Fast Multispectral2Gray

A standard approach to generating a grayscale equivalent to an input multi-spectral 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 gray 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 color channels behaves, or how the the luminance changes, or how overall integrability is affected by each sign choice. Instead, we would like to circumvent the sign problem in the first place, and also avoid calculating the costly eigenvector decomposition. We suggest replacing the eigenvector approach by generating a grayscale gradient equal to the maximum gradient amongst the color or multi-spectral channels’ gradients, in each of x, y. color or 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. In a novel approach, 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 grayscale structure tensor to best match the original, multi-spectral, one. If we use only forward-facing derivatives, a fast Fourier-based solution is possible. But instead, we find that a simple scheme that equally weights maxima in the forward-facing and backward-facing directions produces superlative results if a reset step is included, in a spatial-domain solution. Grayscale results are shown to be excellent, and the algorithm is very fast.