🍩 Database of Original & Non-Theoretical Uses of Topology
(found 3 matches in 0.001952s)
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Localization in the Crowd With Topological Constraints (2020)
Shahira Abousamra, Minh Hoai, Dimitris Samaras, Chao ChenAbstract
We address the problem of crowd localization, i.e., the prediction of dots corresponding to people in a crowded scene. Due to various challenges, a localization method is prone to spatial semantic errors, i.e., predicting multiple dots within a same person or collapsing multiple dots in a cluttered region. We propose a topological approach targeting these semantic errors. We introduce a topological constraint that teaches the model to reason about the spatial arrangement of dots. To enforce this constraint, we define a persistence loss based on the theory of persistent homology. The loss compares the topographic landscape of the likelihood map and the topology of the ground truth. Topological reasoning improves the quality of the localization algorithm especially near cluttered regions. On multiple public benchmarks, our method outperforms previous localization methods. Additionally, we demonstrate the potential of our method in improving the performance in the crowd counting task. -
Optimal Topological Cycles and Their Application in Cardiac Trabeculae Restoration (2017)
Pengxiang Wu, Chao Chen, Yusu Wang, Shaoting Zhang, Changhe Yuan, Zhen Qian, Dimitris Metaxas, Leon AxelAbstract
In cardiac image analysis, it is important yet challenging to reconstruct the trabeculae, namely, fine muscle columns whose ends are attached to the ventricular walls. To extract these fine structures, traditional image segmentation methods are insufficient. In this paper, we propose a novel method to jointly detect salient topological handles and compute the optimal representations of them. The detected handles are considered hypothetical trabeculae structures. They are further screened using a classifier and are then included in the final segmentation. We show in experiments the significance of our contribution compared with previous standard segmentation methods without topological priors, as well as with previous topological method in which non-optimal representations of topological handles are used.