DeepAI AI Chat
Log In Sign Up

Linear Time Recognition Algorithms for Topological Invariants in 3D

by   Li Chen, et al.
George Washington University

In this paper, we design linear time algorithms to recognize and determine topological invariants such as the genus and homology groups in 3D. These properties can be used to identify patterns in 3D image recognition. This has tremendous amount of applications in 3D medical image analysis. Our method is based on cubical images with direct adjacency, also called (6,26)-connectivity images in discrete geometry. According to the fact that there are only six types of local surface points in 3D and a discrete version of the well-known Gauss-Bonnett Theorem in differential geometry, we first determine the genus of a closed 2D-connected component (a closed digital surface). Then, we use Alexander duality to obtain the homology groups of a 3D object in 3D space.


page 1

page 2

page 3

page 4


Genus Computing for 3D digital objects: algorithm and implementation

This paper deals with computing topological invariants such as connected...

On the digital homology groups of digital images

In this article we study the digital homology groups of digital images w...

Structure from Motion: Theoretical Foundations of a Novel Approach Using Custom Built Invariants

We rephrase the problem of 3D reconstruction from images in terms of int...

Digital topological groups

In this article, we develop the basic theory of digital topological grou...

Roughness Index and Roughness Distance for Benchmarking Medical Segmentation

Medical image segmentation is one of the most challenging tasks in medic...

Iterated Belief Revision Under Resource Constraints: Logic as Geometry

We propose a variant of iterated belief revision designed for settings w...

Feature Lines for Illustrating Medical Surface Models: Mathematical Background and Survey

This paper provides a tutorial and survey for a specific kind of illustr...