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Validation of image segmentation methods is of critical importance. Probabilistic image segmentation is increasingly popular as it captures uncertainty in the results. Image segmentation methods that support multi-region (as opposed to…
This paper investigates the algorithmic dimension spectra of lines in the Euclidean plane. Given any line L with slope a and vertical intercept b, the dimension spectrum sp(L) is the set of all effective Hausdorff dimensions of individual…
Constant dimension codes (CDCs) are essential for error correction in random network coding. A fundamental problem of CDCs is to determine their maximal possible size for given parameters. Inserting construction and multilevel construction…
Discrete geometric estimators approach geometric quantities on digitized shapes without any knowledge of the continuous shape. A classical yet difficult problem is to show that an estimator asymptotically converges toward the true geometric…
Two-dimensional superconductivity has become a major frontier in condensed matter physics. It holds the key to the mechanism of high-temperature superconductors and offers an exceptional arena to stabilize emergent quantum states enabled by…
Motivated by the problem of dealing with incomplete or imprecise acquisition of data in computer vision and computer graphics, we extend results concerning the stability of persistent homology with respect to function perturbations to…
We study the configurations of pixels that occur when two digitized straight lines meet each other.
We construct a continuously differentiable curve in the plane that can be covered by a collection of lines such that every line intersects the curve at a single point and the union of the lines has Hausdorff dimension 1. We show that for…
Persistence diagrams (PDs) are used as signatures of point cloud data. Two clouds of points can be compared using the bottleneck distance d_B between their PDs. A potential drawback of this pipeline is that point clouds sampled from…
Accurate image segmentation plays a crucial role in medical image analysis, yet it faces great challenges of various shapes, diverse sizes, and blurry boundaries. To address these difficulties, square kernel-based encoder-decoder…
In high-dimension, low-sample size (HDLSS) data, it is not always true that closeness of two objects reflects a hidden cluster structure. We point out the important fact that it is not the closeness, but the "values" of distance that…
The term "digital twin" (DT) has become a key theme of the cyber-physical systems (CPSs) area, while remaining vaguely defined as a virtual replica of an entity. This article identifies DT characteristics essential for enhancing CPS…
This paper is concerned with screening features in ultrahigh dimensional data analysis, which has become increasingly important in diverse scientific fields. We develop a sure independence screening procedure based on the distance…
Chamfer Distance (CD) and Earth Mover's Distance (EMD) are two broadly adopted metrics for measuring the similarity between two point sets. However, CD is usually insensitive to mismatched local density, and EMD is usually dominated by…
Deploying high-performing 3D medical image segmenters (e.g., nnU-Net) is often limited by memory footprint and inference latency. Compression is therefore necessary, but compact 3D encoders tend to lose fine structural cues (small lesions…
Line segment detection is a fundamental low-level task in computer vision, and improvements in this task can impact more advanced methods that depend on it. Most new methods developed for line segment detection are based on Convolutional…
This paper presents new results about digital straight segments, their recognition and related properties. They come from the study of the arithmetically based recognition algorithm proposed by I. Debled-Rennesson and J.-P. Reveill\`es in…
We relate various concepts of fractal dimension of the limiting set C in fractal percolation to the dimensions of the set consisting of connected components larger than one point and its complement in C (the "dust"). In two dimensions, we…
Line segments are ubiquitous in our human-made world and are increasingly used in vision tasks. They are complementary to feature points thanks to their spatial extent and the structural information they provide. Traditional line detectors…
Recent studies have shown that the nonlinear optical response of crystalline systems is fundamentally a quantum geometric property. In this work, we propose two-dimensional coherent spectroscopy (2DCS), which measures the nonlinear…