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1. Helical Contour Dynamics

   https://doi.org/10.1134/S1560354721060022  

   Chu, Tianyi ; Llewellyn Smith, Stefan G. ( November 2021 , Regular and Chaotic Dynamics)
2. Contour Algorithm for Connectivity

   Du, Zhihui ; Alvarado Rodriguez, Oliver ; Li, Fuhuan ; Dindoost, Mohammad ; Bader, David ( December 2023 , The 30th IEEE International Conference on High Performance Computing, Data, and Analytics (HiPC))

   Finding connected components in a graph is a fundamental problem in graph analysis. In this work, we present a novel minimum-mapping based Contour algorithm to efficiently solve the connectivity problem. We prove that the Contour algorithm with two or higher order operators can identify all connected components of an undirected graph within O(log d_max) iterations, with each iteration involving O(m) work, where d_max represents the largest diameter among all components in the given graph, and m is the total number of edges in the graph. Importantly, each iteration is highly parallelizable, making use of the efficient minimum-mapping operator applied to all edges. To further enhance its practical performance, we optimize the Contour algorithm through asynchronous updates, early convergence checking, eliminating atomic operations, and choosing more efficient mapping operators. Our implementation of the Contour algorithm has been integrated into the open-source framework Arachne. Arachne extends Arkouda for large-scale interactive graph analytics, providing a Python API powered by the high-productivity parallel language Chapel. Experimental results on both real-world and synthetic graphs demonstrate the superior performance of our proposed Contour algorithm compared to state-of-the-art large-scale parallel algorithm FastSV and the fastest shared memory algorithm ConnectIt. On average, Contour achieves a speedup of 7.3x and 1.4x compared to FastSV and ConnectIt, respectively. All code for the Contour algorithm and the Arachne framework is publicly available on GitHub {https://github.com/Bears-R-Us/arkouda-njit), ensuring transparency and reproducibility of our work. 

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3. Generalized Contour Dynamics: A Review

   https://doi.org/10.1134/S1560354718050027  

   Llewellyn Smith, Stefan G. ; Chang, Ching ; Chu, Tianyi ; Blyth, Mark ; Hattori, Yuji ; Salman, Hayder ( September 2018 , Regular and Chaotic Dynamics)
4. The Contour to Classification Game

   Lee, Irene ; Ali, Safinah ( May 2021 , Proceedings of the AAAI Conference on Artificial Intelligence)

   null (Ed.)

   The Contour to Classification game is a browser-based game that teaches middle school students basic concepts in supervised learning. The game is an online variant of the Neural Network game that was presented at AAAI Fall Symposium Teaching AI in K-12 track in 2019. We share preliminary findings from implementing the online version of the original Neural Network game in a pilot research study and describe the game’s evolution to the Contour to Classification game. The new game uses a simulation of a neural network to engage students, through digital drawing and selection interactions, in the classification of images. The players act as nodes in a multi-step process of compositing salient smaller features to form larger features and ultimately a partial contour of an object that is used to make a prediction. After evaluating the prediction, information is sent back through the network in processes mimicking back propagation and gradient descent. Additional rounds of the game can be played to witness how the network evolves and gets “better” at classifying images from contours. Through this game, we aimed for students to learn the structure, components, and functioning of a neural network, and the processes involved in supervised learning. The Contour to Classification game supports online student learning by providing the image classification experience using purely visual inputs to each layer. We will conclude with a discussion of if and how the evolving design addresses classroom needs and scaling considerations. 

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5. Guided Pluralistic Building Contour Completion

   https://doi.org/10.1007/s00371-022-02532-z  

   Zhang, Xiaowei ; Ma, Wufei ; Varinlioglu, Gunder ; Rauh, Nick ; He, Liu ; Aliaga, Daniel ( September 2022 , The visual computer)

   Image/sketch completion is a core task that addresses the problem of completing the missing regions of an image/sketch with realistic and semantically consistent content. We address one type of completion which is producing a tentative completion of an aerial view of the remnants of a building structure. The inference process may start with as little as 10% of the structure and thus is fundamentally pluralistic (e.g., multiple completions are possible). We present a novel pluralistic building contour completion framework. A feature suggestion component uses an entropy-based model to request information from the user for the next most informative location in the image. Then, an image completion component trained using self-supervision and procedurally-generated content produces a partial or full completion. In our synthetic and real-world experiments for archaeological sites in Turkey, with up to only 4 iterations, we complete building footprints having only 10-15% of the ancient structure initially visible. We also compare to various state-of-the-art methods and show our superior quantitative/qualitative performance. While we show results for archaeology, we anticipate our method can be used for restoring highly incomplete historical sketches and for modern day urban reconstruction despite occlusions. 

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