Biomedical Imaging

and the other directions follow analogously. Even more advanced edge detection is possible if differentiation filtering is combined with further (nonlinear) steps, such as in the Canny algorithm [5]:

1. The image is smoothed, e.g., by a Gaussian filter.
2. The edges are detected by a combination of Sobel filters $\sqrt{D_x^2+D_y^2}$.
3. The direction of the gradient is determined for each pixel by arctan(Dy/Dx).
4. The edges are thinned to a single pixel by putting pixels which are not maxima in the direction of the gradient to zero.
5. Finally, a thresholding procedure is carried out. All pixels with modulus of the gradient g < T1 are put to zero, all pixels larger than T2 are kept as edge pixels. Then edges are searched in the vicinity of the pixels with g > T2, and ...