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In this paper we consider the fundamental operations dilation and erosion of mathematical morphology. Many powerful image filtering operations are based on their combinations. We establish homomorphism between max-plus semi-ring of integers…
Correlation clustering is a widely-used approach for clustering large data sets based only on pairwise similarity information. In recent years, there has been a steady stream of better and better classical algorithms for approximating this…
We present a rectangle-based segmentation algorithm that sets up a graph and performs a graph cut to separate an object from the background. However, graph-based algorithms distribute the graph's nodes uniformly and equidistantly on the…
We show for a broad class of counting problems, correlation decay (strong spatial mixing) implies FPTAS on planar graphs. The framework for the counting problems considered by us is the Holant problems with arbitrary constant-size domain…
The shape of homogeneous, generic, smooth convex bodies as described by the Euclidean distance with nondegenerate critical points, measured from the center of mass represents a rather restricted class M_C of Morse-Smale functions on S^2.…
In this paper, we will study the following pattern recognition problem: Every pattern is a 3-dimensional graph, its surface can be split up into some regions, every region is composed of the pixels with the approximately same colour value…
Quantitative tracking of features from video images is a basic technique employed in many areas of science. Here, we present a method for the tracking of features that partially overlap, in order to be able to track so-called colloidal…
Super-resolution theory aims to estimate the discrete components lying in a continuous space that constitute a sparse signal with optimal precision. This work investigates the potential of recent super-resolution techniques for spectral…
Scientists, engineers, biologists, and technology specialists universally leverage image segmentation to extract shape ensembles containing many thousands of curves representing patterns in observations and measurements. These large curve…
This paper presents an efficient approach to image segmentation that approximates the piecewise-smooth (PS) functional in [12] with explicit solutions. By rendering some rational constraints on the initial conditions and the final solutions…
This paper presents a co-clustering technique that, given a collection of images and their hierarchies, clusters nodes from these hierarchies to obtain a coherent multiresolution representation of the image collection. We formalize the…
Discrete tomography is a well-established method to investigate finite point sets, in particular finite subsets of periodic systems. Here, we start to develop an efficient approach for the treatment of finite subsets of mathematical…
Semantic segmentation with fine-grained pixel-level accuracy is a fundamental component of a variety of computer vision applications. However, despite the large improvements provided by recent advances in the architectures of convolutional…
Cylindrical algebraic decomposition is a classical construction in real algebraic geometry. Although there are many algorithms to compute a cylindrical algebraic decomposition, their practical performance is still very limited. In this…
We recently introduced a notion of tilings of geometric realizations of finite relative simplicial complexes and related those tilings to the discrete Morse theory of R. Forman, especially when they have the property of being shellable, a…
We present a new approach for solving (minimum disagreement) correlation clustering that results in sublinear algorithms with highly efficient time and space complexity for this problem. In particular, we obtain the following algorithms for…
Renormalized homotopy continuation on toric varieties is introduced as a tool for solving sparse systems of polynomial equations, or sparse systems of exponential sums. The cost of continuation depends on a renormalized condition length,…
Image stitching for two images without a global transformation between them is notoriously difficult. In this paper, noticing the importance of planar structure under perspective geometry, we propose a new image stitching method which…
We provide an algorithm for computing an effective basis of homology of elliptic surfaces over the complex projective line on which integration of periods can be carried out. This allows the heuristic recovery of several algebraic…
We analyze a probabilistic algorithm for matching shapes modeled by planar regions under translations and rigid motions (rotation and translation). Given shapes $A$ and $B$, the algorithm computes a transformation $t$ such that with high…