Related papers: Critical configurations for three projective views
We investigate the enumerative geometry of point configurations in projective space. We define "projective configuration counts": these enumerate configurations of points in projective space such that certain specified subsets are in fixed…
Time-of-flight cameras provide depth information, which is complementary to the photometric appearance of the scene in ordinary images. It is desirable to merge the depth and colour information, in order to obtain a coherent scene…
One way to characterize configurations of points up to congruence is by considering the distribution of all mutual distances between points. This paper deals with the question if point configurations are uniquely determined by this…
The concept of viewing graph solvability has gained significant interest in the context of structure-from-motion. A viewing graph is a mathematical structure where nodes are associated to cameras and edges represent the epipolar geometry…
This paper addresses the problem of mirror surface reconstruction, and proposes a solution based on observing the reflections of a moving reference plane on the mirror surface. Unlike previous approaches which require tedious calibration,…
Essential matrix averaging, i.e., the task of recovering camera locations and orientations in calibrated, multiview settings, is a first step in global approaches to Euclidean structure from motion. A common approach to essential matrix…
The capacity of automatically modeling photographic composition is valuable for many real-world machine vision applications such as digital photography, image retrieval, image understanding, and image aesthetics assessment. The triangle…
Finding local features that are repeatable across multiple views is a cornerstone of sparse 3D reconstruction. The classical image matching paradigm detects keypoints per-image once and for all, which can yield poorly-localized features and…
Central configurations play an important role in the dynamics of the $n$-body problem: they occur as relative equilibria and as asymptotic configurations in colliding trajectories. We illustrate how they can be found as projective fixed…
We present a technique for a complete 3D reconstruction of small objects moving in front of a textured background. It is a particular variation of multibody structure from motion, which specializes to two objects only. The scene is captured…
This study investigates the exact geometry of the configuration space in three-dimensional rotational motion planning. A parameterization of configuration space obstacles is derived for a given triangulated or ball-approximated scene with…
Critical loci for projective reconstruction from three views in four dimensional projective space are defined by an ideal generated by maximal minors of suitable $4 \times 3$ matrices, $N,$ of linear forms. Such loci are classified in this…
We state an elementary inequality for the structure from motion problem for m cameras and n points. This structure from motion inequality relates space dimension, camera parameter dimension, the number of cameras and number points and…
This paper is concerned with recovery of motion and structure parameters from multiframes under orthogonal projection when only points are traced. The main question is how many points and/or how many frames are necessary for the task. It is…
Motivated by automated junction recognition in tracking data, we study a problem of placing a square or disc of fixed size in an arrangement of lines or line segments in the plane. We let distances among the intersection points of the lines…
In this article, for the first time, one develops a nonparametric methodology for an analysis of shapes of configurations of landmarks on real 3D objects from regular camera photographs, thus making 3D shape analysis very accessible. A…
Rigid structure-from-motion (RSfM) and non-rigid structure-from-motion (NRSfM) have long been treated in the literature as separate (different) problems. Inspired by a previous work which solved directly for 3D scene structure by factoring…
Reconstructing 3D geometry and appearance from a sparse set of fixed cameras is a foundational task with broad applications, yet it remains fundamentally constrained by the limited viewpoints. We show that this bound can be broken by…
Visual navigation and three-dimensional (3D) scene reconstruction are essential for robotics to interact with the surrounding environment. Large-scale scenes and critical camera motions are great challenges facing the research community to…
$3$D structure recovery from a collection of $2$D images requires the estimation of the camera locations and orientations, i.e. the camera motion. For large, irregular collections of images, existing methods for the location estimation…