Differentially private $K$-means clustering enables releasing cluster centers derived from a dataset while protecting the privacy of the individuals. Non-interactive clustering techniques based on privatized histograms are attractive because the released data synopsis can be reused for other downstream tasks without additional privacy loss. The choice of the number of grids for discretizing the data points is crucial, as it directly controls the quantization bias and the amount of noise injected to preserve privacy. The widely adopted strategy selects a grid size that is independent of the number of clusters and also relies on empirical tuning. In this work, we revisit this choice and propose a refined grid-size selection rule derived by minimizing an upper bound on the expected deviation in the K-means objective function, leading to a more principled discretization strategy for non-interactive private clustering. Compared to prior work, our grid resolution differs both in its dependence on the number of clusters and in the scaling with dataset size and privacy budget. Extensive numerical results elucidate that the proposed strategy results in accurate clustering compared to the state-of-the-art techniques, even under tight privacy budgets.

Despite significant progress in pixel-level medical image analysis, existing medical image segmentation models rarely explore medical segmentation and diagnosis tasks jointly. However, it is crucial for patients that models can provide explainable diagnoses along with medical segmentation results. In this paper, we introduce a medical vision-language task named Medical Diagnosis Segmentation (MDS), which aims to understand clinical queries for medical images and generate the corresponding segmentation masks as well as diagnostic results. To facilitate this task, we first present the Multimodal Multi-disease Medical Diagnosis Segmentation (M3DS) dataset, containing diverse multimodal multi-disease medical images paired with their corresponding segmentation masks and diagnosis chain-of-thought, created via an automated diagnosis chain-of-thought generation pipeline. Moreover, we propose Sim4Seg, a novel framework that improves the performance of diagnosis segmentation by taking advantage of the Region-Aware Vision-Language Similarity to Mask (RVLS2M) module. To improve overall performance, we investigate a test-time scaling strategy for MDS tasks. Experimental results demonstrate that our method outperforms the baselines in both segmentation and diagnosis.

Next, we supply discussions on the easy initialization property of our Shape-As-Points representation in Section 3. Additional results and ablations for the optimization-based and We solve the PDEs using spectral methods [3]. Work done while at UC Berkeley. Please refer to Section 4.3 for a more in-depth discussion to motivate the use of the We optimize IGR for 15000 iterations on each object until convergence. For Point2Mesh, we follow the official implementation and use 6000 iterations for each object. We generate the initial mesh required by Point2Mesh following the description of the original paper.

We present DPPE, a dense pose estimation algorithm that functions over a Plenoxels environment. Recent advances in neural radiance field techniques have shown that it is a powerful tool for environment representation. More recent neural rendering algorithms have significantly improved both training duration and rendering speed. Plenoxels introduced a fully-differentiable radiance field technique that uses Plenoptic volume elements contained in voxels for rendering, offering reduced training times and better rendering accuracy, while also eliminating the neural net component. In this work, we introduce a 6-DoF monocular RGB-only pose estimation procedure for Plenoxels, which seeks to recover the ground truth camera pose after a perturbation. We employ a variation on classical template matching techniques, using stochastic gradient descent to optimize the pose by minimizing errors in re-rendering. In particular, we examine an approach that takes advantage of the rapid rendering speed of Plenoxels to numerically approximate part of the pose gradient, using a central differencing technique. We show that such methods are effective in pose estimation. Finally, we perform ablations over key components of the problem space, with a particular focus on image subsampling and Plenoxel grid resolution. Project website: https://sites.google.com/view/dppe

Improving the predictive capability and computational cost of dynamical models is often at the heart of augmenting computational physics with machine learning (ML). However, most learning results are limited in interpretability and generalization over different computational grid resolutions, initial and boundary conditions, domain geometries, and physical or problem-specific parameters. In the present study, we simultaneously address all these challenges by developing the novel and versatile methodology of unified neural partial delay differential equations. We augment existing/low-fidelity dynamical models directly in their partial differential equation (PDE) forms with both Markovian and non-Markovian neural network (NN) closure parameterizations. The melding of the existing models with NNs in the continuous spatiotemporal space followed by numerical discretization automatically allows for the desired generalizability. The Markovian term is designed to enable extraction of its analytical form and thus provides interpretability. The non-Markovian terms allow accounting for inherently missing time delays needed to represent the real world. We obtain adjoint PDEs in the continuous form, thus enabling direct implementation across differentiable and non-differentiable computational physics codes, different ML frameworks, and treatment of nonuniformly-spaced spatiotemporal training data. We demonstrate the new generalized neural closure models (gnCMs) framework using four sets of experiments based on advecting nonlinear waves, shocks, and ocean acidification models. Our learned gnCMs discover missing physics, find leading numerical error terms, discriminate among candidate functional forms in an interpretable fashion, achieve generalization, and compensate for the lack of complexity in simpler models. Finally, we analyze the computational advantages of our new framework.

Optical Image Stabilization (OIS) system in mobile devices reduces image blurring by steering lens to compensate for hand jitters. However, OIS changes intrinsic camera parameters (i.e. $\mathrm{K}$ matrix) dynamically which hinders accurate camera pose estimation or 3D reconstruction. Here we propose a novel neural network-based approach that estimates $\mathrm{K}$ matrix in real-time so that pose estimation or scene reconstruction can be run at camera native resolution for the highest accuracy on mobile devices. Our network design takes gratified projection model discrepancy feature and 3D point positions as inputs and employs a Multi-Layer Perceptron (MLP) to approximate $f_{\mathrm{K}}$ manifold. We also design a unique training scheme for this network by introducing a Back propagated PnP (BPnP) layer so that reprojection error can be adopted as the loss function. The training process utilizes precise calibration patterns for capturing accurate $f_{\mathrm{K}}$ manifold but the trained network can be used anywhere. We name the proposed Dynamic Intrinsic Manifold Estimation network as DIME-Net and have it implemented and tested on three different mobile devices. In all cases, DIME-Net can reduce reprojection error by at least $64\%$ indicating that our design is successful.

Mapping people dynamics is a crucial skill, because it enables robots to coexist in human-inhabited environments. However, learning a model of people dynamics is a time consuming process which requires observation of large amount of people moving in an environment. Moreover, approaches for mapping dynamics are unable to transfer the learned models across environments: each model only able to describe the dynamics of the environment it has been built in. However, the effect of architectural geometry on people movement can be used to estimate their dynamics, and recent work has looked into learning maps of dynamics from geometry. So far however, these methods have evaluated their performance only on small-size synthetic data, leaving the actual ability of these approaches to generalize to real conditions unexplored. In this work we propose a novel approach to learn people dynamics from geometry, where a model is trained and evaluated on real human trajectories in large-scale environments. We then show the ability of our method to generalize to unseen environments, which is unprecedented for maps of dynamics.

UV radiation has been used as a disinfection strategy to deactivate a wide range of pathogens, but existing irradiation strategies do not ensure sufficient exposure of all environmental surfaces and/or require long disinfection times. We present a near-optimal coverage planner for mobile UV disinfection robots. The formulation optimizes the irradiation time efficiency, while ensuring that a sufficient dosage of radiation is received by each surface. The trajectory and dosage plan are optimized taking collision and light occlusion constraints into account. We propose a two-stage scheme to approximate the solution of the induced NP-hard optimization, and, for efficiency, perform key irradiance and occlusion calculations on a GPU. Empirical results show that our technique achieves more coverage for the same exposure time as strategies for existing UV robots, can be used to compare UV robot designs, and produces near-optimal plans. This is an extended version of the paper originally contributed to ICRA2021.

A Neural Network (NN) based numerical method is formulated and implemented for solving Boundary Value Problems (BVPs) and numerical results are presented to validate this method by solving Laplace equation with Dirichlet boundary condition and Poisson's equation with mixed boundary conditions. The principal advantage of NN based numerical method is the discrete data points where the field is computed, can be unstructured and do not suffer from issues of meshing like traditional numerical methods such as Finite Difference Time Domain or Finite Element Method. Numerical investigations are carried out for both uniform and non-uniform training grid distributions to understand the efficacy and limitations of this method and to provide qualitative understanding of various parameters involved.