Edge and Junction Detection Improvement Using the Canny Algorithm with a Fourth Order Accurate Derivative Filter

The Canny algorithm has been extensively adopted to perform edge detection in images. The Derivative of Gaussian (DoG) proposed by Canny has been shown to be the optimal edge detector to compute the image gradient due to its robustness to noise. However, the DoG has some important drawbacks in relation to images with thin edges of a few pixels width and junctions. The excessive blurring provided by the DoG affects the detection of the double and triple junctions that sometimes appear broken while the corners appear rounded. Such a loss in detail is due to the second order approximation of the finite difference (FD) operator adopted to discretize the DoG detector. In this work an improvement of the Canny algorithm is proposed for images having thin edges, computing the edge detector as a convolution of a fourth order accurate FD with the smoothed Gaussian image. The modified wave number analysis of the FD formulation is adopted to motivate the improvement in the edge resolution gained by the fourth order FD discretization. Quantitative comparisons performed with a second order FD discretization of the edge detector adopting both synthetic and benchmark images highlight an improvement in edge localization and in junction detection.