Vertex coloring of plane graphs with nonrepetitive boundary paths

A sequence $s_1,s_2,...,s_k,s_1,s_2,...,s_k$ is a repetition. A sequence $S$ is nonrepetitive, if no subsequence of consecutive terms of $S$ form a repetition. Let $G$ be a vertex colored graph. A path of $G$ is nonrepetitive, if the sequence of colors on its vertices is nonrepetitive. If $G$ is a plane graph, then a facial nonrepetitive vertex coloring of $G$ is a vertex coloring such that any facial path is nonrepetitive. Let $\pi_f(G)$ denote the minimum number of colors of a facial nonrepetitive vertex coloring of $G$. Jendro\vl and Harant posed a conjecture that $\pi_f(G)$ can be bounded from above by a constant. We prove that $\pi_f(G)\le 24$ for any plane graph $G$

On the facial Thue choice index via entropy compression

A sequence is nonrepetitive if it contains no identical consecutive subsequences. An edge colouring of a path is nonrepetitive if the sequence of colours of its consecutive edges is nonrepetitive. By the celebrated construction of Thue, it is possible to generate nonrepetitive edge colourings for arbitrarily long paths using only three colours. A recent generalization of this concept implies that we may obtain such colourings even if we are forced to choose edge colours from any sequence of lists of size 4 (while sufficiency of lists of size 3 remains an open problem). As an extension of these basic ideas, Havet, Jendrol', Sot\'ak and \v{S}krabul'\'akov\'a proved that for each plane graph, 8 colours are sufficient to provide an edge colouring so that every facial path is nonrepetitively coloured. In this paper we prove that the same is possible from lists, provided that these have size at least 12. We thus improve the previous bound of 291 (proved by means of the Lov\'asz Local Lemma). Our approach is based on the Moser-Tardos entropy-compression method and its recent extensions by Grytczuk, Kozik and Micek, and by Dujmovi\'c, Joret, Kozik and Wood

Segmentation and Classification of Polarimetric SAR Data based on the KummerU Distribution

International audienceThinner spatial features can be observed from the high resolution of newly available spaceborne and airborne SAR images. Heterogeneous clutter models should be used to model the covariance matrix because each resolution cell contains only a small number of scatterers. In this paper, we focus on the use of a Fisher probability density function (pdf) to model the SAR clutter. First, the benefit of using such a pdf is exposed. Covariance matrix statistics are then analyzed in details. For a Fisher distributed texture, the covariance matrix follows a KummerU pdf. Asymptotic cases of this pdf are presented. Finally, the KummerU pdf is implemented in both hierarchical segmentation and classification algorithms. Segmentation and classification results are shown on both synthetic and real data

Segmentation and Classification of Polarimetric SAR Data based on the KummerU Distribution

International audienceThinner spatial features can be observed from the high resolution of newly available spaceborne and airborne SAR images. Heterogeneous clutter models should be used to model the covariance matrix because each resolution cell contains only a small number of scatterers. In this paper, we focus on the use of a Fisher probability density function (pdf) to model the SAR clutter. First, the benefit of using such a pdf is exposed. Covariance matrix statistics are then analyzed in details. For a Fisher distributed texture, the covariance matrix follows a KummerU pdf. Asymptotic cases of this pdf are presented. Finally, the KummerU pdf is implemented in both hierarchical segmentation and classification algorithms. Segmentation and classification results are shown on both synthetic and real data

Using Quad‐Pol and Single‐Pol RADARSAT‐2 Data for Monitoring Cold Alpine and Outlet Antarctic Glaciers

International audienceThis paper presents some applications of the Maximum Likelihood (ML) texture tracking on displacement estimation of some alpine and antarctic glaciers surfaces. This method is adapted to the statistical characteristic of the new High Resolution (HR) Polarimetric SAR (Pol- SAR) data. The ML texture tracking method is firstly reminded and a statistical model of HR PolSAR data is explained. The main part of this paper is focused on the application of this method on glaciers monitoring. Three different glaciers have been chosen to test the algorithm: a cold alpine glacier, a temperate alpine glacier and an outlet antarctic glacier. The accuracy and limits of the method are highlighted in each case and results application is discussed

Maximum Likelihood Shift Estimation using High Resolution Polarimetric SAR Clutter Model

International audienceThis paper deals with a Maximum Likelihood (ML) shift estimation method in the context of High Resolution (HR) Polarimetric SAR (PolSAR) clutter. Texture modeling is exposed and the generalized ML texture tracking method is extended to the merging of various sensors. Some results on displacement estimation on the Argentiere glacier in the Mont Blanc massif using dual-pol TerraSAR-X (TSX) and quad-pol RADARSAT-2 (RS2) sensors are finally discussed

Red fluorescence of the triplefin Tripterygion delaisi is increasingly visible against background light with increasing depth

The light environment in water bodies changes with depth due to the absorption of short and long wavelengths. Below 10 m depth, red wavelengths are almost completely absent rendering any red-reflecting animal dark and achromatic. However, fluorescence may produce red coloration even when red light is not available for reflection. A large number of marine taxa including over 270 fish species are known to produce red fluorescence, yet it is unclear under which natural light environment fluorescence contributes perceptively to their colours. To address this question we: (i) characterized the visual system of Tripterygion delaisi, which possesses fluorescent irides, (ii) separated the colour of the irides into its reflectance and fluorescence components and (iii) combined these data with field measurements of the ambient light environment to calculate depth-dependent perceptual chromatic and achromatic contrasts using visual modelling. We found that triplefins have cones with at least three different spectral sensitivities, including differences between the two members of the double cones, giving them the potential for trichromatic colour vision. We also show that fluorescence contributes increasingly to the radiance of the irides with increasing depth. Our results support the potential functionality of red fluorescence, including communicative roles such as species and sex identity, and non-communicative roles such as camouflage