Accelerating Random Kaczmarz Algorithm Based on Clustering Information

Kaczmarz algorithm is an efficient iterative algorithm to solve overdetermined consistent system of linear equations. During each updating step, Kaczmarz chooses a hyperplane based on an individual equation and projects the current estimate for the exact solution onto that space to get a new estimate. Many vairants of Kaczmarz algorithms are proposed on how to choose better hyperplanes. Using the property of randomly sampled data in high-dimensional space, we propose an accelerated algorithm based on clustering information to improve block Kaczmarz and Kaczmarz via Johnson-Lindenstrauss lemma. Additionally, we theoretically demonstrate convergence improvement on block Kaczmarz algorithm

Where2Explore: Few-shot Affordance Learning for Unseen Novel Categories of Articulated Objects

Articulated object manipulation is a fundamental yet challenging task in robotics. Due to significant geometric and semantic variations across object categories, previous manipulation models struggle to generalize to novel categories. Few-shot learning is a promising solution for alleviating this issue by allowing robots to perform a few interactions with unseen objects. However, extant approaches often necessitate costly and inefficient test-time interactions with each unseen instance. Recognizing this limitation, we observe that despite their distinct shapes, different categories often share similar local geometries essential for manipulation, such as pullable handles and graspable edges - a factor typically underutilized in previous few-shot learning works. To harness this commonality, we introduce 'Where2Explore', an affordance learning framework that effectively explores novel categories with minimal interactions on a limited number of instances. Our framework explicitly estimates the geometric similarity across different categories, identifying local areas that differ from shapes in the training categories for efficient exploration while concurrently transferring affordance knowledge to similar parts of the objects. Extensive experiments in simulated and real-world environments demonstrate our framework's capacity for efficient few-shot exploration and generalization

DSM-Net: Disentangled Structured Mesh Net for Controllable Generation of Fine Geometry

3D shape generation is a fundamental operation in computer graphics. While significant progress has been made, especially with recent deep generative models, it remains a challenge to synthesize high-quality geometric shapes with rich detail and complex structure, in a controllable manner. To tackle this, we introduce DSM-Net, a deep neural network that learns a disentangled structured mesh representation for 3D shapes, where two key aspects of shapes, geometry and structure, are encoded in a synergistic manner to ensure plausibility of the generated shapes, while also being disentangled as much as possible. This supports a range of novel shape generation applications with intuitive control, such as interpolation of structure (geometry) while keeping geometry (structure) unchanged. To achieve this, we simultaneously learn structure and geometry through variational autoencoders (VAEs) in a hierarchical manner for both, with bijective mappings at each level. In this manner we effectively encode geometry and structure in separate latent spaces, while ensuring their compatibility: the structure is used to guide the geometry and vice versa. At the leaf level, the part geometry is represented using a conditional part VAE, to encode high-quality geometric details, guided by the structure context as the condition. Our method not only supports controllable generation applications, but also produces high-quality synthesized shapes, outperforming state-of-the-art methods

COPILOT: Human Collision Prediction and Localization from Multi-view Egocentric Videos

To produce safe human motions, assistive wearable exoskeletons must be equipped with a perception system that enables anticipating potential collisions from egocentric observations. However, previous approaches to exoskeleton perception greatly simplify the problem to specific types of environments, limiting their scalability. In this paper, we propose the challenging and novel problem of predicting human-scene collisions for diverse environments from multi-view egocentric RGB videos captured from an exoskeleton. By classifying which body joints will collide with the environment and predicting a collision region heatmap that localizes potential collisions in the environment, we aim to develop an exoskeleton perception system that generalizes to complex real-world scenes and provides actionable outputs for downstream control. We propose COPILOT, a video transformer-based model that performs both collision prediction and localization simultaneously, leveraging multi-view video inputs via a proposed joint space-time-viewpoint attention operation. To train and evaluate the model, we build a synthetic data generation framework to simulate virtual humans moving in photo-realistic 3D environments. This framework is then used to establish a dataset consisting of 8.6M egocentric RGBD frames to enable future work on the problem. Extensive experiments suggest that our model achieves promising performance and generalizes to unseen scenes as well as real world. We apply COPILOT to a downstream collision avoidance task, and successfully reduce collision cases by 29% on unseen scenes using a simple closed-loop control algorithm.Comment: 8 pages, 6 figure