We propose a novel variational method to compute a highly accurate global signed distance function (SDF) to a given point cloud. To this end, the jump set of the gradient of the SDF, which coincides with the medial axis of the surface, is explicitly taken into account through a higher-order variational formulation that enforces linear growth along the gradient direction away from this discontinuity set. The eikonal equation and the zero-level set of the SDF are enforced as constraints. To make this variational problem computationally tractable, a phase field approximation of Ambrosio-Tortorelli type is employed. The associated phase field function implicitly describes the medial axis. The method is implemented for surfaces represented by unoriented point clouds using neural network approximations of both the SDF and the phase field. Experiments demonstrate the method's accuracy both in the near field and globally. Quantitative and qualitative comparisons with other approaches show the advantages of the proposed method.
Quasi-Medial Distance Field (Q-MDF): A Robust Method for Approximating and Discretizing Neural Medial Axes
S-Lab, Nanyang Technological University（南洋理工大学S实验室）；School of Mathematics, Nanjing University of Aeronautics and Astronautics（南京航空航天大学数学学院）；School of Computer Science and Technology, Shandong University（山东大学计算机科学与技术学院）；Key Laboratory of System Software (CAS), Institute of Software, Chinese Academy of Sciences（中国科学院软件研究所系统软件重点实验室）；University of Chinese Academy of Sciences（中国科学院大学）；SenseTime Research（商汤科技研究院）
Transferable and Undefendable Point Cloud Attacks via Medial Axis Transform
Cyberspace Institute of Advanced Technology, Guangzhou University（高级科技 cyber 空间研究所，广州大学）；School of Computer Science and Cyber Engineering, Guangzhou University（计算机科学与网络工程学院，广州大学）；Department of Automation, University of Science and Technology of China（自动化系，中国科学技术大学）；School of Artificial Intelligence, Optics and Electronics (iOPEN), Northwestern Polytechnical University（人工智能、光学与电子学（iOPEN）学院，西北工业大学）
University of Pennsylvania（宾夕法尼亚大学）；National University of Colombia（哥伦比亚国立大学）
We present the CPMA, a new method for medial axis pruning with noise robustness and equivariance to isometric transformations. Our method leverages the discrete cosine transform to create smooth versions of a shape $Ω$. We use the smooth shapes to compute a score function $\scorefunction$ that filters out spurious branches from the medial axis. We extensively compare the CPMA with state-of-the-art pruning methods and highlight our method's noise robustness and isometric equivariance. We found that our pruning approach achieves competitive results and yields stable medial axes even in scenarios…
University of British Columbia（不列颠哥伦比亚大学）；Simon Fraser University（西蒙菲莎大学）；Google Research（谷歌研究院）；Stanford University（斯坦福大学）；University of Toronto（多伦多大学）
Implicit representations of geometry, such as occupancy fields or signed distance fields (SDF), have recently re-gained popularity in encoding 3D solid shape in a functional form. In this work, we introduce medial fields: a field function derived from the medial axis transform (MAT) that makes available information about the underlying 3D geometry that is immediately useful for a number of downstream tasks. In particular, the medial field encodes the local thickness of a 3D shape, and enables O(1) projection of a query point onto the medial axis. To construct the medial field we require nothin…
We introduce Appearance-MAT (AMAT), a generalization of the medial axis transform for natural images, that is framed as a weighted geometric set cover problem. We make the following contributions: i) we extend previous medial point detection methods for color images, by associating each medial point with a local scale; ii) inspired by the invertibility property of the binary MAT, we also associate each medial point with a local encoding that allows us to invert the AMAT, reconstructing the input image; iii) we describe a clustering scheme that takes advantage of the additional scale and appear…
McGill University（麦吉尔大学）；University of Toronto（多伦多大学）；Samsung Toronto AI Research Center（三星多伦多人工智能研究中心）；Vector Institute for Artificial Intelligence（向量人工智能研究所）
We combine ideas from shock graph theory with more recent appearance-based methods for medial axis extraction from complex natural scenes, improving upon the present best unsupervised method, in terms of efficiency and performance. We make the following specific contributions: i) we extend the shock graph representation to the domain of real images, by generalizing the shock type definitions using local, appearance-based criteria; ii) we then use the rules of a Shock Grammar to guide our search for medial points, drastically reducing run time when compared to other methods, which exhaustively …
Deep Medial Voxels: Learned Medial Axis Approximations for Anatomical Shape Modeling
Graz University of Technology, Institute of Computer Graphics and Vision（格拉茨技术大学计算机图形学与视觉研究所）；Ruhr University Bochum, Faculty of Mathematics（博德大学数学系）；Essen University Hospital, Institute for Artificial Intelligence in Medicine（埃森大学医院人工智能医学研究所）；University of Stuttgart（斯图加特大学）
The University of Hong Kong（香港大学）；RWTH Aachen University（亚琛工业大学）；Tsinghua University（清华大学）；Beijing National Research Center for Information Science and Technology（北京信息科学与技术国家研究中心）；Shandong University（山东大学）
Segmenting arbitrary 3D objects into constituent parts that are structurally meaningful is a fundamental problem encountered in a wide range of computer graphics applications. Existing methods for 3D shape segmentation suffer from complex geometry processing and heavy computation caused by using low-level features and fragmented segmentation results due to the lack of global consideration. We present an efficient method, called SEG-MAT, based on the medial axis transform (MAT) of the input shape. Specifically, with the rich geometrical and structural information encoded in the MAT, we are able…
Indian Institute of Technology Kharagpur（印度理工学院卡拉格普尔分校）
Thinning of character images is a big challenge. Removal of strokes or deformities in thinning is a difficult problem. In this paper, we have proposed a medial axis based thinning strategy used for performing skeletonization of printed and handwritten character images. In this method, we have used shape characteristics of text to get skeleton of nearly same as the true character shape. This approach helps to preserve the local features and true shape of the character images. The proposed algorithm produces one pixel width thin skeleton. As a by-product of our thinning approach, the skeleton al…
McGill University（麦吉尔大学）；University of Toronto（多伦多大学）
The computer vision community has witnessed recent advances in scene categorization from images, with the state-of-the art systems now achieving impressive recognition rates on challenging benchmarks such as the Places365 dataset. Such systems have been trained on photographs which include color, texture and shading cues. The geometry of shapes and surfaces, as conveyed by scene contours, is not explicitly considered for this task. Remarkably, humans can accurately recognize natural scenes from line drawings, which consist solely of contour-based shape cues. Here we report the first computer v…
UC San Diego（加州大学圣迭戈分校）；Johns Hopkins University（约翰斯·霍普金斯大学）
Recent work has made significant progress on using implicit functions, as a continuous representation for 3D rigid object shape reconstruction. However, much less effort has been devoted to modeling general articulated objects. Compared to rigid objects, articulated objects have higher degrees of freedom, which makes it hard to generalize to unseen shapes. To deal with the large shape variance, we introduce Articulated Signed Distance Functions (A-SDF) to represent articulated shapes with a disentangled latent space, where we have separate codes for encoding shape and articulation. We assume n…
University of Toronto（多伦多大学）；Epson（爱普生）；Lund University（隆德大学）
The role of symmetry in computer vision has waxed and waned in importance during the evolution of the field from its earliest days. At first figuring prominently in support of bottom-up indexing, it fell out of favor as shape gave way to appearance and recognition gave way to detection. With a strong prior in the form of a target object, the role of the weaker priors offered by perceptual grouping was greatly diminished. However, as the field returns to the problem of recognition from a large database, the bottom-up recovery of the parts that make up the objects in a cluttered scene is critica…
The University of Hong Kong（香港大学）；University College London（伦敦大学学院）；Texas A&M University（德克萨斯A&M大学）
We introduce Point2Skeleton, an unsupervised method to learn skeletal representations from point clouds. Existing skeletonization methods are limited to tubular shapes and the stringent requirement of watertight input, while our method aims to produce more generalized skeletal representations for complex structures and handle point clouds. Our key idea is to use the insights of the medial axis transform (MAT) to capture the intrinsic geometric and topological natures of the original input points. We first predict a set of skeletal points by learning a geometric transformation, and then analyze…
RibPull: Implicit Occupancy Fields and Medial Axis Extraction for CT Ribcage Scans
Electrical and Computer Engineering Department, University of California, Santa Cruz（加州大学圣克ruz分校电子与计算机工程系）；Inria, Univ. Rennes, CNRS, IRISA, M2S, Rennes（Inria，里尔大学，CNRS，IRISA，M2S，里尔）；LIRIS - CNRS - Université Claude Bernard Lyon 1（LIRIS-CNRS-里尔1大学）；Computer Science Engineering Department, University of California, Santa Cruz（加州大学圣克ruz分校计算机科学工程系）
MIND: Material Interface Generation from UDFs for Non-Manifold Surface Reconstruction
Key Laboratory of System Software and State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences（中国科学院软件研究所系统软件重点实验室、计算机科学国家重点实验室）；University of Chinese Academy of Sciences（中国科学院大学）；Department of Computer Science, Stony Brook University（石溪大学计算机科学系）；College of Computing and Data Science, Nanyang Technological University（南洋理工大学计算与数据科学学院）
LRSLAM: Low-rank Representation of Signed Distance Fields in Dense Visual SLAM System
Dept of Computer Science and Engineering, Korea University, Seoul, Korea（韩国大学计算机科学与工程系）；Dept of Electrical and Electronic Engineering, Yonsei University, Seoul, Korea（延世大学电气与电子工程系）；Meta Reality Labs, Pittsburgh, PA 15222, USA（Meta Reality Labs）
