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To recover the three dimensional (3D) volumetric distribution of matter in an object, images of the object are captured from multiple directions and locations. Using these images tomographic computations extract the distribution. In highly…
Computed Tomography (CT) is an imaging technique where information about an object are collected at different angles (called projections or scans). Then the cross-sectional image showing the internal structure of the slice is produced by…
In this paper we present a collection of results pertaining to haplotyping. The first set of results concerns the combinatorial problem of reconstructing haplotypes from incomplete and/or imperfectly sequenced haplotype data. More…
Reconstructing hand-held objects in 3D from monocular images remains a significant challenge in computer vision. Most existing approaches rely on implicit 3D representations, which produce overly smooth reconstructions and are…
Recovering textured 3D models of non-rigid human body shapes is challenging due to self-occlusions caused by complex body poses and shapes, clothing obstructions, lack of surface texture, background clutter, sparse set of cameras with…
We present a topology-informed inverse rendering approach for reconstructing high-genus surface meshes from multi-view images. Compared to 3D representations like voxels and point clouds, mesh-based representations are preferred as they…
Column-convex polyominoes are by now a well-explored model. So far, however, no attention has been given to polyominoes whose columns can have either one or two connected components. This little known kind of polyominoes seems not to be…
The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…
We propose three fast algorithms for solving the inverse problem of the thermoacoustic tomography corresponding to certain acquisition geometries. Two of these methods are designed to process the measurements done with point-like detectors…
X-ray computed tomographic infrastructures are medical imaging modalities that rely on the acquisition of rays crossing examined objects while measuring their intensity decrease. Physical measurements are post-processed by mathematical…
Compressed sensing (CS) is an innovative technique allowing to represent signals through a small number of their linear projections. In this paper we address the application of CS to the scenario of progressive acquisition of 2D visual…
Energy minimization has been an intensely studied core problem in computer vision. With growing image sizes (2D and 3D), it is now highly desirable to run energy minimization algorithms in parallel. But many existing algorithms, in…
We study the structure of the set of all possible affine hyperplane sections of a convex polytope. We present two different cell decompositions of this set, induced by hyperplane arrangements. Using our decomposition, we bound the number of…
Discrete tomography deals with the reconstruction of images from projections collected along a few given directions. Different approaches can be considered, according to different models. In this paper we adopt the grid model, where pixels…
Ptychography has rapidly grown in the fields of X-ray and electron imaging for its unprecedented ability to achieve nano or atomic scale resolution while simultaneously retrieving chemical or magnetic information from a sample. A…
Image recovery in optical interferometry is an ill-posed nonlinear inverse problem arising from incomplete power spectrum and bispectrum measurements. We reformulate this nonlin- ear problem as a linear problem for the supersymmetric rank-1…
The need for tomographic reconstruction from sparse measurements arises when the measurement process is potentially harmful, needs to be rapid, or is uneconomical. In such cases, prior information from previous longitudinal scans of the…
Reconstruction of a 3D shape from a single 2D image is a classical computer vision problem, whose difficulty stems from the inherent ambiguity of recovering occluded or only partially observed surfaces. Recent methods address this challenge…
Man-made environments typically comprise planar structures that exhibit numerous geometric relationships, such as parallelism, coplanarity, and orthogonality. Making full use of these relationships can considerably improve the robustness of…
We consider the problem of reconstructing binary images from their horizontal and vertical projections. We present a condition that the projections must necessarily satisfy when there exist two disjoint reconstructions from those…