Parallel Data Processing based on Homotopy Connectivity: Applications to Stereoscopic Vision and Biomedical Data

Par-HoT aims to construct a novel conceptual homotopy-based model HoT(D) promoting computer parallelism for analysing general topological data D. As a proof for the applicability of this model to real engineering problems, a simple but broadly applicable framework for representation, analysis, recognition and learning of digital image data is to be as well developed. The proposed mathematical model is based on homotopy connectivity information of a subdivided object which is represented by a new version of the classical notion of abstract cell complex called Organelle Complex (OC, for short). OC representation provides a combinatorial topological scenario that: (a) describes completely, jointly and harmoniously the processes of homology and homotopy computation; (b) it is well adapted to promote parallelism within this context and (c) it admits a purely topological scale-space treatment. From HoT(D), it is possible to automatically deduce not only classical homological characteristics of D but also connectivity models in which its global homological information is included and homotopically interconnected. For general non topologically structured data, we plan to generate novel efficient algorithms (data topologization processes) for constructing their associated OCs. In order to assess the potential applicability of the theoretical homotopy-based model, two software demonstrators related to aerial and medical images will be developed: a) Stereoscopic Vision: Parallel algorithms will be designed and implemented to improve the stereoscopic correspondence of various images of the same scene captured by different cameras. These algorithms will help, for instance, the real time tracking and navigation of Unmanned Aerial Vehicles. b) Neuroscience Data Analysis: Parallel algorithms will be designed and implemented for the topological registration, analysis and recognition of biomedical images, and topological machine learning applied to biomedical data. These algorithms will help, for instance, to extract useful information from 3D+t functional magnetic resonance images of human brains. For both problems, Par-HoT will provide various novel solutions for topologization of image data, dealing with images that are represented by a spatial array, as a point in an n-dimensional Euclidean space (vector of characteristics) or as the combination of text and visual information associated to the image. Par-HoT is a continuation of the non-technologically driven research project MTM-2016:81030-P: “Topological Recognition of 4D Digital Images”. Par-HoT is beyond the stage of simply adjusting or modifying the successful generic parallel algorithmic techniques for topologically processing digital images obtained in the latter. It provides a new and powerful framework of parallel computational topology for analysing general data, reliably demonstrating its applicability to real problems related to image data.

PI: Pedro Real Jurado / Fernando Díaz del Río
Reference: PID2019-110455GB-I00
Funding by: Ministerio de Economía y Competitividad
Start date: 01-06-2020
End date: 30-05-2023
Web Page:

Mª José Morón Fernández
Daniel Cagigas Muñiz
Daniel Cascado Caballero
Helena Molina Abril
Cristina Suárez Mejías
Amaro García Suárez
Claudio Alemán Morillo
Pablo Sánchez Cuevas
Javier Castillo Delgado
Agatino Giuliano Mirabella Galvin
Darian Onchis Moaca
Codruta Istin