Related papers: Problems and related results in Algebraic Vision a…
We investigate a challenging task of dynamic scene geometry estimation, which requires representing both spatial and temporal features. Typically, existing methods align the two features into a unified latent space to model scene geometry.…
Auxiliary lines are essential for solving complex geometric problems but remain challenging for large vision-language models (LVLMs). Recent attempts construct auxiliary lines via code-driven rendering, a strategy that relies on accurate…
Image classifiers play a critical role in detecting diseases in medical imaging and identifying anomalies in manufacturing processes. However, their predefined behaviors after extensive training make post hoc model editing difficult,…
We characterize the problem of pose estimation for rigid objects in terms of determining viewpoint to explain coarse pose and keypoint prediction to capture the finer details. We address both these tasks in two different settings - the…
This is the first paper in a series (of four) designed to show how to use geometric algebras of multivectors and extensors to a novel presentation of some topics of differential geometry which are important for a deeper understanding of…
Large language models have shown impressive results for multi-hop mathematical reasoning when the input question is only textual. Many mathematical reasoning problems, however, contain both text and image. With the ever-increasing adoption…
Methods for 3D reconstruction from posed frames require prior knowledge about the scene metric range, usually to recover matching cues along the epipolar lines and narrow the search range. However, such prior might not be directly available…
3D recovery from multi-stereo and stereo images, as an important application of the image-based perspective geometry, serves many applications in computer vision, remote sensing and Geomatics. In this chapter, the authors utilize the…
Correspondences estimation or feature matching is a key step in the image-based 3D reconstruction problem. In this paper, we propose two algebraic properties for correspondences. The first is a rank deficient matrix construct from the…
The main purpose of our paper is a new approach to design of algorithms of Kaczmarz type in the framework of operators in Hilbert space. Our applications include a diverse list of optimization problems, new Karhunen-Lo\`eve transforms, and…
The multiview variety of an arrangement of cameras is the Zariski closure of the images of world points in the cameras. The prime vanishing ideal of this complex projective variety is called the multiview ideal. We show that the bifocal and…
In image set classification, a considerable progress has been made by representing original image sets on Grassmann manifolds. In order to extend the advantages of the Euclidean based dimensionality reduction methods to the Grassmann…
Reconstructing photo-realistic large-scale scenes from images, for example at city scale, is a long-standing problem in computer graphics. Neural rendering is an emerging technique that enables photo-realistic image synthesis from…
Modern 3D semantic scene graph estimation methods utilize ground truth 3D annotations to accurately predict target objects, predicates, and relationships. In the absence of given 3D ground truth representations, we explore leveraging only…
We describe a new algorithm for computing Whitney stratifications of complex projective varieties. The main ingredients are (a) an algebraic criterion, due to L\^e and Teissier, which reformulates Whitney regularity in terms of conormal…
Using geometric landmarks like lines and planes can increase navigation accuracy and decrease map storage requirements compared to commonly-used LiDAR point cloud maps. However, landmark-based registration for applications like loop closure…
Real algebraic geometry adapts the methods and ideas from (complex) algebraic geometry to study the real solutions to systems of polynomial equations and polynomial inequalities. As it is the real solutions to such systems modeling…
Weak gravitational lensing on a cosmological scales can provide strong constraints both on the nature of dark matter and the dark energy equation of state. Most current weak lensing studies are restricted to (two-dimensional) projections,…
Simultaneous reconstruction of geometry and reflectance properties in uncontrolled environments remains a challenging problem. In this paper, we propose an efficient method to reconstruct the scene's 3D geometry and reflectance from…
Visual odometry algorithms tend to degrade when facing low-textured scenes -from e.g. human-made environments-, where it is often difficult to find a sufficient number of point features. Alternative geometrical visual cues, such as lines,…