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The article considers the problem of existence and uniqueness of centrally symmetrical convex body for which the projection curvature radius function coincides with a given flag function. A necessary and sufficient condition is found that…
We propose to recover 3D shape structures from single RGB images, where structure refers to shape parts represented by cuboids and part relations encompassing connectivity and symmetry. Given a single 2D image with an object depicted, our…
X-ray ptychography is a powerful and robust coherent imaging method providing access to the complex object and probe (illumination). Ptychography reconstruction is typically performed using first-order methods due to their computational…
Tree convex sets refer to a collection of sets such that each set in the collection is a subtree of a tree whose nodes are the elements of these sets. They extend the concept of row convex sets each of which is an interval over a total…
We present a novel method for reconstructing clothed humans from a sparse set of, e.g., 1 to 6 RGB images. Despite impressive results from recent works employing deep implicit representation, we revisit the volumetric approach and…
Tomography is an imaging technique that works by reconstructing a scene from acquired data in the form of line integrals of the imaging domain. A fundamental underlying assumption in the reconstruction procedure is the precise alignment of…
In parallel magnetic resonance imaging (pMRI), to find a joint solution for the image and coil sensitivity functions is a nonlinear and nonconvex problem. A class of algorithms reconstruct sensitivity encoded images of the coils first…
We study inverse problems of reconstructing static and dynamic discrete structures from tomographic data (with a special focus on the `classical' task of reconstructing finite point sets in $\mathbb{R}^d$). The main emphasis is on recent…
This paper presents a method for improved analysis of objects with an axial symmetry using X-ray Computed Tomography (CT). Cylindrical coordinates about an axis fixed to the object form the most natural base to check certain characteristics…
Speed-of-sound is a biomechanical property for quantitative tissue differentiation, with great potential as a new ultrasound-based image modality. A conventional ultrasound array transducer can be used together with an acoustic mirror, or…
Fast image reconstruction techniques are becoming important with the increasing number of scientific cases in high resolution micro and nano tomography. The processing of the large scale three-dimensional data demands new mathematical tools…
A topology preserving skeleton is a synthetic representation of an object that retains its topology and many of its significant morphological properties. The process of obtaining the skeleton, referred to as skeletonization or thinning, is…
A new approach is proposed for reconstruction of images from Radon projections. Based on Fourier expansions in orthogonal polynomials of two and three variables, instead of Fourier transforms, the approach provides a new algorithm for the…
Visibility graph reconstruction, which asks us to construct a polygon that has a given visibility graph, is a fundamental problem with unknown complexity (although visibility graph recognition is known to be in PSPACE). We show that two…
Phase recovery from intensity-only measurements forms the heart of coherent imaging techniques and holography. Here we demonstrate that a neural network can learn to perform phase recovery and holographic image reconstruction after…
Computed Tomography (CT) is an essential non-destructive three dimensional imaging modality used in medicine, security screening, and inspection of manufactured components. Typical CT data acquisition entails the collection of a thousand or…
Convex approximation sets for multiobjective optimization problems are a well-studied relaxation of the common notion of approximation sets. Instead of approximating each image of a feasible solution by the image of some solution in the…
A method is proposed for high-resolution, three-dimensional reconstruction of internal structure of objects from planar transmission images. The described approach can be used with any form of radiation or matter waves, in principle,…
Vector tomography methods intend to reconstruct and visualize vector fields in restricted domains by measuring line integrals of projections of these vector fields. Here, we deal with the reconstruction of irrotational vector functions from…
The relationship between convex geometry and algebraic geometry has deep historical roots, tracing back to classical works in enumerative geometry. In this paper, we continue this theme by studying two interconnected problems regarding…