Related papers: A Critical Connectivity Radius for Segmenting Rand…
An arithmetical discrete plane is said to have critical connecting thickness if its thickness is equal to the infimum of the set of values that preserve its $2$-connectedness. This infimum thickness can be computed thanks to the fully…
We take a different look at the problem of testing the independence of two metric-space-valued random variables using the distance correlation. Instead of testing if the distance correlation vanishes exactly, we are interested in the…
Besides per-pixel accuracy, topological correctness is also crucial for the segmentation of images with fine-scale structures, e.g., satellite images and biomedical images. In this paper, by leveraging the theory of digital topology, we…
It has been known that the distribution of the random distances between two uniformly distributed points within a convex polygon can be obtained based on its chord length distribution (CLD). In this report, we first verify the existing…
We consider the problem of high-dimensional Ising (graphical) model selection. We propose a simple algorithm for structure estimation based on the thresholding of the empirical conditional variation distances. We introduce a novel criterion…
Fractal geometry proved to be an effective mathematical tool for exploring real geographical space based on digital maps and remote sensing images. Whether the fractal theory tool can be applied to abstract geographical space has not been…
Modes and ridges of the probability density function behind observed data are useful geometric features. Mode-seeking clustering assigns cluster labels by associating data samples with the nearest modes, and estimation of density ridges…
The pivotal quality of proximity graphs is connectivity, i.e. all nodes in the graph are connected to one another either directly or via intermediate nodes. These types of graphs are robust, i.e., they are able to function well even if they…
Interactive image segmentation is a challenging task and receives increasing attention recently; however, two major drawbacks exist in interactive segmentation approaches. First, the segmentation performance of ROI-based methods is…
Networks may, or may not, be wired to have a core that is both itself densely connected and central in terms of graph distance. In this study we propose a coefficient to measure if the network has such a clear-cut core-periphery dichotomy.…
Piecewise constant image approximations of sequential number of segments or clusters of disconnected pixels are treated. The method of majorizing of optimal approximation sequence by hierarchical sequence of image approximations is…
The size of large, geo-located datasets has reached scales where visualization of all data points is inefficient. Random sampling is a method to reduce the size of a dataset, yet it can introduce unwanted errors. We describe a method for…
Visual defect detection plays an important role in intelligent industry. Patch based methods consider visual images as a collection of image patches according to positions, which have stronger discriminative ability for small defects in…
A novel algorithm is proposed for segmenting an image into multiple levels using its mean and variance. Starting from the extreme pixel values at both ends of the histogram plot, the algorithm is applied recursively on sub-ranges computed…
Calculation of near-neighbor interactions among high dimensional, irregularly distributed data points is a fundamental task to many graph-based or kernel-based machine learning algorithms and applications. Such calculations, involving…
We consider a random geometric graph with vertices sampled from a probability measure supported on $\mathbb R^d$, and study its connectivity. We show the graph is typically disconnected, unless the sampling density has superexponential…
Image analysis frequently deals with shape estimation and image reconstruction. The ob jects of interest in these problems may be thought of as random sets, and one is interested in finding a representative, or expected, set. We consider a…
Percolation threshold of a network is the critical value such that when nodes or edges are randomly selected with probability below the value, the network is fragmented but when the probability is above the value, a giant component…
In this paper, we analyze various critical transmitting/sensing ranges for connectivity and coverage in three-dimensional sensor networks. As in other large-scale complex systems, many global parameters of sensor networks undergo phase…
Information theoretical measures, such as entropy, mutual information, and various divergences, exhibit robust characteristics in image registration applications. However, the estimation of these quantities is computationally intensive in…