A topology-based descriptor for 3D point cloud modeling: Theory and experiments

William J. Beksi; Nikolaos Papanikolopoulos

doi:10.1016/j.imavis.2019.05.004

A topology-based descriptor for 3D point cloud modeling: Theory and experiments

William J. Beksi, Nikolaos Papanikolopoulos

Computer Science and Engineering

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

This paper presents a topology-based global descriptor that allows for efficient 3D point cloud processing tasks associated with the analysis of shapes. The descriptor is called the Signature of Topologically Persistent Points (STPP). By using persistent homology, STPP is formed by the computation of topological invariants involving the zeroth and first homology groups. Persistent homology is a methodology that finds the features of a topological space at different spatial resolutions. STPP requires no preprocessing and uses a single tuning parameter. It is an effective 3D point cloud descriptor with robustness to noisy sensor data. The paper highlights this aspect with experimental comparisons to the state of the art. Our research has been validated on a publicly available RGB-D dataset. The results show that STPP can be used as a distinctive signature by employing a small number of features with object detection and classification benefiting from its usage.

Original language	English (US)
Pages (from-to)	84-95
Number of pages	12
Journal	Image and Vision Computing
Volume	88
DOIs	https://doi.org/10.1016/j.imavis.2019.05.004
State	Published - Aug 2019

Bibliographical note

Funding Information:
This material is based upon work supported by the National Science Foundation through grants #CNS-1338042 , #IIS-1427014 , #CNS-1439728 , #CNS-1531330 and #CNS-1544887 . The authors acknowledge the Minnesota Supercomputing Institute at the University of Minnesota for providing software, computational, and storage resources that contributed to these research results. The University of Minnesota Informatics Institute (UMII) has partially supported the work of William Beksi.

Funding Information:
This material is based upon work supported by the National Science Foundation through grants #CNS-1338042, #IIS-1427014, #CNS-1439728, #CNS-1531330 and #CNS-1544887. The authors acknowledge the Minnesota Supercomputing Institute at the University of Minnesota for providing software, computational, and storage resources that contributed to these research results. The University of Minnesota Informatics Institute (UMII) has partially supported the work of William Beksi.

Publisher Copyright:
© 2019 Elsevier B.V.

Keywords

Object classification
Persistent homology
Shape analysis
Topological data analysis

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10.1016/j.imavis.2019.05.004

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title = "A topology-based descriptor for 3D point cloud modeling: Theory and experiments",

abstract = "This paper presents a topology-based global descriptor that allows for efficient 3D point cloud processing tasks associated with the analysis of shapes. The descriptor is called the Signature of Topologically Persistent Points (STPP). By using persistent homology, STPP is formed by the computation of topological invariants involving the zeroth and first homology groups. Persistent homology is a methodology that finds the features of a topological space at different spatial resolutions. STPP requires no preprocessing and uses a single tuning parameter. It is an effective 3D point cloud descriptor with robustness to noisy sensor data. The paper highlights this aspect with experimental comparisons to the state of the art. Our research has been validated on a publicly available RGB-D dataset. The results show that STPP can be used as a distinctive signature by employing a small number of features with object detection and classification benefiting from its usage.",

keywords = "Object classification, Persistent homology, Shape analysis, Topological data analysis",

author = "Beksi, {William J.} and Nikolaos Papanikolopoulos",

note = "Funding Information: This material is based upon work supported by the National Science Foundation through grants #CNS-1338042 , #IIS-1427014 , #CNS-1439728 , #CNS-1531330 and #CNS-1544887 . The authors acknowledge the Minnesota Supercomputing Institute at the University of Minnesota for providing software, computational, and storage resources that contributed to these research results. The University of Minnesota Informatics Institute (UMII) has partially supported the work of William Beksi. Funding Information: This material is based upon work supported by the National Science Foundation through grants #CNS-1338042, #IIS-1427014, #CNS-1439728, #CNS-1531330 and #CNS-1544887. The authors acknowledge the Minnesota Supercomputing Institute at the University of Minnesota for providing software, computational, and storage resources that contributed to these research results. The University of Minnesota Informatics Institute (UMII) has partially supported the work of William Beksi. Publisher Copyright: {\textcopyright} 2019 Elsevier B.V.",

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language = "English (US)",

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N2 - This paper presents a topology-based global descriptor that allows for efficient 3D point cloud processing tasks associated with the analysis of shapes. The descriptor is called the Signature of Topologically Persistent Points (STPP). By using persistent homology, STPP is formed by the computation of topological invariants involving the zeroth and first homology groups. Persistent homology is a methodology that finds the features of a topological space at different spatial resolutions. STPP requires no preprocessing and uses a single tuning parameter. It is an effective 3D point cloud descriptor with robustness to noisy sensor data. The paper highlights this aspect with experimental comparisons to the state of the art. Our research has been validated on a publicly available RGB-D dataset. The results show that STPP can be used as a distinctive signature by employing a small number of features with object detection and classification benefiting from its usage.

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A topology-based descriptor for 3D point cloud modeling: Theory and experiments

Abstract

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Keywords

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