Related papers: Geodesic Convolutional Shape Optimization
Shape optimization is commonly applied in engineering to optimize shapes with respect to an objective functional relying on PDE solutions. In this paper, we view shape optimization as optimization on Riemannian shape manifolds. We consider…
Feature descriptors play a crucial role in a wide range of geometry analysis and processing applications, including shape correspondence, retrieval, and segmentation. In this paper, we introduce Geodesic Convolutional Neural Networks…
A common approach to compute distances on continuous surfaces is by considering a discretized polygonal mesh approximating the surface and estimating distances on the polygon. We show that exact geodesic distances restricted to the polygon…
The reconstruction of a discrete surface from a point cloud is a fundamental geometry processing problem that has been studied for decades, with many methods developed. We propose the use of a deep neural network as a geometric prior for…
In the field of medical image, deep convolutional neural networks(ConvNets) have achieved great success in the classification, segmentation, and registration tasks thanks to their unparalleled capacity to learn image features. However,…
We propose two deep learning models that fully automate shape parameterization for aerodynamic shape optimization. Both models are optimized to parameterize via deep geometric learning to embed human prior knowledge into learned geometric…
The aerodynamic optimization process of cars requires multiple iterations between aerodynamicists and stylists. Response Surface Modeling and Reduced-Order Modeling are commonly used to eliminate the overhead due to Computational Fluid…
Breakthroughs in aerodynamic optimization have made it possible to develop efficient modes of transport with lesser exploitation of valuable resources. This makes it crucial for technical professionals such as engineers and scientists to…
Airborne magnetic data are commonly used to produce preliminary geological maps. Machine learning has the potential to partly fulfill this task rapidly and objectively, as geological mapping is comparable to a semantic segmentation problem.…
In this work, we propose to employ information-geometric tools to optimize a graph neural network architecture such as the graph convolutional networks. More specifically, we develop optimization algorithms for the graph-based…
Geophysical inversion attempts to estimate the distribution of physical properties in the Earth's interior from observations collected at or above the surface. Inverse problems are commonly posed as least-squares optimization problems in…
Reconstruction of geometry based on different input modes, such as images or point clouds, has been instrumental in the development of computer aided design and computer graphics. Optimal implementations of these applications have…
This paper presents a novel method, named geodesic deformable networks (GDN), that for the first time enables the learning of geodesic flows of deformation fields derived from images. In particular, the capability of our proposed GDN being…
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…
This paper describes an interdisciplinary approach to geometry modeling of geospatial boundaries. The objective is to extract surfaces from irregular spatial patterns using differential geometry and obtain coherent directional predictions…
Geodesics are essential in many geometry processing applications. However, traditional algorithms for computing geodesic distances and paths on 3D mesh models are often inefficient and slow. This makes them impractical for scenarios that…
This paper introduces a fast Central Processing Unit (CPU) implementation of geodesic morphological operations using stream processing. In contrast to the current state-of-the-art, that focuses on achieving insensitivity to the filter sizes…
Topology optimization is computationally demanding that requires the assembly and solution to a finite element problem for each material distribution hypothesis. As a complementary alternative to the traditional physics-based topology…
3D shape reconstruction from a single image is a highly ill-posed problem. Modern deep learning based systems try to solve this problem by learning an end-to-end mapping from image to shape via a deep network. In this paper, we aim to solve…
We present robust algorithms for set operations and Euclidean transformations of curved shapes in the plane using approximate geometric primitives. We use a refinement algorithm to ensure consistency. Its computational complexity is…