相关论文: The consistency principle for a digitization proce…

This paper proposes a new cubical space model for the representation of continuous objects and surfaces in the n-dimensional Euclidean space by discrete sets of points. The cubical space model concerns the process of converting a continuous…

Using digital topology approach, we construct digital models of closed surfaces as the intersection graphs of LCL covers of the surfaces. It is proved that digital models of closed surfaces are digital 2-dimensional surfaces preserving the…

Transformations of digital spaces preserving local and global topology play an important role in thinning, skeletonization and simplification of digital images. In the present paper, we introduce and study contractions of simple pair of…

We define LCL decompositions of the plane and investigate the advantages of using such decompositions in the context of digital topology. We show that discretization schemes based on such decompositions associate, to each LCL tiling of the…

In this paper, we show how to construct graph theoretical models of n-dimensional continuous objects and manifolds. These models retain topological properties of their continuous counterparts. An LCL collection of n-cells in Euclidean space…

This work aims to define the concept of manifold, which has a very important place in the topology, on digital images. So, a general perspective is provided for two and three-dimensional imaging studies on digital curves and digital…

Image registration is a process of aligning two or more images of same objects using geometric transformation. Most of the existing approaches work on the assumption of location invariance. These approaches require object-centric images to…

This paper describes the systematic application of local topological methods for detecting interfaces and related anomalies in complicated high-dimensional data. By examining the topology of small regions around each point, one can…

Topological data analysis (TDA) is a rising branch in modern applied mathematics. It extracts topological structures as features of a given space and uses these features to analyze digital data. Persistent homology, one of the central tools…

This paper proposes a concise coding of the cells of n-dimensional finite regular grids. It induces a simple, generic and efficient framework for implementing classical digital topology data structures and algorithms. Discrete subsets of…

Recent research on graph embedding has achieved success in various applications. Most graph embedding methods preserve the proximity in a graph into a manifold in an embedding space. We argue an important but neglected problem about this…

The aim of this paper is to generalize some of the properties and results regarding both the coincidence point set and the common fixed point set of any two digitally continuous maps to the case of several (more than two) digitally…

This paper presents the classification of digital n-manifolds based on the notion of complexity and homotopy equivalence. We introduce compressed n-manifolds and study their properties. We show that any n-manifold with p points is homotopy…

Image segmentation is to extract meaningful objects from a given image. For degraded images due to occlusions, obscurities or noises, the accuracy of the segmentation result can be severely affected. To alleviate this problem, prior…

Mathematical morphology (MM) is a powerful and widely used framework in image processing. Through set-theoretic and discrete geometric principles, MM operations such as erosion, dilation, opening, and closing effectively manipulate digital…

A regularized version of Mixture Models is proposed to learn a principal graph from a distribution of $D$-dimensional data points. In the particular case of manifold learning for ridge detection, we assume that the underlying manifold can…

Metric embeddings traditionally study how to map $n$ items to a target metric space such that distance lengths are not heavily distorted; but what if we only care to preserve the relative order of the distances (and not their length)? In…

Under a set of assumptions on a family of submanifolds $\subset {\mathbb R}^D$, we derive a series of geometric properties that remain valid after finite-dimensional and almost isometric Diffusion Maps (DM), including almost uniform…

We propose a method for learning topology-preserving data representations (dimensionality reduction). The method aims to provide topological similarity between the data manifold and its latent representation via enforcing the similarity in…

We give an answer to the question given by T.Y.Kong in his article "Can 3-D Digital Topology be Based on Axiomatically Defined Digital Spaces?" In this article he asks the question, if so called "good pairs" of neighborhood relations can be…