# Linear time recognition algorithms for topological invariants in 3D

@article{Chen2008LinearTR, title={Linear time recognition algorithms for topological invariants in 3D}, author={Li M. Chen and Yongwu Rong}, journal={2008 19th International Conference on Pattern Recognition}, year={2008}, pages={1-4} }

In this paper, we design linear time algorithms to recognize and determine topological invariants such as genus and homology groups in 3D. These invariants can be used to identify patterns in 3D image recognition and 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…

## 14 Citations

### Algorithms for Computing Topological Invariants in 2D and 3D Digital Spaces

- Computer ScienceArXiv
- 2013

This paper designed fast algorithms for topological invariants such as connected components, hole counting in 2D and boundary surface genus for 3D and also O(n) time algorithm to get genus of the closed surface.

### Algorithms for Computing Topological Invariants in Digital Spaces

- Computer ScienceISGV
- 2021

This paper includes fast algorithms and implementations for topological invariants such as connected components, hole counting in 2D, and boundary surface genus for 3D and a linear time algorithm to solve the hole counting problem.

### Digital Curvatures Applied to 3D Object Analysis and Recognition: A Case Study

- Computer ScienceIWCIA
- 2012

It is found that Gaussian curvatures mainly describe the global features and average characteristics such as the five regions of a human face, however, mean curvatures can be used to find local features and extreme points such as nose in 3D facial data.

### Some Results on Simplical Homology Groups of 2D Digital Images.

- Mathematics
- 2012

In this paper we study some results related to the simplicial homology groups of 2D digital images. We show that if a bounded digital image Z X ⊂ is nonempty and κ -connected, then its homology…

### Repairing 3D binary images using the BCC grid with a 4-valued combinatorial coordinate system

- Computer Science, MathematicsInf. Sci.
- 2019

### On Some Local Topological Properties of Naive Discrete Sphere

- Mathematics, Computer ScienceCTIC
- 2016

Novel results on the local topological properties of the naive model of discrete sphere are presented, which follow from the bijection of each quadraginta octant of naive sphere with its projection map on the corresponding functional plane and from the characterization of certain jumps in the f-map.

### Contributions to Topological Data Analysis for Scientific Visualization

- Computer Science
- 2016

This thesis presents new research directions, supported by recent preliminary results for the topological analysis of uncertain and bivariate scalar fields, and discusses practical challenges that recently arose with the ongoing development of high performance computing resources.

### Topology Verification for Isosurface Extraction

- Computer ScienceIEEE Transactions on Visualization and Computer Graphics
- 2012

A framework for verification of isosurfacing implementations to check topological properties is extended and stratified Morse theory and digital topology are used to design algorithms which verify topological invariants.

### Reproducing Expert-Like Motion in Deformable Environments Using Active Learning and IOC

- Computer ScienceISRR
- 2015

This work hypothesizes that the relative sensitivities of deformable objects are encoded in the expert’s demonstrated motion, and presents a framework which is able to imitate an expert's behavior by learning a sensitivity-based cost function under which the expert's motion is optimal.

### Enabling Motion Planning and Execution for Tasks Involving Deformation and Uncertainty

- Engineering
- 2017

This work focuses on two important areas of poorly controlled robotic manipulation: motion planning for deformable objects and in deformable environments; and manipulation with uncertainty, which incorporates contact with the environment and compliance of the robot to generate motion policies which are then adapted during execution to reflect actual robot behavior.

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