相关论文: Tensors, Differential Geometry and Statistical Sha…

This paper addresses detecting anomalous patterns in images, time-series, and tensor data when the location and scale of the pattern is unknown a priori. The multiscale scan statistic convolves the proposed pattern with the image at various…

We present an image segmentation method that iteratively evolves a polygon. At each iteration, the vertices of the polygon are displaced based on the local value of a 2D shift map that is inferred from the input image via an encoder-decoder…

Predicting salient regions in natural images requires the detection of objects that are present in a scene. To develop robust representations for this challenging task, high-level visual features at multiple spatial scales must be extracted…

The perturbative expansion of tensorial field theories in Feynman graphs can be interpreted as weighted generating series of some piecewise linear varieties. This simple fact establishes a link between two a priori distinct fields: the…

Sparse incidence tensors can represent a variety of structured data. For example, we may represent attributed graphs using their node-node, node-edge, or edge-edge incidence matrices. In higher dimensions, incidence tensors can represent…

Using the tool of Hodge-Morrey decomposition of forms, we prove a new decomposition of symmetric rank-2 tensors on Ricci flat manifolds with boundary. Using this we reconstruct a new cosmological perturbation theory that allows for the…

In these notes we discuss tools and concepts that emerge when studying high-dimensional random landscapes, i.e., random functions on high-dimensional spaces. As an illustrative example, we consider an inference problem in two forms:…

The complexity of a learning task is increased by transformations in the input space that preserve class identity. Visual object recognition for example is affected by changes in viewpoint, scale, illumination or planar transformations.…

Reflection and braid equations for rank two $q$-tensors are derived from the covariance properties of quantum vectors by using the $R$-matrix formalism.

Graphs emerge in almost every real-world application domain, ranging from online social networks all the way to health data and movie viewership patterns. Typically, such real-world graphs are big and dynamic, in the sense that they evolve…

We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…

Hyperspectral super-resolution is commonly accomplished by the fusing of a hyperspectral imaging of low spatial resolution with a multispectral image of high spatial resolution, and many tensor-based approaches to this task have been…

Gravitational theories with multiple scalar fields coupled to the metric and each other --- a natural extension of the well studied single-scalar-tensor theories --- are interesting phenomenological frameworks to describe deviations from…

The development of energy selective, photon counting X-ray detectors allows for a wide range of new possibilities in the area of computed tomographic image formation. Under the assumption of perfect energy resolution, here we propose a…

This paper presents a novel method of foreground segmentation that distinguishes moving objects from their moving cast shadows in monocular image sequences. The models of background, edge information, and shadow are set up and adaptively…

Deep generative models such as GANs, normalizing flows, and diffusion models are powerful regularizers for inverse problems. They exhibit great potential for helping reduce ill-posedness and attain high-quality results. However, the latent…

We present a framework for efficient perceptual inference that explicitly reasons about the segmentation of its inputs and features. Rather than being trained for any specific segmentation, our framework learns the grouping process in an…

Local feature matching is essential for many applications, such as localization and 3D reconstruction. However, it is challenging to match feature points accurately in various camera viewpoints and illumination conditions. In this paper, we…

The recent statistical theory of neural networks focuses on nonparametric denoising problems that treat randomness as additive noise. Variability in image classification datasets does, however, not originate from additive noise but from…

Image anomaly detection consists in detecting images or image portions that are visually different from the majority of the samples in a dataset. The task is of practical importance for various real-life applications like biomedical image…