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In this paper, we design parallel write-efficient geometric algorithms that perform asymptotically fewer writes than standard algorithms for the same problem. This is motivated by emerging non-volatile memory technologies with read…

This paper introduces the MeshAC package, which generates three-dimensional adaptive meshes tailored for the efficient and robust implementation of multiscale coupling methods. While Delaunay triangulation is commonly used for mesh…

Variational Physics-Informed Neural Networks often suffer from poor convergence when using stochastic gradient-descent-based optimizers. By introducing a Least Squares solver for the weights of the last layer of the neural network, we…

Object oriented bounding box tree (OBB-Tree for short) has many applications in collision detection, real-time rendering, etc. It has a wide range of applications. The construction of the hierarchical directed bounding box of the solid mesh…

A concurrent binary tree (CBT) is a GPU-friendly data-structure suitable for the generation of bisection based terrain tessellations, i.e., adaptive triangulations over square domains. In this paper, we expand the benefits of this…

In a series of recent works, we have generalised the consistency results in the stochastic block model literature to the case of uniform and non-uniform hypergraphs. The present paper continues the same line of study, where we focus on…

We use Deep Convolutional Neural Networks (DCNNs) for image segmentation problems. DCNNs can well extract the features from natural images. However, the classification functions in the existing network architecture of CNNs are simple and…

The set of 2-dimensional packing problems builds an important class of optimization problems and Strip Packing together with 2-dimensional Bin Packing and 2-dimensional Knapsack is one of the most famous of these problems. Given a set of…

The irregular geometry and high inter-slice variability in computerized tomography (CT) scans of the human pancreas make an accurate segmentation of this crucial organ a challenging task for existing data-driven deep learning methods. To…

Convolutional Neural Network (CNN)-based machine learning systems have made breakthroughs in feature extraction and image recognition tasks in two dimensions (2D). Although there is significant ongoing work to apply CNN technology to…

Urban reconstruction from a video captured by a surveying vehicle constitutes a core module of automated mapping. When computational power represents a limited resource and, a detailed map is not the primary goal, the reconstruction can be…

3D hierarchical semantic segmentation (3DHS) is crucial for embodied intelligence applications that demand a multi-grained and multi-hierarchy understanding of 3D scenes. Despite the progress, previous 3DHS methods have overlooked following…

The spread of a finite set of points is the ratio between the longest and shortest pairwise distances. We prove that the Delaunay triangulation of any set of n points in R^3 with spread D has complexity O(D^3). This bound is tight in the…

Point matching refers to the process of finding spatial transformation and correspondences between two sets of points. In this paper, we focus on the case that there is only partial overlap between two point sets. Following the approach of…

Brain tumor segmentation plays a pivotal role in medical image processing. In this work, we aim to segment brain MRI volumes. 3D convolution neural networks (CNN) such as 3D U-Net and V-Net employing 3D convolutions to capture the…

Convexity is a fundamental geometric prior that underlies many natural and man-made structures, yet remains challenging to impose effectively in end-to-end trainable segmentation networks. We revisit convexity from a functional perspective…

Convolutional neural networks (CNNs) have made resounding success in many computer vision tasks such as image classification and object detection. However, their performance degrades rapidly on tougher tasks where images are of low…

We describe a new algorithm to compute the geometric intersection number between two curves, given as edge vectors on an ideal triangulation. Most importantly, this algorithm runs in polynomial time in the bit-size of the two edge vectors.…

Treemaps have been widely applied to the visualization of hierarchical data. A treemap takes a weighted tree and visualizes its leaves in a nested planar geometric shape, with sub-regions partitioned such that each sub-region has an area…

3D Gaussian Splatting (3DGS) has emerged as a powerful technique for radiance field rendering, but it typically requires millions of redundant Gaussian primitives, overwhelming memory and rendering budgets. Existing compaction approaches…