Sachit Rao

Ranjani Niranjan, Sachit Rao

Standard metrics of performance of classifiers, such as accuracy and sensitivity, do not reveal the trust or confidence in the predicted labels of data. While other metrics such as the computed probability of a label or the signed distance from a hyperplane can act as a trust measure, these are subjected to heuristic thresholds. This paper presents a convex optimization-based supervised classifier that sequentially partitions a dataset into several ellipsoids, where each ellipsoid contains nearly all points of the same label. By stating classification rules based on this partitioning, Bayes' formula is then applied to calculate a trust score to a label assigned to a test datapoint determined from these rules. The proposed Sequential Ellipsoidal Partitioning Classifier (SEP-C) exposes dataset irregularities, such as degree of overlap, without requiring a separate exploratory data analysis. The rules of classification, which are free of hyperparameters, are also not affected by class-imbalance, the underlying data distribution, or number of features. SEP-C does not require the use of non-linear kernels when the dataset is not linearly separable. The performance, and comparison with other methods, of SEP-C is demonstrated on the XOR-problem, circle dataset, and other open-source datasets.

Prateeth Rao, Sachit Rao

A key component of Visual Simultaneous Localization and Mapping (VSLAM) is estimating relative camera poses using matched keypoints. Accurate estimation is challenged by noisy correspondences. Classical methods rely on stochastic hypothesis sampling and iterative estimation, while learning-based methods often lack explicit geometric structure. In this work, we reformulate relative pose estimation as a relational inference problem over epipolar correspondence graphs, where matched keypoints are nodes and nearby ones are connected by edges. Graph operations such as pruning, message passing, and pooling estimate a quaternion rotation, translation vector, and the Essential Matrix (EM). Minimizing a loss comprising (i) $\mathcal{L}_2$ differences with ground truth (GT), (ii) Frobenius norm between estimated and GT EMs, (iii) singular value differences, (iv) heading angle differences, and (v) scale differences, yields the relative pose between image pairs. The dense detector-free method LoFTR is used for matching. Experiments on indoor and outdoor benchmarks show improved robustness to dense noise and large baseline variation compared to classical and learning-guided approaches, highlighting the effectiveness of global relational consensus.