Edge detection in two-dimensional images through model polynomial fitting and first order derivative

Abstract

An innovative edge detection method based on model polynomial fitting and calculation of first order derivative of two-dimensional images is here proposed. The two partial first order derivatives of the model function are calculated. The square root of the sum of the squares of the partial first order derivatives is called FOD and is calculated at the intra-pixel point (x, y). The image is thus re-sampled using the surface of the FOD. The methodology is tested with theoretical images and with Magnetic Resonance Images. Results are compared within a set of five model polynomial functions designed to have three gradients: two along the main spatial coordinates; and one along the covariate direction. FOD images provide clear and sharp edges and similar edge detection behaviour. The implications of this methodology are in image processing and more specifically in edge detection. The advantage of the method is to be computationally fast.