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Author |
Olivier Penacchio |
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Title |
Mixed Hodge Structures and Equivariant Sheaves on the Projective Plane |
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Journal Article |
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Year |
2011 |
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Mathematische Nachrichten |
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MN |
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284 |
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4 |
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526-542 |
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Mixed Hodge structures, equivariant sheaves, MSC (2010) Primary: 14C30, Secondary: 14F05, 14M25 |
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Abstract |
We describe an equivalence of categories between the category of mixed Hodge structures and a category of equivariant vector bundles on a toric model of the complex projective plane which verify some semistability condition. We then apply this correspondence to define an invariant which generalizes the notion of R-split mixed Hodge structure and give calculations for the first group of cohomology of possibly non smooth or non-complete curves of genus 0 and 1. Finally, we describe some extension groups of mixed Hodge structures in terms of equivariant extensions of coherent sheaves. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim |
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WILEY-VCH Verlag |
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R. Mennicken |
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1522-2616 |
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Admin @ si @ Pen2011 |
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1721 |
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Author |
C. Alejandro Parraga; Jordi Roca; Maria Vanrell |
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Title |
Do Basic Colors Influence Chromatic Adaptation? |
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Journal Article |
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Year |
2011 |
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Journal of Vision |
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VSS |
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11 |
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11 |
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85 |
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Color constancy (the ability to perceive colors relatively stable under different illuminants) is the result of several mechanisms spread across different neural levels and responding to several visual scene cues. It is usually measured by estimating the perceived color of a grey patch under an illuminant change. In this work, we hypothesize whether chromatic adaptation (without a reference white or grey) could be driven by certain colors, specifically those corresponding to the universal color terms proposed by Berlin and Kay (1969). To this end we have developed a new psychophysical paradigm in which subjects adjust the color of a test patch (in CIELab space) to match their memory of the best example of a given color chosen from the universal terms list (grey, red, green, blue, yellow, purple, pink, orange and brown). The test patch is embedded inside a Mondrian image and presented on a calibrated CRT screen inside a dark cabin. All subjects were trained to “recall” their most exemplary colors reliably from memory and asked to always produce the same basic colors when required under several adaptation conditions. These include achromatic and colored Mondrian backgrounds, under a simulated D65 illuminant and several colored illuminants. A set of basic colors were measured for each subject under neutral conditions (achromatic background and D65 illuminant) and used as “reference” for the rest of the experiment. The colors adjusted by the subjects in each adaptation condition were compared to the reference colors under the corresponding illuminant and a “constancy index” was obtained for each of them. Our results show that for some colors the constancy index was better than for grey. The set of best adapted colors in each condition were common to a majority of subjects and were dependent on the chromaticity of the illuminant and the chromatic background considered. |
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1534-7362 |
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Admin @ si @ PRV2011 |
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1759 |
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Fahad Shahbaz Khan; Joost Van de Weijer; Maria Vanrell |
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Title |
Modulating Shape Features by Color Attention for Object Recognition |
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Journal Article |
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Year |
2012 |
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International Journal of Computer Vision |
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IJCV |
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98 |
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1 |
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49-64 |
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Bag-of-words based image representation is a successful approach for object recognition. Generally, the subsequent stages of the process: feature detection,feature description, vocabulary construction and image representation are performed independent of the intentioned object classes to be detected. In such a framework, it was found that the combination of different image cues, such as shape and color, often obtains below expected results. This paper presents a novel method for recognizing object categories when using ultiple cues by separately processing the shape and color cues and combining them by modulating the shape features by category specific color attention. Color is used to compute bottom up and top-down attention maps. Subsequently, these color attention maps are used to modulate the weights of the shape features. In regions with higher attention shape features are given more weight than in regions with low attention. We compare our approach with existing methods that combine color and shape cues on five data sets containing varied importance of both cues, namely, Soccer (color predominance), Flower (color and hape parity), PASCAL VOC 2007 and 2009 (shape predominance) and Caltech-101 (color co-interference). The experiments clearly demonstrate that in all five data sets our proposed framework significantly outperforms existing methods for combining color and shape information. |
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Springer Netherlands |
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0920-5691 |
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Admin @ si @ KWV2012 |
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1864 |
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Javier Vazquez; J. Kevin O'Regan; Maria Vanrell; Graham D. Finlayson |
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A new spectrally sharpened basis to predict colour naming, unique hues, and hue cancellation |
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2012 |
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Journal of Vision |
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VSS |
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12 |
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6 (7) |
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1-14 |
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When light is reflected off a surface, there is a linear relation between the three human photoreceptor responses to the incoming light and the three photoreceptor responses to the reflected light. Different colored surfaces have different linear relations. Recently, Philipona and O'Regan (2006) showed that when this relation is singular in a mathematical sense, then the surface is perceived as having a highly nameable color. Furthermore, white light reflected by that surface is perceived as corresponding precisely to one of the four psychophysically measured unique hues. However, Philipona and O'Regan's approach seems unrelated to classical psychophysical models of color constancy. In this paper we make this link. We begin by transforming cone sensors to spectrally sharpened counterparts. In sharp color space, illumination change can be modeled by simple von Kries type scalings of response values within each of the spectrally sharpened response channels. In this space, Philipona and O'Regan's linear relation is captured by a simple Land-type color designator defined by dividing reflected light by incident light. This link between Philipona and O'Regan's theory and Land's notion of color designator gives the model biological plausibility. We then show that Philipona and O'Regan's singular surfaces are surfaces which are very close to activating only one or only two of such newly defined spectrally sharpened sensors, instead of the usual three. Closeness to zero is quantified in a new simplified measure of singularity which is also shown to relate to the chromaticness of colors. As in Philipona and O'Regan's original work, our new theory accounts for a large variety of psychophysical color data. |
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Admin @ si @ VOV2012 |
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1998 |
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Javier Vazquez; Maria Vanrell; Ramon Baldrich; Francesc Tous |
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Title |
Color Constancy by Category Correlation |
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Journal Article |
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2012 |
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IEEE Transactions on Image Processing |
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TIP |
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21 |
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4 |
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1997-2007 |
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Finding color representations which are stable to illuminant changes is still an open problem in computer vision. Until now most approaches have been based on physical constraints or statistical assumptions derived from the scene, while very little attention has been paid to the effects that selected illuminants have
on the final color image representation. The novelty of this work is to propose
perceptual constraints that are computed on the corrected images. We define the
category hypothesis, which weights the set of feasible illuminants according to their ability to map the corrected image onto specific colors. Here we choose these colors as the universal color categories related to basic linguistic terms which have been psychophysically measured. These color categories encode natural color statistics, and their relevance across different cultures is indicated by the fact that they have received a common color name. From this category hypothesis we propose a fast implementation that allows the sampling of a large set of illuminants. Experiments prove that our method rivals current state-of-art performance without the need for training algorithmic parameters. Additionally, the method can be used as a framework to insert top-down information from other sources, thus opening further research directions in solving for color constancy. |
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1057-7149 |
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Admin @ si @ VVB2012 |
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1999 |
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