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Arpan Kusari

Arpan Kusari contributes to research discovery and scholarly infrastructure.

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Computer Vision Artificial Intelligence Computational Geometry Machine Learning Robotics

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preprint2026arXiv

Encoding Robust Topological Signatures for Hyperdimensional Computing

Hyperdimensional (HD) computing offers an attractive alternative to deep networks for edge learning due to its simplicity, fast prototype-based inference, and compatibility with online updates. However, standard pixel-based HD encoders are brittle: small distribution shifts such as rotation, noise, or occlusion can drastically reduce accuracy. We extract discrete topological primitives-most notably holes-from binarized shapes and pair them with rotation/translation/scale (RTS)-invariant shape signatures. Our method constructs RTS-stable descriptors for (i) the outer shape using a spatial-pyramid variant of Zernike moments and (ii) each hole using an intrinsic Fourier descriptor of its radial signature together with RTS-canonical relative geometry. Each primitive is mapped to a bipolar hypervector via randomized projection and role binding, and variable-cardinality hole sets are aggregated by permutation-invariant bundling to form a single image hypervector. To avoid over-weighting any cue, we learn nonnegative reliability weights for the Zernike and hole channels on a validation set via late fusion of cosine similarities. Experiments on MNIST and EMNIST under controlled corruptions (rotation, Gaussian noise, salt-and-pepper, cutout, zoom) show that Topology-guided HD computing substantially improves robustness compared with a naive HD baseline, maintaining high accuracy across multiple corruption families and benefiting from lightweight online training. Compared with a compact CNN trained on clean data, our method achieves competitive clean accuracy while offering markedly stronger robustness to several pixel-level corruptions, demonstrating that explicit topological structure is a practical route to robust HD representations. The code is provided at https://github.com/arpan-kusari/Topological-HDC.

preprint2022arXiv

Graph-theoretical approach to robust 3D normal extraction of LiDAR data

Low dimensional primitive feature extraction from LiDAR point clouds (such as planes) forms the basis of majority of LiDAR data processing tasks. A major challenge in LiDAR data analysis arises from the irregular nature of LiDAR data that forces practitioners to either regularize the data using some form of gridding or utilize a triangular mesh such as triangulated irregular network (TIN). While there have been a handful applications using LiDAR data as a connected graph, a principled treatment of utilizing graph-theoretical approach for LiDAR data modelling is still lacking. In this paper, we try to bridge this gap by utilizing graphical approach for normal estimation from LiDAR point clouds. We formulate the normal estimation problem in an optimization framework, where we find the corresponding normal vector for each LiDAR point by utilizing its nearest neighbors and simultaneously enforcing a graph smoothness assumption based on point samples. This is a non-linear constrained convex optimization problem which can then be solved using projected conjugate gradient descent to yield an unique solution. As an enhancement to our optimization problem, we also provide different weighted solutions based on the dot product of the normals and Euclidean distance between the points. In order to assess the performance of our proposed normal extraction method and weighting strategies, we first provide a detailed analysis on repeated randomly generated datasets with four different noise levels and four different tuning parameters. Finally, we benchmark our proposed method against existing state-of-the-art approaches on a large scale synthetic plane extraction dataset. The code for the proposed approach along with the simulations and benchmarking is available at https://github.com/arpan-kusari/graph-plane-extraction-simulation.

preprint2020arXiv

Predicting optimal value functions by interpolating reward functions in scalarized multi-objective reinforcement learning

A common approach for defining a reward function for Multi-objective Reinforcement Learning (MORL) problems is the weighted sum of the multiple objectives. The weights are then treated as design parameters dependent on the expertise (and preference) of the person performing the learning, with the typical result that a new solution is required for any change in these settings. This paper investigates the relationship between the reward function and the optimal value function for MORL; specifically addressing the question of how to approximate the optimal value function well beyond the set of weights for which the optimization problem was actually solved, thereby avoiding the need to recompute for any particular choice. We prove that the value function transforms smoothly given a transformation of weights of the reward function (and thus a smooth interpolation in the policy space). A Gaussian process is used to obtain a smooth interpolation over the reward function weights of the optimal value function for three well-known examples: GridWorld, Objectworld and Pendulum. The results show that the interpolation can provide very robust values for sample states and action space in discrete and continuous domain problems. Significant advantages arise from utilizing this interpolation technique in the domain of autonomous vehicles: easy, instant adaptation of user preferences while driving and true randomization of obstacle vehicle behavior preferences during training.

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