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Motivated by the fact that the medial axis transform is able to encode nearly the complete shape, we propose to use as few medial balls as possible to approximate the original enclosed volume by the boundary surface. We progressively select…
The spinor representation is developed and used to investigate minimal surfaces in ${\bfR}^3$ with embedded planar ends. The moduli spaces of planar-ended minimal spheres and real projective planes are determined, and new families of…
Sphere packings are essential to the development of physical models for powders, composite materials, and the atomic structure of the liquid state. There is a strong scientific need to be able to assess the fit of packing models to data,…
Impressive progress in 3D shape extraction led to representations that can capture object geometries with high fidelity. In parallel, primitive-based methods seek to represent objects as semantically consistent part arrangements. However,…
Shape abstraction is an important task for simplifying complex geometric structures while retaining essential features. Sweep surfaces, commonly found in human-made objects, aid in this process by effectively capturing and representing…
We propose a novel method for determining the radius of a spherical surface based on the distances measured between points on this surface. We consider the most general case of determining the radius when the distances are measured with…
Mathematically representing the shape of an object is a key ingredient for solving inverse rendering problems. Explicit representations like meshes are efficient to render in a differentiable fashion but have difficulties handling topology…
Sculptors often deviate from geometric accuracy in order to enhance the appearance of their sculpture. These subtle stylizations may emphasize anatomy, draw the viewer's focus to characteristic features of the subject, or symbolize textures…
This paper investigates the shape reconstructions of sub-wavelength objects from near-field measurements in transverse electromagnetic scattering. This geometric inverse problem is notoriously ill-posed and challenging. We develop a novel…
3D Shape representation has substantial effects on 3D shape reconstruction. Primitive-based representations approximate a 3D shape mainly by a set of simple implicit primitives, but the low geometrical complexity of the primitives limits…
We consider the problem of establishing dense correspondences within a set of related shapes of strongly varying geometry. For such input, traditional shape matching approaches often produce unsatisfactory results. We propose an ensemble…
We examine implicit representations of parametric or point cloud models, based on interpolation matrices, which are not sensitive to base points. We show how interpolation matrices can be used for ray shooting of a parametric ray with a…
Gaussian Splatting has become the method of choice for 3D reconstruction and real-time rendering of captured real scenes. However, fine appearance details need to be represented as a large number of small Gaussian primitives, which can be…
We propose an extrapolation technique that allows accuracy improvement of the discrete dipole approximation computations. The performance of this technique was studied empirically based on extensive simulations for 5 test cases using many…
Segmentation, a useful/powerful technique in pattern recognition, is the process of identifying object outlines within images. There are a number of efficient algorithms for segmentation in Euclidean space that depend on the variational…
This paper presents a new axis-based shape representation scheme along with a matching framework to address the problem of generic shape recognition. The main idea is to define the relative spatial arrangement of local symmetry axes and…
We propose the Medial Skeletal Diagram, a novel skeletal representation that tackles the prevailing issues around skeleton sparsity and reconstruction accuracy in existing skeletal representations. Our approach augments the continuous…
Convexity prior is one of the main cue for human vision and shape completion with important applications in image processing, computer vision. This paper focuses on characterization methods for convex objects and applications in image…
We provide a topological procedure to obtain geometric realizations of both classical and `exotic' $G$-manifolds, such as spheres, bundles over spheres and Kervaire manifolds. As an application, we apply the process known as Cheeger…
Particle-based shape modeling (PSM) is a popular approach to automatically quantify shape variability in populations of anatomies. The PSM family of methods employs optimization to automatically populate a dense set of corresponding…