A new technique for color reduction of complex document images is presented in this article. It reduces significantly the number of colors of the document image (less than 15 colors in most of the cases) so as to have solid characters and uniform local backgrounds. Therefore, this technique can be used as a preprocessing step by text information extraction applications. Specifically, using the ...

This paper presents a new method for edge-preserving color image denoising based on the tensor voting framework, a robust perceptual grouping technique used to extract salient information from noisy data. The tensor voting framework is adapted to encode color information through tensors in order to propagate them in a neighborhood by using a specific voting process. This voting process is speci...

A colored eulerian digraph is an eulerian digraph G where a color is assigned to the tail of each edge and a color is assigned to the head of each edge. A compatible circuit is an eulerian circuit such that for every two consecutive edges uv and vw of the circuit, the color of the head of uv is different from the color of the tail of vw. Let S3 be the set of vertices of outdegree and indegree t...

Let G be an edge-colored graph and v a vertex of G. The color degree of v is the number of colors appearing on the edges incident to v. A rainbow triangle in G is one in which all edges have distinct colors. In this paper, we first prove that an edge-colored graph on n vertices contains a rainbow triangle if the color degree sum of any two adjacent vertices is at least n+ 1. Afterwards, we char...

In this paper, we present a new method for quantifying color information so as to detect edges in color images. Our method uses the volume of a pixel in the HSI color space, allied with noise reduction, thresholding and edge thinning. We implement our algorithm using NVIDIA Compute Unified Device Architecture (CUDA) for direct execution on Graphics Processing Units (GPUs). Our experimental resu...

We consider finite graphs with no self-loops and no multiple edges. A graph is valid if all edges incident on a vertex have different colors. We prove Vizing’s Theorem. All the edges of a graph of maximum degree less than N can be colored using N colors so that the graph is valid. We call a color incident on a vertex if an edge incident on that vertex has that color; otherwise, the color is fre...

In this letter we propose to denoise digital color images via an improved geometric diffusion scheme. By introducing edges detected from all three color channels into the diffusion the proposed scheme avoids color smearing artifacts. Vector valued diffusion is used to control the smoothing and the geometry of color images are taken into consideration. Color edge strength function computed from ...

In a properly edge colored graph, a subgraph using every color at most once is called rainbow. In this thesis, we study rainbow cycles and paths in proper edge colorings of complete graphs, and we prove that in every proper edge coloring of Kn, there is a rainbow path on (3/4− o(1))n vertices, improving on the previously best bound of (2n + 1)/3 from [?]. Similarly, a k-rainbow path in a proper...

In early 2000’s, Rivest [1,2] and Micali [2] introduced the notion of transitive signature, which allows a third party with public key to generate a valid signature for a composed edge (vi,vk), from the signatures for two edges (vi,v j) and (v j,vk). Since then, a number of works, including [2,3,4,5,6], have been devoted on transitive signatures. Most of them address the undirected transitive s...