Related papers: 2D Embeddings of Multi-dimensional Partitionings

One of the founding paradigms of machine learning is that a small number of variables is often sufficient to describe high-dimensional data. The minimum number of variables required is called the intrinsic dimension (ID) of the data.…

Thinning is the removal of contour pixels/points of connected components in an image to produce their skeleton with retained connectivity and structural properties. The output requirements of a thinning procedure often vary with…

In medical imaging analysis, deep learning has shown promising results. We frequently rely on volumetric data to segment medical images, necessitating the use of 3D architectures, which are commended for their capacity to capture interslice…

Unsupervised dimensionality reduction is one of the commonly used techniques in the field of high dimensional data recognition problems. The deep autoencoder network which constrains the weights to be non-negative, can learn a low…

Dimensionality reduction techniques are widely used for visualizing high-dimensional data in two dimensions. Existing methods are typically designed to preserve either local (e.g., $t$-SNE, UMAP) or global (e.g., MDS, PCA) structure of the…

3D modeling is becoming a well-developed field of medicine, but its applicability can be limited due to the lack of software allowing for easy utilizations of generated 3D visualizations. By leveraging recent advances in virtual reality, we…

Most contemporary robots have depth sensors, and research on semantic segmentation with RGBD images has shown that depth images boost the accuracy of segmentation. Since it is time-consuming to annotate images with semantic labels per…

Convolutional neural networks are state-of-the-art for various segmentation tasks. While for 2D images these networks are also computationally efficient, 3D convolutions have huge storage requirements and therefore, end-to-end training is…

In computed tomography, the approximation quality of a scan of a physical object is typically limited by the acquisition modalities, especially the hardware including X-ray detectors. To improve upon this, we experiment with a…

There has been an intense recent activity in embedding of very high dimensional and nonlinear data structures, much of it in the data science and machine learning literature. We survey this activity in four parts. In the first part we cover…

In recent years, deep learning has rapidly become a method of choice for the segmentation of medical images. Deep Neural Network (DNN) architectures such as UNet have achieved state-of-the-art results on many medical datasets. To further…

Finding correspondences is a fundamental and extensively researched problem in computer vision and graphics. In this work, we examine the underexplored task of estimating segmentation-to-segmentation correspondence between images in the…

A new family of combined subdivision schemes with one tension parameter is proposed by the interpolatory and approximating subdivision schemes. The displacement vectors between the points of interpolatory and approximating subdivision…

Despite there being significant work on developing spectral, and metric embedding based approximation algorithms for hypergraph generalizations of conductance, little is known regarding the approximability of hypergraph partitioning…

3D semantic segmentation is a critical task in many real-world applications, such as autonomous driving, robotics, and mixed reality. However, the task is extremely challenging due to ambiguities coming from the unstructured, sparse, and…

Large-scale parallel numerical simulations are essential for a wide range of engineering problems that involve complex, coupled physical processes interacting across a broad range of spatial and temporal scales. The data structures involved…

While the existence of low-dimensional embedding manifolds has been shown in patterns of collective motion, the current battery of nonlinear dimensionality reduction methods are not amenable to the analysis of such manifolds. This is mainly…

Many recent medical segmentation systems rely on powerful deep learning models to solve highly specific tasks. To maximize performance, it is standard practice to evaluate numerous pipelines with varying model topologies, optimization…

Multi-robot systems of increasing size and complexity are used to solve large-scale problems, such as area exploration and search and rescue. A key decision in human-robot teaming is dividing a multi-robot system into teams to address…

This paper presents a well-scaling parallel algorithm for the computation of Morse-Smale (MS) segmentations, including the region separators and region boundaries. The segmentation of the domain into ascending and descending manifolds,…