Related papers: Critical configurations for two projective views, …
We present a sufficient condition for recovering unique texture and viewpoints from unknown orthographic projections of a flat texture process. We show that four observations are sufficient in general, and we characterize the ambiguous…
Given a random binary picture $P_n$ of size $n$, i.e., an $n\times n$ grid filled with zeros and ones uniformly at random, when is it possible to reconstruct $P_n$ from its $k$-deck, i.e., the multiset of all its $k\times k$ subgrids? We…
This paper extends previous research in that sense that for orthogonal projections of rigid smooth (true-3D) curves moving totally free it reduces the number of required traceable points to two only (the best results known so far to the…
Motivated by a $2$-dimensional (unsupervised) image segmentation task whereby local regions of pixels are clustered via edge detection methods, a more general probabilistic mathematical framework is devised. Critical thresholds are…
In this work, we consider a class of convex optimization problems in a real Hilbert space that can be solved by performing a single projection, i.e., by projecting an infeasible point onto the feasible set. Our results improve those…
Human has an incredible ability to effortlessly perceive the viewpoint difference between two images containing the same object, even when the viewpoint change is astonishingly vast with no co-visible regions in the images. This remarkable…
We provide criteria for deciding whether a given planar curve is an image of a given spatial curve, obtained by a central or a parallel projection with unknown parameters. These criteria reduce the projection problem to a certain…
Construction robots operate in unstructured construction sites, where effective visual perception is crucial for ensuring safe and seamless operations. However, construction robots often handle large elements and perform tasks across…
The task of recognizing an algebraic surface from a single apparent contour can be reduced to the recovering of a homogeneous equation in four variables from its discriminant. In this paper, we use the fact that Darboux cyclides have a…
In dynamic tomography the object undergoes changes while projections are being acquired sequentially in time. The resulting inconsistent set of projections cannot be used directly to reconstruct an object corresponding to a time instant.…
We investigate the possibility of 3D scene reconstruction from two or more overlapping webcam streams. A large, and growing, number of webcams observe places of interest and are publicly accessible. The question naturally arises: can we…
A method to define the complex structure and separate the conformal mode is proposed for a surface constructed by two-dimensional dynamical triangulation. Applications are made for surfaces coupled to matter fields such as $n$ scalar fields…
This paper proposes a novel and exact method to reconstruct line-based 3D structure from a single image using Manhattan world assumption. This problem is a distinctly unsolved problem because there can be multiple 3D reconstructions from a…
Thin structures, such as wire-frame sculptures, fences, cables, power lines, and tree branches, are common in the real world. It is extremely challenging to acquire their 3D digital models using traditional image-based or depth-based…
In parallel beam computed tomography (CT), an object is reconstructed from a series of projections taken at different angles. However, in some industrial and biomedical imaging applications, the projection geometry is unknown, completely or…
We consider the configuration space of planar $n$-gons with fixed perimeter, which is diffeomorphic to the complex projective space $\mathbb{C}P^{n-2}$. The oriented area function has the minimal number of critical points on the…
Single-image room layout reconstruction aims to reconstruct the enclosed 3D structure of a room from a single image. Most previous work relies on the cuboid-shape prior. This paper considers a more general indoor assumption, i.e., the room…
Triangulation refers to the problem of finding a 3D point from its 2D projections on multiple camera images. For solving this problem, it is the common practice to use so-called optimal triangulation method, which we call the L2 method in…
Learning to reconstruct 3D shapes using 2D images is an active research topic, with benefits of not requiring expensive 3D data. However, most work in this direction requires multi-view images for each object instance as training…
We classify the full set of convex central configurations in the Newtonian four-body problem. Particular attention is given to configurations possessing some type of symmetry or defining geometric property. Special cases considered include…