🍩 Database of Original & Non-Theoretical Uses of Topology

(found 5 matches in 0.001345s)

  1. Topology-Aware Segmentation Using Discrete Morse Theory (2021)

    Xiaoling Hu, Yusu Wang, Li Fuxin, Dimitris Samaras, Chao Chen
    Abstract In the segmentation of fine-scale structures from natural and biomedical images, per-pixel accuracy is not the only metric of concern. Topological correctness, such as vessel connectivity and membrane closure, is crucial for downstream analysis tasks. In this paper, we propose a new approach to train deep image segmentation networks for better topological accuracy. In particular, leveraging the power of discrete Morse theory (DMT), we identify global structures, including 1D skeletons and 2D patches, which are important for topological accuracy. Trained with a novel loss based on these global structures, the network performance is significantly improved especially near topologically challenging locations (such as weak spots of connections and membranes). On diverse datasets, our method achieves superior performance on both the DICE score and topological metrics.

  2. 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 Axel
    Abstract 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.

  3. Topological Detection of Trojaned Neural Networks (2021)

    Songzhu Zheng, Yikai Zhang, Hubert Wagner, Mayank Goswami, Chao Chen
    Abstract Deep neural networks are known to have security issues. One particular threat is the Trojan attack. It occurs when the attackers stealthily manipulate the model’s behavior through Trojaned training samples, which can later be exploited. Guided by basic neuroscientific principles, we discover subtle – yet critical – structural deviation characterizing Trojaned models. In our analysis we use topological tools. They allow us to model high-order dependencies in the networks, robustly compare different networks, and localize structural abnormalities. One interesting observation is that Trojaned models develop short-cuts from shallow to deep layers. Inspired by these observations, we devise a strategy for robust detection of Trojaned models. Compared to standard baselines it displays better performance on multiple benchmarks.

  4. Localization in the Crowd With Topological Constraints (2020)

    Shahira Abousamra, Minh Hoai, Dimitris Samaras, Chao Chen
    Abstract 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.

  5. TopoGAN: A Topology-Aware Generative Adversarial Network (2020)

    Fan Wang, Huidong Liu, Dimitris Samaras, Chao Chen
    Abstract Existing generative adversarial networks (GANs) focus on generating realistic images based on CNN-derived image features, but fail to preserve the structural properties of real images. This can be fatal in applications where the underlying structure (e.g.., neurons, vessels, membranes, and road networks) of the image carries crucial semantic meaning. In this paper, we propose a novel GAN model that learns the topology of real images, i.e., connectedness and loopy-ness. In particular, we introduce a new loss that bridges the gap between synthetic image distribution and real image distribution in the topological feature space. By optimizing this loss, the generator produces images with the same structural topology as real images. We also propose new GAN evaluation metrics that measure the topological realism of the synthetic images. We show in experiments that our method generates synthetic images with realistic topology. We also highlight the increased performance that our method brings to downstream tasks such as segmentation.

    Community Resources