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Many tasks in geometry processing are modeled as variational problems solved numerically using the finite element method. For solid shapes, this requires a volumetric discretization, such as a boundary conforming tetrahedral mesh.…

Accurate surround-view depth estimation provides a competitive alternative to laser-based sensors and is essential for 3D scene understanding in autonomous driving. While empirical studies have proposed various approaches that primarily…

Model merging offers an effective strategy to combine the strengths of multiple finetuned models into a unified model that preserves the specialized capabilities of each. Existing methods merge models in a global manner, performing…

We study multilevel techniques, commonly used in PDE multigrid literature, to solve structured optimization problems. For a given hierarchy of levels, we formulate a coarse model that approximates the problem at each level and provides a…

Open-vocabulary 3D semantic segmentation aims to segment arbitrary categories beyond the training set. Existing methods predominantly rely on distilling knowledge from 2D open-vocabulary models. However, aligning 3D features to the 2D…

A surface moving mesh method is presented for general surfaces with or without explicit parameterization. The method can be viewed as a nontrivial extension of the moving mesh partial differential equation method that has been developed for…

This paper focuses on the challenging task of learning 3D object surface reconstructions from single RGB images. Existing methods achieve varying degrees of success by using different geometric representations. However, they all have their…

Asset management requires accurate 3D models to inform the maintenance, repair, and assessment of buildings, maritime vessels, and other key structures as they age. These downstream applications rely on high-fidelity models produced from…

Global optimization techniques are increasingly preferred over human-driven methods in the design of electromagnetic structures such as metasurfaces, and careful construction and parameterization of the physical structure is critical in…

Voronoi diagrams naturally produce convex, watertight, and topologically consistent cells, making them an appealing representation for 3D shape reconstruction. However, standard differentiable Voronoi approaches typically optimize generator…

We present a novel shape-approximating anisotropic re-meshing algorithm as a geometric generalization of the adaptive moving mesh method. Conventional moving mesh methods reduce the interpolation error of a mesh that discretizes a given…

This paper further develops the Method of Matched Sections (MMS), a robust numerical framework for the solution of boundary value problems governed by partial differential equations. It demonstrates its unique applicability to the…

We introduce a novel deep learning-based framework to interpret 3D urban scenes represented as textured meshes. Based on the observation that object boundaries typically align with the boundaries of planar regions, our framework achieves…

In many applications, maintaining a consistent dense map of the environment is key to enabling robotic platforms to perform higher level decision making. Several works have addressed the challenge of creating precise dense 3D maps from…

Zero-shot 3D point cloud understanding can be achieved via 2D Vision-Language Models (VLMs). Existing strategies directly map Vision-Language Models from 2D pixels of rendered or captured views to 3D points, overlooking the inherent and…

In this paper, we introduce a novel parametric method for segmentation of three-dimensional images. We consider a piecewise constant version of the Mumford-Shah and the Chan-Vese functionals and perform a region-based segmentation of 3D…

3D reconstruction techniques have widely been used for digital documentation of archaeological fragments. However, efficient digital capture of fragments remains as a challenge. In this work, we aim to develop a portable, high-throughput,…

Deep model fusion/merging is an emerging technique that merges the parameters or predictions of multiple deep learning models into a single one. It combines the abilities of different models to make up for the biases and errors of a single…

We propose a two-level structural optimization method for obtaining an approximate optimal shape of piecewise developable surface without specifying internal boundaries between surface patches. The condition for developability of a…

The 3D building modelling is important in urban planning and related domains that draw upon the content of 3D models of urban scenes. Such 3D models can be used to visualize city images at multiple scales from individual buildings to entire…