Related papers: Variational Shape Approximation of Point Set Surfa…
Particle-based shape modeling (PSM) is a family of approaches that automatically quantifies shape variability across anatomical cohorts by positioning particles (pseudo landmarks) on shape surfaces in a consistent configuration. Recent…
We introduce a method called multi-scale local shape analysis, or MLSA, for extracting features that describe the local structure of points within a dataset. The method uses both geometric and topological features at multiple levels of…
Given two arbitrary closed sets in Euclidean space, a simple transversality condition guarantees that the method of alternating projections converges locally, at linear rate, to a point in the intersection. Exact projection onto nonconvex…
Vectorized high-definition map online construction has garnered considerable attention in the field of autonomous driving research. Most existing approaches model changeable map elements using a fixed number of points, or predict local maps…
Polygonal meshes have become the standard for discretely approximating 3D shapes, thanks to their efficiency and high flexibility in capturing non-uniform shapes. This non-uniformity, however, leads to irregularity in the mesh structure,…
Accurate segmentation of aortic vascular structures is critical for diagnosing and treating cardiovascular diseases.Traditional Transformer-based models have shown promise in this domain by capturing long-range dependencies between vascular…
Real-scanned point clouds are often incomplete due to viewpoint, occlusion, and noise. Existing point cloud completion methods tend to generate global shape skeletons and hence lack fine local details. Furthermore, they mostly learn a…
Nonlinear parabolic equations are frequently encountered in applications and efficient approximating techniques for their solution are of great importance. In order to provide an effective scheme for the temporal approximation of such…
This paper proposes a variational framework for multi-objective level set topology optimization. The approach interprets the level set function as a generalized coordinate of a fictitious material and derives its equation of motion from…
This paper explores the point set representation for tubular structure extraction tasks. Compared with the traditional mask representation, the point set representation enjoys its flexibility and representation ability, which would not be…
A systematic model development for oil flow in quasi-3D (1D + 2D) is presented. Our approach provides a unified modeling scheme. Besides, additional terms are obtained, which allows for tubing area variation along the flow direction. The…
This paper proposes a level set-based method for optimizing shell structures with large design changes in shape and topology. Conventional shell optimization methods, whether parametric or nonparametric, often only allow limited design…
We propose a weakly-supervised multi-view learning approach to learn category-specific surface mapping without dense annotations. We learn the underlying surface geometry of common categories, such as human faces, cars, and airplanes, given…
In this contribution, we introduce a multilevel approximation method with T-splines for fitting scattered point clouds iteratively, with an application to land remote sensing. This new procedure provides a local surface approximation by an…
In this work, we present a novel approach for solving stochastic shape optimization problems. Our method is the extension of the classical stochastic gradient method to infinite-dimensional shape manifolds. We prove convergence of the…
Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions…
Variable projection solves structured optimization problems by completely minimizing over a subset of the variables while iterating over the remaining variables. Over the last 30 years, the technique has been widely used, with empirical and…
Non-rigid 3D mesh matching is a critical step in computer vision and computer graphics pipelines. We tackle matching meshes that contain topological artefacts which can break the assumption made by current approaches. While Functional Maps…
Simultaneous sparse approximation (SSA) seeks to represent a set of dependent signals using sparse vectors with identical supports. The SSA model has been used in various signal and image processing applications involving multiple…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…