相关论文: Geometry-informed neural atlas for boundary value …

This paper explores the challenge of teaching a machine how to reverse-engineer the grid-marked surfaces used to represent data in 3D surface plots of two-variable functions. These are common in scientific and economic publications; and…

Geometry problem solving (GPS) represents a critical frontier in artificial intelligence, with profound applications in education, computer-aided design, and computational graphics. Despite its significance, automating GPS remains…

Many anatomical structures can be described by surface or volume meshes. Machine learning is a promising tool to extract information from these 3D models. However, high-fidelity meshes often contain hundreds of thousands of vertices, which…

Artificial intelligence is beginning to reduce the manual effort in the CAD-to-mesh pipeline. Written for meshing and geometry practitioners with limited AI background, this survey organizes recent work by workflow step. We cover part…

Biological and artificial intelligence systems navigate the fundamental efficiency-robustness tradeoff for optimal encoding, i.e., they must efficiently encode numerous attributes of the input space while also being robust to noise. This…

We consider the problem of efficiently approximating and encoding high-dimensional data sampled from a probability distribution $\rho$ in $\mathbb{R}^D$, that is nearly supported on a $d$-dimensional set $\mathcal{M}$ - for example…

Automatic mesh-based shape generation is of great interest across a wide range of disciplines, from industrial design to gaming, computer graphics and various other forms of digital art. While most traditional methods focus on primitive…

Choosing the right representation for geometry is crucial for making 3D models compatible with existing applications. Focusing on piecewise-smooth man-made shapes, we propose a new representation that is usable in conventional CAD modeling…

Many robotic tasks involving some form of 3D visual perception greatly benefit from a complete knowledge of the working environment. However, robots often have to tackle unstructured environments and their onboard visual sensors can only…

Geometric trees are characterized by their tree-structured layout and spatially constrained nodes and edges, which significantly impacts their topological attributes. This inherent hierarchical structure plays a crucial role in domains such…

Reconstructing complex 3D interfaces from indirect measurements remains a grand challenge in scientific computing, particularly for ill-posed inverse problems like Electrical Impedance Tomography (EIT). Traditional shape optimization…

Learning 3D representations that generalize well to arbitrarily oriented inputs is a challenge of practical importance in applications varying from computer vision to physics and chemistry. We propose a novel multi-resolution convolutional…

Many scientific problems require to process data in the form of geometric graphs. Unlike generic graph data, geometric graphs exhibit symmetries of translations, rotations, and/or reflections. Researchers have leveraged such inductive bias…

Understanding the topological characteristics of data is important to many areas of research. Recent work has demonstrated that synthetic 4D image-type data can be useful to train 4D convolutional neural network models to see topological…

We propose a local-to-global representation learning algorithm for 3D point cloud data, which is appropriate to handle various geometric transformations, especially rotation, without explicit data augmentation with respect to the…

Deep neural networks are workhorse models in machine learning with multiple layers of non-linear functions composed in series. Their loss function is highly non-convex, yet empirically even gradient descent minimisation is sufficient to…

Geometry is central to PDE-governed systems, motivating shape optimization and inversion. Classical pipelines conduct costly forward simulation with geometry processing, requiring substantial expert effort. Neural surrogates accelerate…

Understanding and controlling the shape of thin, soft objects has been the focus of significant research efforts among physicists, biologists, and engineers in the last decade. These studies aim to utilize advanced materials in novel,…

Neural implicit representations have become a popular choice for modeling surfaces due to their adaptability in resolution and support for complex topology. While previous works have achieved impressive reconstruction quality by training on…

Despite significant advances in the field of deep learning in applications to various fields, explaining the inner processes of deep learning models remains an important and open question. The purpose of this article is to describe and…