Information Geometric Framework For Point Cloud Data
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914788329652224 |
|---|---|
| author | Vishwakarma, Amit Moosath, KS Subrahamanian |
| author_facet | Vishwakarma, Amit Moosath, KS Subrahamanian |
| contents | In this paper, we introduce a novel method for comparing 3D point clouds, a critical task in various machine learning applications. By interpreting point clouds as samples from underlying probability density functions, the statistical manifold structure is given to the space of point clouds. This manifold structure will help us to use the information geometric tools to analyze the point clouds. Our method uses the Gaussian Mixture Model (GMM) to find the probability density functions and the Modified Symmetric KL divergence to measure how similar the corresponding probability density functions are. This method of comparing the point clouds takes care of the geometry of the objects represented by the point clouds. To demonstrate the effectiveness of our approach, we take up five distinct case studies:(i) comparison of basic geometric shapes, (ii) comparison of 3D human body shapes within the MP FAUST dataset, (iii) comparison of animal shapes, (iv) comparison of human and animal datasets and (v) comparison of audio signals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04864 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Information Geometric Framework For Point Cloud Data Vishwakarma, Amit Moosath, KS Subrahamanian Differential Geometry 53B12 (Primary), 53Bxx, 62B11 (Secondary) In this paper, we introduce a novel method for comparing 3D point clouds, a critical task in various machine learning applications. By interpreting point clouds as samples from underlying probability density functions, the statistical manifold structure is given to the space of point clouds. This manifold structure will help us to use the information geometric tools to analyze the point clouds. Our method uses the Gaussian Mixture Model (GMM) to find the probability density functions and the Modified Symmetric KL divergence to measure how similar the corresponding probability density functions are. This method of comparing the point clouds takes care of the geometry of the objects represented by the point clouds. To demonstrate the effectiveness of our approach, we take up five distinct case studies:(i) comparison of basic geometric shapes, (ii) comparison of 3D human body shapes within the MP FAUST dataset, (iii) comparison of animal shapes, (iv) comparison of human and animal datasets and (v) comparison of audio signals. |
| title | Information Geometric Framework For Point Cloud Data |
| topic | Differential Geometry 53B12 (Primary), 53Bxx, 62B11 (Secondary) |
| url | https://arxiv.org/abs/2405.04864 |