arXiv subjects

Jiayuan Wang

Publications and source records attributed to Jiayuan Wang.

26 records · Page 2Linked to original sources

arXiv2024

Coincidences between intervals in two partial orders on complex reflection groups

In a finite real reflection group, the reflection length of each element is equal to the codimension of its fixed space, and the two coincident functions determine a partial order structure called the absolute order. In complex reflection groups, the reflection length is no longer always equal to the codimension of fixed space, and the two functions give rise to two different partial orders on the group. We characterize the elements $w$ in the combinatorial family $G(m, p, n)$ of complex reflection groups for which the intervals below $w$ in these two posets coincide. We also explore the relationship between this property and other natural properties of elements in complex reflection groups; some general theory of posets arising from subadditive functions on groups; and the particular case of subadditive functions on the symmetric group.

math.CO↗

arXiv2023

An Attentive-based Generative Model for Medical Image Synthesis

Magnetic resonance (MR) and computer tomography (CT) imaging are valuable tools for diagnosing diseases and planning treatment. However, limitations such as radiation exposure and cost can restrict access to certain imaging modalities. To address this issue, medical image synthesis can generate one modality from another, but many existing models struggle with high-quality image synthesis when multiple slices are present in the dataset. This study proposes an attention-based dual contrast generative model, called ADC-cycleGAN, which can synthesize medical images from unpaired data with multiple slices. The model integrates a dual contrast loss term with the CycleGAN loss to ensure that the synthesized images are distinguishable from the source domain. Additionally, an attention mechanism is incorporated into the generators to extract informative features from both channel and spatial domains. To improve performance when dealing with multiple slices, the $K$-means algorithm is used to cluster the dataset into $K$ groups, and each group is used to train a separate ADC-cycleGAN. Experimental results demonstrate that the proposed ADC-cycleGAN model produces comparable samples to other state-of-the-art generative models, achieving the highest PSNR and SSIM values of 19.04385 and 0.68551, respectively. We publish the code at https://github.com/JiayuanWang-JW/ADC-cycleGAN.

eess.IV↗

arXiv2022

DC-cycleGAN: Bidirectional CT-to-MR Synthesis from Unpaired Data

Magnetic resonance (MR) and computer tomography (CT) images are two typical types of medical images that provide mutually-complementary information for accurate clinical diagnosis and treatment. However, obtaining both images may be limited due to some considerations such as cost, radiation dose and modality missing. Recently, medical image synthesis has aroused gaining research interest to cope with this limitation. In this paper, we propose a bidirectional learning model, denoted as dual contrast cycleGAN (DC-cycleGAN), to synthesize medical images from unpaired data. Specifically, a dual contrast loss is introduced into the discriminators to indirectly build constraints between real source and synthetic images by taking advantage of samples from the source domain as negative samples and enforce the synthetic images to fall far away from the source domain. In addition, cross-entropy and structural similarity index (SSIM) are integrated into the DC-cycleGAN in order to consider both the luminance and structure of samples when synthesizing images. The experimental results indicate that DC-cycleGAN is able to produce promising results as compared with other cycleGAN-based medical image synthesis methods such as cycleGAN, RegGAN, DualGAN, and NiceGAN. The code will be available at https://github.com/JiayuanWang-JW/DC-cycleGAN.

eess.IV↗

arXiv2021

A note on fully commutative elements in complex reflection groups

Fully commutative elements in types $B$ and $D$ are completely characterized and counted by Stembridge. Recently, Feinberg-Kim-Lee-Oh have extended the study of fully commutative elements from Coxeter groups to the complex setting, giving an enumeration of such elements in $G(m,1,n)$. In this note, we prove a connection between fully commutative elements in $B_n$ and in $G(m,1,n)$, which allows us to characterize fully commutative elements in $G(m,1,n )$ by pattern avoidance. Further, we present a counting formula for such elements in $G(m,1,n)$.

math.CO↗

arXiv2021

The Hurwitz action in complex reflection groups

We enumerate Hurwitz orbits of shortest reflection factorizations of an arbitrary element in the infinite family $G(m, p, n)$ of complex reflection groups. As a consequence, we characterize the elements for which the action is transitive and give a simple criterion to tell when two shortest reflection factorizations belong to the same Hurwitz orbit. We also characterize the quasi-Coxeter elements (those with a shortest reflection factorization that generates the whole group) in $G(m, p, n)$.

math.CO↗

arXiv2019

Road Network Reconstruction from Satellite Images with Machine Learning Supported by Topological Methods

Automatic Extraction of road network from satellite images is a goal that can benefit and even enable new technologies. Methods that combine machine learning (ML) and computer vision have been proposed in recent years which make the task semi-automatic by requiring the user to provide curated training samples. The process can be fully automatized if training samples can be produced algorithmically. Of course, this requires a robust algorithm that can reconstruct the road networks from satellite images reliably so that the output can be fed as training samples. In this work, we develop such a technique by infusing a persistence-guided discrete Morse based graph reconstruction algorithm into ML framework. We elucidate our contributions in two phases. First, in a semi-automatic framework, we combine a discrete-Morse based graph reconstruction algorithm with an existing CNN framework to segment input satellite images. We show that this leads to reconstructions with better connectivity and less noise. Next, in a fully automatic framework, we leverage the power of the discrete-Morse based graph reconstruction algorithm to train a CNN from a collection of images without labelled data and use the same algorithm to produce the final output from the segmented images created by the trained CNN. We apply the discrete-Morse based graph reconstruction algorithm iteratively to improve the accuracy of the CNN. We show promising experimental results of this new framework on datasets from SpaceNet Challenge.

cs.CV↗

arXiv2018

Graph Reconstruction by Discrete Morse Theory

Recovering hidden graph-like structures from potentially noisy data is a fundamental task in modern data analysis. Recently, a persistence-guided discrete Morse-based framework to extract a geometric graph from low-dimensional data has become popular. However, to date, there is very limited theoretical understanding of this framework in terms of graph reconstruction. This paper makes a first step towards closing this gap. Specifically, first, leveraging existing theoretical understanding of persistence-guided discrete Morse cancellation, we provide a simplified version of the existing discrete Morse-based graph reconstruction algorithm. We then introduce a simple and natural noise model and show that the aforementioned framework can correctly reconstruct a graph under this noise model, in the sense that it has the same loop structure as the hidden ground-truth graph, and is also geometrically close. We also provide some experimental results for our simplified graph-reconstruction algorithm.

cs.CG↗

arXiv2017

Declutter and Resample: Towards parameter free denoising

In many data analysis applications the following scenario is commonplace: we are given a point set that is supposed to sample a hidden ground truth $K$ in a metric space, but it got corrupted with noise so that some of the data points lie far away from $K$ creating outliers also termed as {\em ambient noise}. One of the main goals of denoising algorithms is to eliminate such noise so that the curated data lie within a bounded Hausdorff distance of $K$. Popular denoising approaches such as deconvolution and thresholding often require the user to set several parameters and/or to choose an appropriate noise model while guaranteeing only asymptotic convergence. Our goal is to lighten this burden as much as possible while ensuring theoretical guarantees in all cases. Specifically, first, we propose a simple denoising algorithm that requires only a single parameter but provides a theoretical guarantee on the quality of the output on general input points. We argue that this single parameter cannot be avoided. We next present a simple algorithm that avoids even this parameter by paying for it with a slight strengthening of the sampling condition on the input points which is not unrealistic. We also provide some preliminary empirical evidence that our algorithms are effective in practice.

cs.CG↗