1. A method for removing an illumination generated shadow in a captured image, the method comprising the steps of: (a) capturing an input image of a scene by an image capture device; (b) plotting each pixel of the captured input image on a two dimensional logarithmic graph, each pixel being a color variation of one of a plurality of color sets in the logarithmic graph; (c) determining a non-linear illumination-invariant kernel as a function of the plurality of color sets; (d) determining an illumination direction for each respective color set in the logarithmic graph, the illumination direction for each respective color set being orthogonal to the non-linear illumination-invariant kernel at each respective intersection between a respective illumination direction of a color set and the non-linear illumination-invariant kernel; (e) projecting a log-chromaticity value of each plotted pixel on the non-linear illumination-invariant kernel, the non-linear illumination-invariant kernel segregated into color set ranges, the color set ranges each associated with a variation of a specific color set, wherein each plotted pixel on the non-linear illumination-invariant kernel represents a color value of the respective pixels of the input image mapped to an illumination-invariant image domain; (f) identifying edges in the input image; (g) identifying edges in the illumination-invariant image domain; (h) comparing the identified edges of the input image to identify edges in the illumination-invariant image domain; (i) determining whether a shadow edge is present in response to an edge identified in the input image and an absence of a correlating edge in the illumination-invariant image domain; and (j) generating a shadow-reduced image for scene analysis by a vehicle vision-based system.