Natural Hydrocarbon Samples Classification by Topological Analysis Method

Nowadays material science involves powerful 3D imaging techniques such as X-ray computed tomography that generates high-resolution images of different structures. These methods are widely used to reveal information about the internal structure of geological cores; therefore, there is a need to develop modern approaches for quantitative analysis of the obtained images, their comparison, and classification. Topological persistence is a useful technique for characterizing the internal structure of 3D images. We show how persistent data analysis provides a useful tool for the classification of porous media structure from 3D images of hydrocarbon reservoirs obtained using computed tomography. We propose a methodology of 3D structure classification based on geometry-topology analysis via persistent homology.

Beyond Topological Persistence: Starting from Networks

Persistent homology enables fast and computable comparison of topological objects. We give some instances of a recent extension of the theory of persistence, guaranteeing robustness and computability for relevant data types, like simple graphs and digraphs. We focus on categorical persistence functions that allow us to study in full generality strong kinds of connectedness—clique communities, k-vertex, and k-edge connectedness—directly on simple graphs and strong connectedness in digraphs.

Marker-Less UAV-LiDAR Strip Alignment in Plantation Forests Based on Topological Persistence Analysis of Clustered Canopy Cover

A holistic strategy is established for automated UAV-LiDAR strip adjustment for plantation forests, based on hierarchical density-based clustering analysis of the canopy cover. The method involves three key stages: keypoint extraction, feature similarity and correspondence, and rigid transformation estimation. Initially, the HDBSCAN algorithm is used to cluster the scanned canopy cover, and the keypoints are marked using topological persistence analysis of the individual clusters. Afterward, the feature similarity is calculated by considering the linear and angular relationships between each point and the pointset centroid. The one-to-one feature correspondence is retrieved by solving the assignment problem on the similarity score function using the Kuhn–Munkres algorithm, generating a set of matching pairs. Finally, 3D rigid transformation parameters are determined by permutations over all conceivable pair combinations within the correspondences, whereas the best pair combination is that which yields the maximum count of matched points achieving distance residuals within the specified tolerance. Experimental data covering eighteen subtropical forest plots acquired from the GreenValley and Riegl UAV-LiDAR platforms in two scan modes are used to validate the method. The results are extremely promising for redwood and poplar tree species from both the Velodyne and Riegl UAV-LiDAR datasets. The minimal mean distance residuals of 31 cm and 36 cm are achieved for the coniferous and deciduous plots of the Velodyne data, respectively, whereas their corresponding values are 32 cm and 38 cm for the Riegl plots. Moreover, the method achieves both higher matching percentages and lower mean distance residuals by up to 28% and 14 cm, respectively, compared to the baseline method, except in the case of plots with extremely low tree height. Nevertheless, the mean planimetric distance residual achieved by the proposed method is lower by 13 cm.

A Topological Method for Comparing Document Semantics

Comparing document semantics is one of the toughest tasks in both Natural Language Processing and Information Retrieval. To date, on one hand, the tools for this task are still rare. On the other hand, most relevant methods are devised from the statistic or the vector space model perspectives but nearly none from a topological perspective. In this paper, we hope to make a different sound. A novel algorithm based on topological persistence for comparing semantics similarity between two documents is proposed. Our experiments are conducted on a document dataset with human judges’ results. A collection of state-of-the-art methods are selected for comparison. The experimental results show that our algorithm can produce highly human-consistent results, and also beats most state-of-the-art methods though ties with NLTK.