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

   https://doi.org/10.1007/978-3-031-19833-5_26  

   Bal, A.B.; Mounir, R.; Aakur, S.; Sarkar, S.; Srivastava, A. (November 2022, European Conference on Computer Vision (ECCV))

   Avidan, S.; Brostow, G.; Cissé, M.; Farinella. G.M.; Hassner, T. (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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2. 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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3. 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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4. Algorithmic Advances for the Adjacency Spectral Embedding

   https://doi.org/10.23919/EUSIPCO55093.2022.9909610  

   Fiori, Marcelo; Marenco, Bernardo; Larroca, Federico; Bermolen, Paola; Mateos, Gonzalo (August 2022, 2022 30th European Signal Processing Conference (EUSIPCO))

   The Random Dot Product Graph (RDPG) is a popular generative graph model for relational data. RDPGs postulate there exist latent positions for each node, and specifies the edge formation probabilities via the inner product of the corresponding latent vectors. The embedding task of estimating these latent positions from observed graphs is usually posed as a non-convex matrix factorization problem. The workhorse Adjacency Spectral Embedding offers an approximate solution obtained via the eigendecomposition of the adjacency matrix, which enjoys solid statistical guarantees but can be computationally intensive and is formally solving a surrogate problem. In this paper, we bring to bear recent non-convex optimization advances and demonstrate their impact to RDPG inference. We develop first-order gradient descent methods to better solve the original optimization problem, and to accommodate broader network embedding applications in an organic way. The effectiveness of the resulting graph representation learning framework is demonstrated on both synthetic and real data. We show the algorithms are scalable, robust to missing network data, and can track the latent positions over time when the graphs are acquired in a streaming fashion. 

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5. Sampling of Graph Signals with Blue Noise Dithering

   https://doi.org/10.1109/DSW.2019.8755603  

   Parada-Mayorga, Alejandro; Lau, Daniel L.; Giraldo, Jhony H.; Arce, Gonzalo R. (June 2019, 2019 IEEE Data Science Workshop)

   This paper discusses the generalization of the concept of blue noise sampling from traditional halftoning to signal processing on graphs. Making use of the spatial properties of blue noise, we generate sampling patterns that provide reconstruction errors that are similar to the ones obtained with state of the art approaches. This sampling scheme presents an alternative to those techniques that require spectral decompositions. 

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