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Spatially varying warps are increasingly popular for image alignment. In particular, as-projective-as-possible (APAP) warps have been proven effective for accurate panoramic stitching, especially in cases with significant depth parallax…
Non-rigid shape deformations pose significant challenges, and most existing methods struggle to handle partial deformations effectively. We propose to learn deformations at the point level, which allows for localized control of 3D surface…
Large kernel convolutions offer a scalable alternative to vision transformers for high-resolution 3D volumetric analysis, yet naively increasing kernel size often leads to optimization instability. Motivated by the spatial bias inherent in…
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…
We propose conformal generative modeling, a framework for generative modeling on 2D surfaces approximated by discrete triangle meshes. Our approach leverages advances in discrete conformal geometry to develop a map from a source triangle…
I survey the use and impact of adaptive mesh refinement (AMR) simulations in numerical astrophysics and cosmology. Two basic techniques are in use to extend the dynamic range of Eulerian grid simulations in multi-dimensions: cell…
Many engineering systems require accurate simulations of complex physical systems. Yet, analytical solutions are only available for simple problems, necessitating numerical approximations such as the Finite Element Method (FEM). The cost…
Establishing a correspondence between two non-rigidly deforming shapes is one of the most fundamental problems in visual computing. Existing methods often show weak resilience when presented with challenges innate to real-world data such as…
Parametric boundary representation models (B-Reps) are the de facto standard in CAD, graphics, and robotics, yet converting them into valid meshes remains fragile. The difficulty originates from the unavoidable approximation of high-order…
Mesh adaption procedures for finite element approximation allows one to adapt the resolution, by local refinement in the regions of strong variation of the function of interest. This procedure plays a key role in numerous applications of…
This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic…
The approximation of nonlinear kernels via linear feature maps has recently gained interest due to their applications in reducing the training and testing time of kernel-based learning algorithms. Current random projection methods avoid the…
Reconstructing surfaces from normals is a key component of photometric stereo. This work introduces an adaptive surface triangulation in the image domain and afterwards performs the normal integration on a triangle mesh. Our key insight is…
Twisted multilayer graphene, characterized by its moir\'e patterns arising from inter-layer rotational misalignment, serves as a rich platform for exploring quantum phenomena. Machine learning interatomic potentials (MLIPs) are a promising…
In this work, we present a novel framework for constructing three-dimensional (3D) objects from two-dimensional (2D) maps, tailored for the analysis of complex structures in the interstellar medium (ISM). The framework extends the Abel…
Therapist-in-the-loop robotic rehabilitation has shown great promise in enhancing rehabilitation outcomes by integrating the strengths of therapists and robotic systems. However, its broader adoption remains limited due to insufficient safe…
Industrial CAD workflows require robust, generalizable 3D geometric representations supporting accuracy and explainability. We introduce Shape, a self-supervised foundation model converting surface meshes into dense per-token embeddings.…
We analyze a probabilistic algorithm for matching shapes modeled by planar regions under translations and rigid motions (rotation and translation). Given shapes $A$ and $B$, the algorithm computes a transformation $t$ such that with high…
3D shape creation and modeling remains a challenging task especially for novice users. Many methods in the field of computer graphics have been proposed to automate the often repetitive and precise operations needed during the modeling of…
Neural 3D representations such as Neural Radiance Fields (NeRF), excel at producing photo-realistic rendering results but lack the flexibility for manipulation and editing which is crucial for content creation. Previous works have attempted…