Gradient-based value mapping for colorization of two-dimensional fields

This paper develops a method for automatic colorization of two-dimensional fields presented as images, in order to visualize local changes in values. In many applications, local changes in values are as important as magnitudes of values. For example, in topography, both elevation and slope often must be considered. Gradient-based value mapping for colorization is a technique to visualize both value (e.g., intensity or elevation) and gradient (e.g., local differences or slope). The method maps pixel values to a color scale in a manner that emphasizes gradients in the image. The value mapping function is monotonically non-decreasing, to maintain ordinal relationships of values on the color scale. The color scale can be a grayscale or pseudocolor scale. The first step of the method is to compute the gradient at each pixel. Then, the pixels (with computed gradients) are sorted by value. The value mapping function is the inverse of the relative cumulative gradient magnitude function computed from the sorted array. The value mapping method is demonstrated with data from comprehensive two-dimensional gas chromatography (GC×GC), using both grayscale and a pseudocolor scale to visualize local changes related to both small and large peaks in the GC×GC data.