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As the most powerful tool in discrepancy theory, the partial coloring method has wide applications in many problems including the Beck-Fiala problem and Spencer's celebrated result. Currently, there are two major algorithmic methods for the…

Data Structures and Algorithms · Computer Science 2024-08-27 Dongrun Cai , Xue Chen , Wenxuan Shu , Haoyu Wang , Guangyi Zou

Humans perceive the world using multi-modal sensory inputs such as vision, audition, and touch. In this work, we investigate the cross-modal connection between vision and touch. The main challenge in this cross-domain modeling task lies in…

Computer Vision and Pattern Recognition · Computer Science 2019-06-17 Yunzhu Li , Jun-Yan Zhu , Russ Tedrake , Antonio Torralba

The human tri-color vision process may be characterized as follows: 1. A requirement of three scalar quantities to fully define a color (for example, intensity, hue, and purity), with 2. These scalar measures linear in the intensity of the…

Neurons and Cognition · Quantitative Biology 2023-07-12 M. L. Sloan

Given a metric space and a set of distances, one constructs the associated distance graph by taking as vertices the points of the space and as edges the pairs whose distance is in the given set. It is a longstanding open question to…

Combinatorics · Mathematics 2013-05-14 Benoît Kloeckner

Transforming a thermal infrared image into a robust perceptual colour Visible image is an ill-posed problem due to the differences in their spectral domains and in the objects' representations. Objects appear in one spectrum but not…

Computer Vision and Pattern Recognition · Computer Science 2020-03-05 Feras Almasri , Olivier Debeir

We consider the problem of learning a measure of distance among vectors in a feature space and propose a hybrid method that simultaneously learns from similarity ratings assigned to pairs of vectors and class labels assigned to individual…

Machine Learning · Computer Science 2012-07-02 Yi-Hao Kao , Benjamin Van Roy , Daniel Rubin , Jiajing Xu , Jessica Faruque , Sandy Napel

In this paper, we study the following two hypercube coloring problems: Given $n$ and $d$, find the minimum number of colors, denoted as ${\chi}'_{d}(n)$ (resp. ${\chi}_{d}(n)$), needed to color the vertices of the $n$-cube such that any two…

Combinatorics · Mathematics 2010-01-14 Fang-Wei Fu , San Ling , Chaoping Xing

A proper coloring of vertices of a graph is equitable if the sizes of any two color classes differ by at most 1. Such colorings have many applications and are interesting by themselves. In this paper, we discuss the state of art and…

Combinatorics · Mathematics 2025-04-22 H. A. Kierstead , Alexandr Kostochka , Zimu Xiang

Image segmentation has been a very active research topic in image analysis area. Currently, most of the image segmentation algorithms are designed based on the idea that images are partitioned into a set of regions preserving homogeneous…

Computer Vision and Pattern Recognition · Computer Science 2015-03-17 Yu Su , Margaret H. Dunham

We study colorings of the hyperbolic plane, analogously to the Hadwiger-Nelson problem for the Euclidean plane. The idea is to color points using the minimum number of colors such that no two points at distance exactly $d$ are of the same…

Combinatorics · Mathematics 2017-01-31 Hugo Parlier , Camille Petit

Image colorization is the process of colorizing grayscale images or recoloring an already-color image. This image manipulation can be used for grayscale satellite, medical and historical images making them more expressive. With the help of…

Computer Vision and Pattern Recognition · Computer Science 2023-09-27 Ahmed Samir Ragab , Shereen Aly Taie , Howida Youssry Abdelnaby

Visualizing very large matrices involves many formidable problems. Various popular solutions to these problems involve sampling, clustering, projection, or feature selection to reduce the size and complexity of the original task. An…

Human-Computer Interaction · Computer Science 2022-06-06 Leland Wilkinson , Hengrui Luo

We propose a new method for recognizing color image sets using quaternionic Grassmannians, which use the power of quaternions to capture color information and represent each color image set as a point on the quaternionic Grassmannian. We…

Computer Vision and Pattern Recognition · Computer Science 2025-07-18 Xiang Xiang Wang , Tin-Yau Tam

Image restoration models are typically trained with a pixel-wise distance loss defined over the RGB color representation space, which is well known to be a source of blurry and unrealistic textures in the restored images. The reason, we…

Image and Video Processing · Electrical Eng. & Systems 2024-02-07 Jaerin Lee , JoonKyu Park , Sungyong Baik , Kyoung Mu Lee

Measuring the colorfulness of a natural or virtual scene is critical for many applications in image processing field ranging from capturing to display. In this paper, we propose the first deep learning-based colorfulness estimation metric.…

Multimedia · Computer Science 2019-08-23 Emin Zerman , Aakanksha Rana , Aljosa Smolic

A $2$-distance $k$-coloring of a graph is a proper $k$-coloring of the vertices where vertices at distance at most 2 cannot share the same color. We prove the existence of a $2$-distance ($\Delta+2$)-coloring for graphs with maximum average…

Combinatorics · Mathematics 2021-09-27 Hoang La , Mickael Montassier

A $t$-tone coloring of a graph $G$ assigns to each vertex a set of $t$ colors such that any pair of vertices $u, v$ with distance $d$ can share at most $d-1$ colors. In this note, we prove several new results on $t$-tone coloring. For…

Combinatorics · Mathematics 2025-10-16 Patrick Bennett , Jade Nichols

Image colorization is a well-known problem in computer vision. However, due to the ill-posed nature of the task, image colorization is inherently challenging. Though several attempts have been made by researchers to make the colorization…

Computer Vision and Pattern Recognition · Computer Science 2022-08-08 Subhankar Ghosh , Prasun Roy , Saumik Bhattacharya , Umapada Pal , Michael Blumenstein

Imperative visual data frequently vanishes when color applications are seen by partially color blind users. A new method for adaptive interface for accommodating color blind users is presented. The method presented here has two sections: 1)…

Human-Computer Interaction · Computer Science 2017-12-12 Abu Zohran Qaiser , Muhammad Taha Khan

Diffusion models have shown great promise in synthesizing visually appealing images. However, it remains challenging to condition the synthesis at a fine-grained level, for instance, synthesizing image pixels following some generic color…

Computer Vision and Pattern Recognition · Computer Science 2025-03-11 Ka Chun Shum , Binh-Son Hua , Duc Thanh Nguyen , Sai-Kit Yeung