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1. Visualizing Point Cloud Classifiers by Curvature Smoothing

   Ziwen, Chen; Wu, Wenxuan; Qi, Zhongang; Fuxin, Li (January 2020, The 31st British Machine Vision Virtual Conference)

   null (Ed.)

   Recently, several networks that operate directly on point clouds have been proposed. There is significant utility in understanding their mechanisms to classify point clouds, which can potentially help diagnosing these networks and designing better architectures. In this paper, we propose a novel approach to visualize features important to the point cloud classifiers. Our approach is based on smoothing curved areas on a point cloud. After prominent features were smoothed, the resulting point cloud can be evaluated on the network to assess whether the feature is important to the classifier. A technical contribution of the paper is an approximated curvature smoothing algorithm, which can smoothly transition from the original point cloud to one of constant curvature, such as a uniform sphere. Based on the smoothing algorithm, we propose PCI-GOS (Point Cloud Integrated-Gradients Optimized Saliency), a visualization technique that can automatically find the minimal saliency map that covers the most important features on a shape. Experiment results revealed insights into different point cloud classifiers. The code is available at https://github.com/arthurhero/PC-IGOS 

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2. Deep Geometric Prior for Surface Reconstruction

   Williams, Francis; Schneider, Teseo; Silva, Claudio; Zorin, Denis; Bruna, Joan; Panozzo, Daniele (June 2019, IEEE Computer Society Conference on Computer Vision and Pattern Recognition)

   The reconstruction of a discrete surface from a point cloud is a fundamental geometry processing problem that has been studied for decades, with many methods developed. We propose the use of a deep neural network as a geometric prior for surface reconstruction. Specifically, we overfit a neural network representing a local chart parameterization to part of an input point cloud using the Wasserstein distance as a measure of approximation. By jointly fitting many such networks to overlapping parts of the point cloud, while enforcing a consistency condition, we compute a manifold atlas. By sampling this atlas, we can produce a dense reconstruction of the surface approximating the input cloud. The entire procedure does not require any training data or explicit regularization, yet, we show that it is able to perform remarkably well: not introducing typical overfitting artifacts, and approximating sharp features closely at the same time. We experimentally show that this geometric prior produces good results for both man-made objects containing sharp features and smoother organic objects, as well as noisy inputs. We compare our method with a number of well-known reconstruction methods on a standard surface reconstruction benchmark. 

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3. Deep Geometric Prior for Surface Reconstruction

   https://doi.org/10.1109/CVPR.2019.01037  

   Williams, Francis; Silva, Claudio; Zorin, Denis; Bruna, Joan; Panozzo, Daniele (January 2019, IEEE Computer Society Conference on Computer Vision and Pattern Recognition)

   The reconstruction of a discrete surface from a point cloud is a fundamental geometry processing problem that has been studied for decades, with many methods developed. We propose the use of a deep neural network as a geometric prior for surface reconstruction. Specifically, we overfit a neural network representing a local chart parameterization to part of an input point cloud using the Wasserstein distance as a measure of approximation. By jointly fitting many such networks to overlapping parts of the point cloud, while enforcing a consistency condition, we compute a manifold atlas. By sampling this atlas, we can produce a dense reconstruction of the surface approximating the input cloud. The entire procedure does not require any training data or explicit regularization, yet, we show that it is able to perform remarkably well: not introducing typical overfitting artifacts, and approximating sharp features closely at the same time. We experimentally show that this geometric prior produces good results for both man-made objects containing sharp features and smoother organic objects, as well as noisy inputs. We compare our method with a number of well-known reconstruction methods on a standard surface reconstruction benchmark. 

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4. Curvature-based Analysis of Network Connectivity in Private Backbone Infrastructures

   https://doi.org/10.1145/3508025  

   Salamatian, Loqman; Anderson, Scott; Matthews, Joshua; Barford, Paul; Willinger, Walter; Crovella, Mark (February 2022, Proceedings of the ACM on Measurement and Analysis of Computing Systems)

   The main premise of this work is that since large cloud providers can and do manipulate probe packets that traverse their privately owned and operated backbones, standard traceroute-based measurement techniques are no longer a reliable means for assessing network connectivity in large cloud provider infrastructures. In response to these developments, we present a new empirical approach for elucidating private connectivity in today's Internet. Our approach relies on using only "light-weight" ( i.e., simple, easily-interpretable, and readily available) measurements, but requires applying a "heavy-weight" or advanced mathematical analysis. In particular, we describe a new method for assessing the characteristics of network path connectivity that is based on concepts from Riemannian geometry ( i.e., Ricci curvature) and also relies on an array of carefully crafted visualizations ( e.g., a novel manifold view of a network's delay space). We demonstrate our method by utilizing latency measurements from RIPE Atlas anchors and virtual machines running in data centers of three large cloud providers to (i) study different aspects of connectivity in their private backbones and (ii) show how our manifold-based view enables us to expose and visualize critical aspects of this connectivity over different geographic scales. 

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5. Neural FIM for learning Fisher information metrics from point cloud data.

   Fasina, O.; Huguet, G.; Tong, A.; Zhang, Y.; Wolf, G.; Nickel, M.; Adelstein, I.; Krishnaswamy, S (January 2003, Proceedings of the 40th International Conference on Machine Learning)

   Although data diffusion embeddings are ubiquitous in unsupervised learning and have proven to be a viable technique for uncovering the underlying intrinsic geometry of data, diffusion embeddings are inherently limited due to their discrete nature. To this end, we propose neural FIM, a method for computing the Fisher information metric (FIM) from point cloud data - allowing for a continuous manifold model for the data. Neural FIM creates an extensible metric space from discrete point cloud data such that information from the metric can inform us of manifold characteristics such as volume and geodesics. We demonstrate Neural FIM’s utility in selecting parameters for the PHATE visualization method as well as its ability to obtain information pertaining to local volume illuminating branching points and cluster centers embeddings of a toy dataset and two single-cell datasets of IPSC reprogramming and PBMCs (immune cells). 

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