Existing edge detection methods provide unsatisfactory results when contrast changes largely within an image due to non-uniform illumination. Koch et al. developed an energy function based upon the Hopfield neural network, whose coefficients were fixed by trial and error, and remain constant for the entire image, irrespective of the differences in intensity level. This paper presents an improved edge detection method for non-uniformly illuminated images. We propose that the energy function coefficients for an image with inconsistent illumination should not remain fixed, rather should vary as a second-order function of the intensity differences between pixels, and actually use a schedule of changing coefficients. The results, compared with those of existing methods, suggest a better strategy for edge detection depending upon both the dynamic range of the original image pixel values as well as their contrast.