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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…

Heterogeneous object modelling is an emerging area where geometric shapes are considered in concert with their internal physically-based attributes. This paper describes a novel theoretical and practical framework for modelling volumetric…

Morphological analysis of the left atrial appendage is an important tool to assess risk of ischemic stroke. Most deep learning approaches for 3D segmentation is guided by binary labelmaps, which results in voxelized segmentations unsuitable…

Computing volumetric correspondences between 3D shapes is a prominent tool for medical and industrial applications. In this work, we pave the way for spectral volume mapping, extending for the first time the surface-based functional maps…

In the field of topology optimization, the homogenization approach has been revived as an important alternative to the established, density-based methods because it can represent the microstructural design at a much finer length-scale than…

Geometric Deep Learning has recently made striking progress with the advent of continuous deep implicit fields. They allow for detailed modeling of watertight surfaces of arbitrary topology while not relying on a 3D Euclidean grid,…

Implicit neural representations have emerged as a powerful tool in learning 3D geometry, offering unparalleled advantages over conventional representations like mesh-based methods. A common type of INR implicitly encodes a shape's boundary…

Illumination of scenes is usually generated in computer graphics using polygonal meshes. In this paper, we present a geometric method using projections. Starting from an implicit polynomial equation of a surface in 3-D or a curve in 2-D, we…

We present a novel methodology based on geometric approach to simulate magnification lens effects. Our aim is to promote new applications of powerful geometric modeling techniques in visual computing. Conventional image…

A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…

We present a new method for generating realistic and view-consistent images with fine geometry from 2D image collections. Our method proposes a hybrid explicit-implicit representation called \textbf{OrthoPlanes}, which encodes fine-grained…

Surface parameterization is a fundamental concept in fields such as differential geometry and computer graphics. It involves mapping a surface in three-dimensional space onto a two-dimensional parameter space. This process allows for the…

Mesh plays an indispensable role in dense real-time reconstruction essential in robotics. Efforts have been made to maintain flexible data structures for 3D data fusion, yet an efficient incremental framework specifically designed for…

Volumetric parameterization problem refers to parameterization of both the interior and boundary of a 3D model. It is a much harder problem compared to surface parameterization where a parametric representation is worked out only for the…

We present a new approach for computing planar hexagonal meshes that approximate a given surface, represented as a triangle mesh. Our method is based on two novel technical contributions. First, we introduce Coordinate Power Fields, which…

Recent advances in implicit neural representations show great promise when it comes to generating numerical solutions to partial differential equations. Compared to conventional alternatives, such representations employ parameterized neural…

Scene representation is a crucial design choice in robotic manipulation systems. An ideal representation is expected to be 3D, dynamic, and semantic to meet the demands of diverse manipulation tasks. However, previous works often lack all…

We present a novel way of approaching image-based 3D reconstruction based on radiance fields. The problem of volumetric reconstruction is formulated as a non-linear least-squares problem and solved explicitly without the use of neural…

Directional fields, including unit vector, line, and cross fields, are essential tools in the geometry processing toolkit. The topology of directional fields is characterized by their singularities. While singularities play an important…

The sparse representation of signals defined on Euclidean domains has been successfully applied in signal processing. Bringing the power of sparse representations to non-regular domains is still a challenge, but promising approaches have…