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Apr 14

A Third-Order Gaussian Process Trajectory Representation Framework with Closed-Form Kinematics for Continuous-Time Motion Estimation

In this paper, we propose a third-order, i.e., white-noise-on-jerk, Gaussian Process (GP) Trajectory Representation (TR) framework for continuous-time (CT) motion estimation (ME) tasks. Our framework features a unified trajectory representation that encapsulates the kinematic models of both SO(3)timesR^3 and SE(3) pose representations. This encapsulation strategy allows users to use the same implementation of measurement-based factors for either choice of pose representation, which facilitates experimentation and comparison to achieve the best model for the ME task. In addition, unique to our framework, we derive the kinematic models with the closed-form temporal derivatives of the local variable of SO(3) and SE(3), which so far has only been approximated based on the Taylor expansion in the literature. Our experiments show that these kinematic models can improve the estimation accuracy in high-speed scenarios. All analytical Jacobians of the interpolated states with respect to the support states of the trajectory representation, as well as the motion prior factors, are also provided for accelerated Gauss-Newton (GN) optimization. Our experiments demonstrate the efficacy and efficiency of the framework in various motion estimation tasks such as localization, calibration, and odometry, facilitating fast prototyping for ME researchers. We release the source code for the benefit of the community. Our project is available at https://github.com/brytsknguyen/gptr.

  • 8 authors
·
Oct 30, 2024

Informed RRT*: Optimal Sampling-based Path Planning Focused via Direct Sampling of an Admissible Ellipsoidal Heuristic

Rapidly-exploring random trees (RRTs) are popular in motion planning because they find solutions efficiently to single-query problems. Optimal RRTs (RRT*s) extend RRTs to the problem of finding the optimal solution, but in doing so asymptotically find the optimal path from the initial state to every state in the planning domain. This behaviour is not only inefficient but also inconsistent with their single-query nature. For problems seeking to minimize path length, the subset of states that can improve a solution can be described by a prolate hyperspheroid. We show that unless this subset is sampled directly, the probability of improving a solution becomes arbitrarily small in large worlds or high state dimensions. In this paper, we present an exact method to focus the search by directly sampling this subset. The advantages of the presented sampling technique are demonstrated with a new algorithm, Informed RRT*. This method retains the same probabilistic guarantees on completeness and optimality as RRT* while improving the convergence rate and final solution quality. We present the algorithm as a simple modification to RRT* that could be further extended by more advanced path-planning algorithms. We show experimentally that it outperforms RRT* in rate of convergence, final solution cost, and ability to find difficult passages while demonstrating less dependence on the state dimension and range of the planning problem.

  • 3 authors
·
Nov 27, 2014

Calibration and Uncertainty for multiRater Volume Assessment in multiorgan Segmentation (CURVAS) challenge results

Deep learning (DL) has become the dominant approach for medical image segmentation, yet ensuring the reliability and clinical applicability of these models requires addressing key challenges such as annotation variability, calibration, and uncertainty estimation. This is why we created the Calibration and Uncertainty for multiRater Volume Assessment in multiorgan Segmentation (CURVAS), which highlights the critical role of multiple annotators in establishing a more comprehensive ground truth, emphasizing that segmentation is inherently subjective and that leveraging inter-annotator variability is essential for robust model evaluation. Seven teams participated in the challenge, submitting a variety of DL models evaluated using metrics such as Dice Similarity Coefficient (DSC), Expected Calibration Error (ECE), and Continuous Ranked Probability Score (CRPS). By incorporating consensus and dissensus ground truth, we assess how DL models handle uncertainty and whether their confidence estimates align with true segmentation performance. Our findings reinforce the importance of well-calibrated models, as better calibration is strongly correlated with the quality of the results. Furthermore, we demonstrate that segmentation models trained on diverse datasets and enriched with pre-trained knowledge exhibit greater robustness, particularly in cases deviating from standard anatomical structures. Notably, the best-performing models achieved high DSC and well-calibrated uncertainty estimates. This work underscores the need for multi-annotator ground truth, thorough calibration assessments, and uncertainty-aware evaluations to develop trustworthy and clinically reliable DL-based medical image segmentation models.

  • 32 authors
·
May 13, 2025