Abstract: There are many works in color that assume illumination change can be modeled by multiplying sensor responses by individual scaling factors. The early research in this area is sometimes grouped under the heading “von Kries adaptation”: the scaling factors are applied to the cone responses. In more recent studies, both in psychophysics and in computational analysis, it has been proposed that scaling factors should be applied to linear combinations of the cones that have narrower support: they should be applied to the so-called “sharp sensors.” In this paper, we generalize the computational approach to spectral sharpening in three important ways. First, we introduce spherical sampling as a tool that allows us to enumerate in a principled way all linear combinations of the cones. This allows us to, second, find the optimal sharp sensors that minimize a variety of error measures including CIE Delta E (previous work on spectral sharpening minimized RMS) and color ratio stability. Lastly, we extend the spherical sampling paradigm to the multispectral case. Here the objective is to model the interaction of light and surface in terms of color signal spectra. Spherical sampling is shown to improve on the state of the art.

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

Abstract: 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.