Related papers: Pixelations of planar semialgebraic sets and shape…

Most of existing superpixel methods are designed to segment standard planar images as pre-processing for computer vision pipelines. Nevertheless, the increasing number of applications based on wide angle capture devices, mainly generating…

The slice decomposition is a bijective method for enumerating planar maps (graphs embedded in the sphere) with control over face degrees. In this paper, we extend the slice decomposition to the richer setting of hypermaps, naturally…

Over the years, the use of superpixel segmentation has become very popular in various applications, serving as a preprocessing step to reduce data size by adapting to the content of the image, regardless of its semantic content. While the…

We describe new algorithms to compute Whitney stratifications of real algebraic varieties. Using either conormal or polar techniques, these algorithms stratify a complexification of a given real variety. We then show that the resulting…

A new approach is developed within the first-order Born approximation to light scattering from a collection of particles with $\mathcal{L}$ types. Two $\mathcal{L}\times\mathcal{L}$ matrices called pair-potential matrix (PPM) and…

Current object segmentation algorithms are based on the hypothesis that one has access to a very large amount of data. In this paper, we aim to segment objects using only tiny datasets. To this extent, we propose a new automatic part-based…

Many computational algorithms applied to geometry operate on discrete representations of shape. It is sometimes necessary to first simplify, or coarsen, representations found in modern datasets for practicable or expedited processing. The…

This paper describes the adaptation of a well-scaling parallel algorithm for computing Morse-Smale segmentations based on path compression to a distributed computational setting. Additionally, we extend the algorithm to efficiently compute…

Single image super-resolution (SISR) is a very popular topic nowadays, which has both research value and practical value. In daily life, we crop a large image into sub-images to do super-resolution and then merge them together. Although…

Though analyzing a single scalar field using Morse complexes is well studied, there are few techniques for visualizing a collection of Morse complexes. We focus on analyses that are enabled by looking at a Morse complex as an embedded…

We address the basic question in discrete Morse theory of combining discrete gradient fields that are partially defined on subsets of the given complex. This is a well-posed question when the discrete gradient field $V$ is generated using a…

We show that for algebraic groups over local fields of characteristic zero, the following are equivalent: Every homomorphism has a closed image, every unitary representation decomposes into a direct sum of finite-dimensional and mixing…

Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of…

Superpixel segmentation consists of partitioning images into regions composed of similar and connected pixels. Its methods have been widely used in many computer vision applications since it allows for reducing the workload, removing…

In geometry processing, symmetry is a universal type of high-level structural information of 3D models and benefits many geometry processing tasks including shape segmentation, alignment, matching, and completion. Thus it is an important…

This paper addresses the search for a fast and meaningful image segmentation in the context of $k$-means clustering. The proposed method builds on a widely-used local version of Lloyd's algorithm, called Simple Linear Iterative Clustering…

We consider the problem of minimizing a sum of several convex non-smooth functions. We introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple…

Given a planar graph G on n vertices and an integer parameter r<n, an r-division of G with few holes is a decomposition of G into O(n/r) regions of size at most r such that each region contains at most a constant number of faces that are…

This paper presents an iterative smoothing technique for polygonal approximation of digital image boundary. The technique starts with finest initial segmentation points of a curve. The contribution of initially segmented points towards…

Partitioning and grouping of similar objects plays a fundamental role in image segmentation and in clustering problems. In such problems a typical goal is to group together similar objects, or pixels in the case of image processing. At the…