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1. Bayesian Tracking of Video Graphs Using Joint Kalman Smoothing and Registration

   Bal, Aditi Basu; Mounir, Ramy; Aakur, Sathyanarayanan; Sarkar, Sudeep; Srivastava, Anuj (October 2022, European Conference on Computer Vision)

   Graph-based representations are becoming increasingly popular for representing and analyzing video data, especially in object tracking and scene understanding applications. Accordingly, an essential tool in this approach is to generate statistical inferences for graphical time series associated with videos. This paper develops a Kalman-smoothing method for estimating graphs from noisy, cluttered, and incomplete data. The main challenge here is to find and preserve the registration of nodes (salient detected objects) across time frames when the data has noise and clutter due to false and missing nodes. First, we introduce a quotient-space representation of graphs that incorporates temporal registration of nodes, and we use that metric structure to impose a dynamical model on graph evolution. Then, we derive a Kalman smoother, adapted to the quotient space geometry, to estimate dense, smooth trajectories of graphs. We demonstrate this framework using simulated data and actual video graphs extracted from the Multiview Extended Video with Activities (MEVA) dataset. This framework successfully estimates graphs despite the noise, clutter, and missed detections. 

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2. Bayesian Tracking of Video Graphs Using Joint Kalman Smoothing and Registration

   Aditi Basu Bal, Ramy Mounir (November 2022, European Conference on Computer Vision)

   Avidan, S. (Ed.)

   Graph-based representations are becoming increasingly popular for representing and analyzing video data, especially in object tracking and scene understanding applications. Accordingly, an essential tool in this approach is to generate statistical inferences for graphical time series associated with videos. This paper develops a Kalman-smoothing method for estimating graphs from noisy, cluttered, and incomplete data. The main challenge here is to find and preserve the registration of nodes (salient detected objects) across time frames when the data has noise and clutter due to false and missing nodes. First, we introduce a quotient-space representation of graphs that incorporates temporal registration of nodes, and we use that metric structure to impose a dynamical model on graph evolution. Then, we derive a Kalman smoother, adapted to the quotient space geometry, to estimate dense, smooth trajectories of graphs. We demonstrate this framework using simulated data and actual video graphs extracted from the Multiview Extended Video with Activities (MEVA) dataset. This framework successfully estimates graphs despite the noise, clutter, and missed detections. 

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3. Shape-Graph Matching Network (SGM-net): Registration for Statistical Shape Analysis

   https://doi.org/10.1109/ISBI56570.2024.10635203  

   Liang, Shenyuan; Srivastava, Anuj; Segundo, Mauricio Pamplona; Sarkar, Sudeep; Aakur, Sathyanarayanan N (May 2024, IEEE)

   This paper focuses on the registration problem of shape graphs, where a shape graph is a set of nodes connected by articulated curves with arbitrary shapes. This registration requires optimization over the permutation group, made challenging by differences in nodes (in terms of numbers, locations) and edges (in terms of shapes, placements, and sizes) across graphs. We tackle this registration problem using a neuralnetwork architecture with an unsupervised loss function based on the elastic shape metric for curves. This architecture results in (1) state-of-the-art matching performance and (2) an order of magnitude reduction in the computational cost relative to baseline approaches. We demonstrate the effectiveness of the proposed approach using both simulated data and real-world 2D retinal blood vessels and 3D microglia graphs. 

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4. Towards Scalable Spectral Embedding and Data Visualization via Spectral Coarsening

   https://doi.org/10.1145/3437963.3441767  

   Zhao, Zhiqiang; Zhang, Ying; Feng, Zhuo (March 2021, ACM International Conference on Web Search and Data Mining)

   null (Ed.)

   This paper proposes a scalable multilevel framework for the spectral embedding of large undirected graphs. The proposed method first computes much smaller yet sparse graphs while preserving the key spectral (structural) properties of the original graph, by exploiting a nearly-linear time spectral graph coarsening approach. Then, the resultant spectrally-coarsened graphs are leveraged for the development of much faster algorithms for multilevel spectral graph embedding (clustering) as well as visualization of large data sets. We conducted extensive experiments using a variety of large graphs and datasets and obtained very promising results. For instance, we are able to coarsen the "coPapersCiteseer" graph with 0.43 million nodes and 16 million edges into a much smaller graph with only 13K (32X fewer) nodes and 17K (950X fewer) edges in about 16 seconds; the spectrally-coarsened graphs allow us to achieve up to 1,100X speedup for multilevel spectral graph embedding (clustering) and up to 60X speedup for t-SNE visualization of large data sets. 

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5. Interactive 2D Periodic Graphs

   https://doi.org/10.4230/LIPIcs.SoCG.2023.63  

   Camero, Alexandra; Streinu, Ileana (June 2023, 39th International Symposium on Computational Geometry (SoCG 2023))

   Chambers, Erin W; Gudmundsson, Joachim (Ed.)

   We present an educational web app for interactively drawing and editing 2D periodic graphs. The user defines the unit cell and the finite set of vertex and edge representatives, from which a sufficiently large fragment of the periodic graph is created for the visualization. The periodic graph can also be modified by applying several transformations, including isometries and relaxations of the unit cell. A finite representation of the infinite periodic graph can be saved in an external file as a quotient graph with Z²-marked edges. Its geometry is recorded using fractional (crystallographic) coordinates. The facial structure of non-crossing periodic graphs can be revealed by the user interactively selecting face representatives. An accompanying video demonstrates the functionality of the web application. 

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