arXiv subjects

Tin Tran

Publications and source records attributed to Tin Tran.

8 recordsLinked to original sources

arXiv2025

KeyPointDiffuser: Unsupervised 3D Keypoint Learning via Latent Diffusion Models

Understanding and representing the structure of 3D objects in an unsupervised manner remains a core challenge in computer vision and graphics. Most existing unsupervised keypoint methods are not designed for unconditional generative settings, restricting their use in modern 3D generative pipelines; our formulation explicitly bridges this gap. We present an unsupervised framework for learning spatially structured 3D keypoints from point cloud data. These keypoints serve as a compact and interpretable representation that conditions an Elucidated Diffusion Model (EDM) to reconstruct the full shape. The learned keypoints exhibit repeatable spatial structure across object instances and support smooth interpolation in keypoint space, indicating that they capture geometric variation. Our method achieves strong performance across diverse object categories, yielding a 6 percentage-point improvement in keypoint consistency compared to prior approaches.

cs.CV↗

arXiv2025

Heteroscedasticity of Denoising Score Matching with Generalised Smooth Noise

Score Matching (SM) is a powerful framework for estimating the log-density derivatives of a distribution without calculating its normalizing constants. This capability has made it a cornerstone across multiple domains, from classical sta- tistical estimation and energy-based models to modern diffusion-based generative models. In practice, these models rely almost exclusively on Denoising Score Matching (DSM) as a tractable proxy for score matching. This ubiquity naturally raises a fundamental question: Is DSM truly "score matching for free"? In this work, we demonstrate that DSM is not a perfect substitute. We prove that the denoising objective is inherently heteroscedastic, the variance of model parame- ters fluctuates unpredictably based on both noise levels and the underlying data geometry. This instability is baked into the mathematical structure of the DSM. To address this, we derive an ideal weighting function that equalizes this variance, yielding a homoscedastic generalization of DSM. Since the ideal weights are of- ten empirically inaccessible, we show that a practical approximation weighting function via Taylor expansion reduces gradient variance during training, at the cost of statistical optimality. Notably, this provides a theoretical justification for an existing heuristic weight used in Isotropic Gaussian Diffusion. We validate our theory across different perturbed distributions and for higher-order scores.

cs.LG↗

arXiv2023

Real matrices whose columns have equal modulus coordinates

We study $m \times n$ matrices whose columns are of the form \[\{(a_{1j},\ldots, a_{nj}): \quad a_{1j} = \lambda_j,\ a_{ij} = \pm\lambda_j\ , \ \lambda_j >0 ,\ j=1,2,\ldots,n\}.\] We explicitly construct for all $a = (a_1,\ldots, a_{\frac{m(m- 1)}{2}}) \in \mathbb{R}^{\frac{m(m-1)}{2}}$ a matrix of the above form whose rows have pairwise dot product equal to $a$. Using Hardamard matrices constructed by Sylvester we classify all matrices of the above form whose rows have pairwise dot product equal to $a$. We also use our results to reformulate the Hadamard conjecture.

math.CO↗

arXiv2022

Comparing Subjective Perceptions of Robot-to-Human Handover Trajectories

Robots must move legibly around people for safety reasons, especially for tasks where physical contact is possible. One such task is handovers, which requires implicit communication on where and when physical contact (object transfer) occurs. In this work, we study whether the trajectory model used by a robot during the reaching phase affects the subjective perceptions of receivers for robot-to-human handovers. We conducted a user study where 32 participants were handed over three objects with four trajectory models: three were versions of a minimum jerk trajectory, and one was an ellipse-fitting-based trajectory. The start position of the handover was fixed for all trajectories, and the end position was allowed to vary randomly around a fixed position by $\pm$3 cm in all axis. The user study found no significant differences among the handover trajectories in survey questions relating to safety, predictability, naturalness, and other subjective metrics. While these results seemingly reject the hypothesis that the trajectory affects human perceptions of a handover, it prompts future research to investigate the effect of other variables, such as robot speed, object transfer position, object orientation at the transfer point, and explicit communication signals such as gaze and speech.

cs.RO↗

arXiv2022

Visibility Maximization Controller for Robotic Manipulation

Occlusions caused by a robot's own body is a common problem for closed-loop control methods employed in eye-to-hand camera setups. We propose an optimization-based reactive controller that minimizes self-occlusions while achieving a desired goal pose. The approach allows coordinated control between the robot's base, arm and head by encoding the line-of-sight visibility to the target as a soft constraint along with other task-related constraints, and solving for feasible joint and base velocities. The generalizability of the approach is demonstrated in simulated and real-world experiments, on robots with fixed or mobile bases, with moving or fixed objects, and multiple objects. The experiments revealed a trade-off between occlusion rates and other task metrics. While a planning-based baseline achieved lower occlusion rates than the proposed controller, it came at the expense of highly inefficient paths and a significant drop in the task success. On the other hand, the proposed controller is shown to improve visibility to the line target object(s) without sacrificing too much from the task success and efficiency. Videos and code can be found at: rhys-newbury.github.io/projects/vmc/.

cs.RO↗

arXiv2021

Demonstrating Cloth Folding to Robots: Design and Evaluation of a 2D and a 3D User Interface

An appropriate user interface to collect human demonstration data for deformable object manipulation has been mostly overlooked in the literature. We present an interaction design for demonstrating cloth folding to robots. Users choose pick and place points on the cloth and can preview a visualization of a simulated cloth before real-robot execution. Two interfaces are proposed: A 2D display-and-mouse interface where points are placed by clicking on an image of the cloth, and a 3D Augmented Reality interface where the chosen points are placed by hand gestures. We conduct a user study with 18 participants, in which each user completed two sequential folds to achieve a cloth goal shape. Results show that while both interfaces were acceptable, the 3D interface was found to be more suitable for understanding the task, and the 2D interface suitable for repetition. Results also found that fold previews improve three key metrics: task efficiency, the ability to predict the final shape of the cloth and overall user satisfaction.

cs.RO↗

arXiv2021

An Experimental Validation and Comparison of Reaching Motion Models for Unconstrained Handovers: Towards Generating Humanlike Motions for Human-Robot Handovers

The Minimum Jerk motion model has long been cited in literature for human point-to-point reaching motions in single-person tasks. While it has been demonstrated that applying minimum-jerk-like trajectories to robot reaching motions in the joint action task of human-robot handovers allows a robot giver to be perceived as more careful, safe, and skilled, it has not been verified whether human reaching motions in handovers follow the Minimum Jerk model. To experimentally test and verify motion models for human reaches in handovers, we examined human reaching motions in unconstrained handovers (where the person is allowed to move their whole body) and fitted against 1) the Minimum Jerk model, 2) its variation, the Decoupled Minimum Jerk model, and 3) the recently proposed Elliptical (Conic) model. Results showed that Conic model fits unconstrained human handover reaching motions best. Furthermore, we discovered that unlike constrained, single-person reaching motions, which have been found to be elliptical, there is a split between elliptical and hyperbolic conic types. We expect our results will help guide generation of more humanlike reaching motions for human-robot handover tasks.

cs.RO↗

arXiv2017

The exact constant for the $\ell_1-\ell_2$ norm inequality

A fundamental inequality for Hilbert spaces is the $\ell_1-\ell_2$-norm inequality which gives that for any $x \in H^n$, $\|x\|_1\le \sqrt{n}\|x\|_2.$ But this is a strict inequality for all but vectors with constant modulus for their coefficients. We will give a trivial method to compute, for each x, the constant $c$ for which $\|x\|_1=c\sqrt{n}\|x\|_2.$ Since this inequality is one of the most used results in Hilbert space theory, we believe this will have unlimited applications in the field. We will also show some variations of this result.

math.FA↗