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.

A Variational Framework for Curve Shortening in Various Geometric Domains.

Geodesics measure the shortest distance (either locally or globally) between two points on a curved surface and serve as a fundamental tool in digital geometry processing. Suppose that we have a parameterized path γ(t)=x(u(t),v(t)) on a surface x=x(u,v) with γ(0)=p and γ(1)=q. We formulate the two-point geodesic problem into a minimization problem [Formula: see text], where H(s) satisfies and H''(s) ≥ 0 for . In our implementation, we choose H(s)=es2-1 and show that it has several unique advantages over other choices such as H(s)=s2 and H(s)=s. It is also a minimizer of the traditional geodesic length variational and able to guarantee the uniqueness and regularity in terms of curve parameterization. In the discrete setting, we construct the initial path by a sequence of moveable points {xi}i=1n and minimize ∑i=1n H(||xi - xi+1||). The resulting points are evenly spaced along the path. It's obvious that our algorithm can deal with parametric surfaces. Considering that meshes, point clouds and implicit surfaces can be transformed into a signed distance function (SDF), we also discuss its implementation on a general SDF. Finally, we show that our method can be extended to solve a general least-cost path problem. We validate the proposed algorithm in terms of accuracy, performance and scalability, and demonstrate the advantages by extensive comparisons.

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.

Application of Nanoparticles in the Treatment of Lung Cancer With Emphasis on Receptors.

Lung cancer is one of the malignant tumors that has seen the most rapid growth in terms of morbidity and mortality in recent years, posing the biggest threat to people's health and lives. In recent years, the nano-drug loading system has made significant progress in the detection, diagnosis, and treatment of lung cancer. Nanomaterials are used to specifically target tumor tissue to minimize therapeutic adverse effects and increase bioavailability. It is achieved primarily through two mechanisms: passive targeting, which entails the use of enhanced penetration and retention (EPR) effect, and active targeting, which entails the loading recognition ligands for tumor marker molecules onto nanomaterials. However, it has been demonstrated that the EPR effect is effective in rodents but not in humans. Taking this into consideration, researchers paid significant attention to the active targeting nano-drug loading system. Additionally, it has been demonstrated to have a higher affinity and specificity for tumor cells. In this review, it describes the development of research into active targeted nano-drug delivery systems for lung cancer treatment from the receptors' or targets' perspective. We anticipate that this study will help biomedical researchers use nanoparticles (NPs) to treat lung cancer by providing more and novel drug delivery strategies or solid ligands.

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.

Negative Pressure Wound Therapy in Necrotizing Fasciitis of the Head and Neck.

PURPOSE: Necrotizing fasciitis is a severe soft tissue infection that is uncommon in the head and neck region. Despite the advancement of care over the past few decades, the mortality rate remains high. Negative pressure wound therapy (NPWT), an advanced wound-healing technique, has become increasingly popular for a wide variety of complicated wounds. Since December 2015, we have used this technique in the management of necrotizing fasciitis of the head and neck. We report a consecutive case series treated with NPWT as the initial surgical procedure. MATERIALS AND METHODS: Seven patients who received a surgical diagnosis of necrotizing fasciitis of the head and neck underwent surgery under general anesthesia. After complete debridement, an NPWT device was applied for positive drainage of the involved areas. The drainage tube was connected to a central negative pressure system. The device was not replaced or removed until the infection was controlled. Then, a conventional drainage approach was used. RESULTS: Of the 7 patients, 6 underwent the surgical procedure and NPWT once; the remaining patient underwent these procedures twice. The infectious cavities showed a clean wound covered with healthy granulation formation during the removal of the NPWT device. The following course was uneventful. The mean time for wound healing was 17.3 ± 6.1 days. CONCLUSIONS: NPWT provides various advantages compared with conventional debridement and drainage, resulting in excellent clinical outcomes. This method could be recommended as an alternative approach in the management of necrotizing fasciitis in the head and neck region.

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.