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Fast Colour2Grey

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A standard approach to generating a greyscale equivalent to an input colour image involves calculating the so-called structure tensor at each image pixel. Defining contrast as associated with the maximum-change direction of this matrix, the grey gradient is identified with the first eigenvector direction, with gradient strength given by the square root of its eigenvalue. However, aside from the inherent complexity of such an approach, each pixel's gradient still possesses a sign ambiguity, since an eigenvector is given only up to a sign. This is ostensibly resolved by looking at how one of the R,G,B colour channels behaves, or how the the luminance changes. Instead, we would like to circumvent the sign problem in the first place, and also avoid calculating the costly eigenvector decomposition. So here we suggest replacing the eigenvector approach by generating a greyscale gradient equal to the maximum gradient amongst the R,G,B gradients, in each of x, y. But in order not to neglect the tensor approach, we consider the relationship between the complex and the simple approaches. We also note that, at each pixel, we have both forward-facing and backward-facing derivatives, which are different, and we consider a tensor formed from both. Then, over a standard training set, we ask for an optimum set of weights for all the maximum gradients such that the simple maxima scheme generates a greyscale structure tensor to best match the original, colour, one. We find that a simple scheme that facilitates fast solutions is best. Greyscale results are shown to be excellent, and the algorithm is very fast.
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Document Type: Research Article

Publication date: January 1, 2008

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  • CIC is the premier annual technical gathering for scientists, technologists, and engineers working in the areas of color science and systems, and their application to color imaging. Participants represent disciplines ranging from psychophysics, optical physics, image processing, color science to graphic arts, systems engineering, and hardware and software development. While a broad mix of professional interests is the hallmark of these conferences, the focus is color. CICs traditionally offer two days of short courses followed by three days of technical sessions that include three keynotes, an evening lecture, a vibrant interactive (poster) papers session, and workshops. An endearing symbol of the meeting is the Cactus Award, given each year to the author(s) of the best interactive paper; there are also Best Paper and Best Student Paper awards.

    Please note: for Purposes of its Digital Library content, IS&T defines Open Access as papers that will be downloadable in their entirety for free in perpetuity. Copyright restrictions on papers vary; see individual paper for details.

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