相关论文: Geometrical Optical Illusion via Sub-Riemannian Ge…

We find geodesics, shortest arcs, cut loci, first conjugate loci for some left-invariant sub-Riemannian metrics on the Lie groups $SU(1,1)\times\mathbb{R}$ and $SO_0(2,1)\times\mathbb{R}$.

Ray optics is an intuitive and computationally efficient model for wave propagation through nonuniform media. However, the underlying geometrical-optics (GO) approximation of ray optics breaks down at caustics, erroneously predicting the…

The purpose of this work is to construct a model for the functional architecture of the primary visual cortex (V1), based on a structure of metric measure space induced by the underlying organization of receptive profiles (RPs) of visual…

A homogeneous Riemannian space $(M= G/H,g)$ is called a geodesic orbit space (shortly, GO-space) if any geodesic is an orbit of one-parameter subgroup of the isometry group $G$. We study the structure of compact GO-spaces and give some…

The theory of geodesic regression aims to find a geodesic curve which is an optimal fit to a given set of data. In this article we restrict ourselves to the Riemannian manifold of positive definite operators (matrices) on a Hilbert space of…

We present a review of known models and a new simple mathematical modelling for border completion in the visual cortex V1 highlighting the striking analogies with bicycle rear wheel motions in the plane.

Visual transformers have driven major progress in remote sensing image analysis, particularly in object detection and segmentation. Recent vision-language and multimodal models further extend these capabilities by incorporating auxiliary…

The authors found geodesics, shortest arcs, cut loci, and conjugate sets for left-invariant sub-Riemannian matric on the Lie group $SL(2)$, which is right-invariant relative to the Lie subgroup $SO(2)\subset SL(2)$ (in other words, for…

We consider a natural extension of the Petitot-Citti-Sarti model of the primary visual cortex. In the extended model, the curvature of contours is taking into account such that occluded contours are completed using sub-Riemannian geodesics…

Machine learning problems have an intrinsic geometric structure as central objects including a neural network's weight space and the loss function associated with a particular task can be viewed as encoding the intrinsic geometry of a given…

The task of generating natural images from 3D scenes has been a long standing goal in computer graphics. On the other hand, recent developments in deep neural networks allow for trainable models that can produce natural-looking images with…

Human-Object Interaction Detection (HOI-DET) aims to localize human-object pairs and identify their interactive relationships. To aggregate contextual cues, existing methods typically propagate information across all detected entities via…

We tackle the task of synthesizing novel views of an object given a few input images and associated camera viewpoints. Our work is inspired by recent 'geometry-free' approaches where multi-view images are encoded as a (global) set-latent…

Recently there has been increased interest in fitting generative graph models to real-world networks. In particular, Bl\"asius et al. have proposed a framework for systematic evaluation of the expressivity of random graph models. We extend…

We find geodesics, shortest arcs, cut loci, first conjugate loci, distances between arbitrary elements for some left-invariant sub-Riemannian metrics on the Lie groups $SU(2)\times\mathbb{R}$ and $SO(3)\times\mathbb{R}$.

Intrinsic image decomposition aims to estimate physically based rendering (PBR) parameters such as albedo, roughness, and metallicity from images. While recent methods achieve strong single-view predictions, applying them independently to…

We present Geodesic Semantic Search (GSS), a retrieval system that learns node-specific Riemannian metrics on citation graphs to enable geometry-aware semantic search. Unlike standard embedding-based retrieval that relies on fixed Euclidean…

Hyperbolic networks are supposed to be congruent with their underlying latent geometry and following geodesics in the hyperbolic space is believed equivalent to navigate through topological shortest paths (TSP). This assumption of…

Geometric relational embeddings map relational data as geometric objects that combine vector information suitable for machine learning and structured/relational information for structured/relational reasoning, typically in low dimensions.…

Geodesic orbit spaces are those Riemannian homogeneous spaces (G/H,g) whose geodesics are orbits of one-parameter subgroups of G. We classify the simply connected geodesic orbit spaces where G is a compact Lie group of rank two. We prove…