Related papers: An Atlas for the Pinhole Camera
We introduce the concept of paravectors to describe the geometry of points in a three dimensional space. After defining a suitable product of paravectors, we introduce the concepts of biparavectors and triparavectors to describe line…
Current CNN-based algorithms for recovering the 3D pose of an object in an image assume knowledge about both the object category and its 2D localization in the image. In this paper, we relax one of these constraints and propose to solve the…
In medical image analysis, constructing an atlas, i.e. a mean representative of an ensemble of images, is a critical task for practitioners to estimate variability of shapes inside a population, and to characterise and understand how…
Segmentation of overlapping convex objects has various applications, for example, in nanoparticles and cell imaging. Often the segmentation method has to rely purely on edges between the background and foreground making the analyzed images…
New ray-optical elements allow generalized refraction of light rays, but geometry imposes limitations on possible mappings between the positions of an object and its geometric image. Here I study the case of an infinite, planar,…
Privacy protection is a growing concern in the digital era, with machine vision techniques widely used throughout public and private settings. Existing methods address this growing problem by, e.g., encrypting camera images or…
This last document is showing the gradual introduction of hierarchical modeling techniques in image analysis. The first chapter is dealing with the first works carried out in the field of industrial applications of pattern recognition. The…
Determining the position and orientation of a calibrated camera from a single image with respect to a 3D model is an essential task for many applications. When 2D-3D correspondences can be obtained reliably, perspective-n-point solvers can…
The cross-depiction problem is that of recognising visual objects regardless of whether they are photographed, painted, drawn, etc. It is a potentially significant yet under-researched problem. Emulating the remarkable human ability to…
A variational model for learning convolutional image atoms from corrupted and/or incomplete data is introduced and analyzed both in function space and numerically. Building on lifting and relaxation strategies, the proposed approach is…
A modulated icosahedral shell with an inclusion is a concise description of many viruses, including recently-discovered large double-stranded DNA ones. Many X-ray scattering patterns of such viruses show major polygonal fringes, which can…
In this paper, we study metric completions of triangulated categories in a representation-theoretic context. We provide a concrete description of completions of bounded derived categories of hereditary finite dimensional algebras of finite…
Point cloud stands as the most widely adopted format for representing 3D shapes and scenes due to its simplicity and geometric fidelity. However, its inherent unordered and irregular nature, exacerbated by sensor noise and occlusions,…
We give an elementary introduction to the theory of triangulated categories covering their axioms, homological algebra in triangulated categories, triangulated subcategories, and Verdier localization. We try to use a minimal set of axioms…
In the problem "Localization and trilateration with the minimum number of landmarks", we faced the 3-Guard and classic Art Gallery Problems. The goal of the art gallery problem is to find the minimum number of guards within a simple polygon…
Techniques from representation theory, symbolic computational algebra, and numerical algebraic geometry are used to find the minimal generators of the ideal of the trifocal variety. An effective test for determining whether a given tensor…
Recent advances in text-to-image diffusion models have been driven by the increasing availability of paired 2D data. However, the development of 3D diffusion models has been hindered by the scarcity of high-quality 3D data, resulting in…
We propose a new framework for the study of homological properties for (compactly generated) triangulated categories such as regularity, finiteness of global or finitistic dimension, gorensteinness or injective generation and the relation…
The human visual system can spot an abnormal image, and reason about what makes it strange. This task has not received enough attention in computer vision. In this paper we study various types of atypicalities in images in a more…
We propose to investigate detecting and characterizing the 3D planar articulation of objects from ordinary videos. While seemingly easy for humans, this problem poses many challenges for computers. We propose to approach this problem by…