GeoUDF: Surface Reconstruction from 3D Point Clouds via Geometry-guided Distance Representation

We present a learning-based method, namely GeoUDF,to tackle the long-standing and challenging problem of reconstructing a discrete surface from a sparse point cloud.To be specific, we propose a geometry-guided learning method for UDF and its gradient estimation that explicitly formulates the unsigned distance of a query point as the learnable affine averaging of its distances to the tangent planes of neighboring points on the surface. Besides,we model the local geometric structure of the input point clouds by explicitly learning a quadratic polynomial for each point. This not only facilitates upsampling the input sparse point cloud but also naturally induces unoriented normal, which further augments UDF estimation. Finally, to extract triangle meshes from the predicted UDF we propose a customized edge-based marching cube module. We conduct extensive experiments and ablation studies to demonstrate the significant advantages of our method over state-of-the-art methods in terms of reconstruction accuracy, efficiency, and generality. The source code is publicly available at https://github.com/rsy6318/GeoUDF

A Sparse Multi-Scale Algorithm for Dense Optimal Transport

Discrete optimal transport solvers do not scale well on dense large problems since they do not explicitly exploit the geometric structure of the cost function. In analogy to continuous optimal transport we provide a framework to verify global optimality of a discrete transport plan locally. This allows construction of an algorithm to solve large dense problems by considering a sequence of sparse problems instead. The algorithm lends itself to being combined with a hierarchical multi-scale scheme. Any existing discrete solver can be used as internal black-box.Several cost functions, including the noisy squared Euclidean distance, are explicitly detailed. We observe a significant reduction of run-time and memory requirements.Comment: Published "online first" in Journal of Mathematical Imaging and Vision, see DO

ACRMiner: An Incremental Approach for Finding Dense and Sparse Rectangular Regions from a 2D Interval Dataset

In many applications, transactions are associated with intervals related to time, temperature, humidity or other similar measures.  The term "2D interval data" or "rectangle data" is used when there are two connected intervals with each transaction. Two connected intervals give rise to a rectangle. The rectangles may overlap producing regions with different density values. The density value or support of a region is the number of rectangles that contain it. A region is closed if its density is strictly bigger than any region properly containing it. For rectangle dataset, these regions are rectangular in shape.In this paper an algorithm named ACRMiner has been proposed that takes as input a sequence of rectangles and computes all closed overlapping rectangles and their density values. The algorithm is incremental and thus is suitable for dynamic environment. Depending on an input threshold the regions can be classified as dense and sparse.Here a tree-based data structure named as ACR-Tree is used. The method has been implemented and tested on synthetic and real-life datasets and results have been reported. Few applications of this algorithm have been discussed. The worst-case time complexity the algorithmis O(n5) where n is the number of input rectangles

Code as Reward: Empowering Reinforcement Learning with VLMs

Pre-trained Vision-Language Models (VLMs) are able to understand visual concepts, describe and decompose complex tasks into sub-tasks, and provide feedback on task completion. In this paper, we aim to leverage these capabilities to support the training of reinforcement learning (RL) agents. In principle, VLMs are well suited for this purpose, as they can naturally analyze image-based observations and provide feedback (reward) on learning progress. However, inference in VLMs is computationally expensive, so querying them frequently to compute rewards would significantly slowdown the training of an RL agent. To address this challenge, we propose a framework named Code as Reward (VLM-CaR). VLM-CaR produces dense reward functions from VLMs through code generation, thereby significantly reducing the computational burden of querying the VLM directly. We show that the dense rewards generated through our approach are very accurate across a diverse set of discrete and continuous environments, and can be more effective in training RL policies than the original sparse environment rewards