Directional edge detection using the logical transform for binary and grayscale images

This paper presents a novel method for edge detection within two-dimensional signals (images). Using Boolean partial derivatives calculated quickly through a logical transform, the algorithm generates a binary edge map. The process is initially described for binary data and then extended for multi-bit (grayscale) images. Computer simulations demonstrate the procedure for three classes of signals: synthetic images (where actual edge maps are known), natural images, and cell-phone images (those taken by a low-resolution, low-quality camera). Results are compared quantitatively (when possible with Pratt’s figure of merit) and visually with six common edge detection techniques: Sobel, Prewitt, Roberts, Laplacian of Gaussian, zero-cross and Canny methods. Comparison with these methods demonstrates that the algorithm presented here is able to consistently perform competitively in the numerical sense, while also detecting major edges and fine details simultaneously. Both of these latter aspects are visually apparent in the binary output image maps produced.