milestone works and recent advancements. Based on one standard pipeline for the solution of computer vision problems, this survey splits the problem into several modules: feature extraction and description, human body models, and modeling methods. Problem modeling methods are approached based on two means of categorization in this survey. One way to categorize includes top-down and bottom-up methods, and another way includes generative and discriminative methods. Considering the fact that one direct application of human pose estimation is to provide initialization for automatic video surveillance, there are additional sections for motion-related methods in all modules: motion features, motion models, and motion-based methods. Finally, the paper also collects 26 publicly available data sets for validation and provides error measurement methods that are frequently used.

Segmentation of renal parenchymal area from ultrasound images using level set evolution.

This paper presents a framework for segmentation of renal parenchymal area from ultrasound images based on a 2-step level set method. We used distance regularized level set evolution method to partition the kidney boundary, followed by region-scalable fitting energy minimization method to segment the kidney collecting system, and determined renal parenchymal area by subtracting the area of the collecting system from the gross kidney area. The proposed method demonstrated excellent validity and low inter-observer variability.

Silhouette smoothing for real-time rendering of mesh surfaces.

Coarse piecewise linear approximation of surfaces causes undesirable polygonal appearance of silhouettes. We present an efficient method for smoothing the silhouettes of coarse triangle meshes using efficient 3D curve reconstruction and simple local re-meshing. It does not assume the availability of a fine mesh and generates only moderate amount of additional data at run time. Furthermore, polygonal feature edges are also smoothed in a unified framework. Our method is based on a novel interpolation scheme over silhouette triangles and this ensures that smooth silhouettes are faithfully reconstructed and always change continuously with respect to continuous movement of the view point or objects. We speed up computation with GPU assistance to achieve real-time rendering of coarse meshes with the smoothed silhouettes. Experiments show that this method outperforms previous methods for silhouette smoothing.