1.1: Finite Difference Operator

By convolving the image with the Dx and Dy kernel, we obtained the gradients in vertical and horizontal changes. We summed the squares of the grandients in the two directions and took the square roots of the sums to compute the gradient magnitudes. We chose a threshold of magnitude >= 0.16 to create the edge image.

1.2: Derivative of Gaussian (DoG) Filter

We created a 2D gaussian kernel by taking the outer product of an 1D kernel of parameters ksize=6, sig=1 with itself.

We repeated the process of 1.1 on the blurred image and noticed that the edge image looks much cleaner with less noise.

We created DoG filters shown below by convolving the guassian kernel with Dx and Dy kernels. The results of convolving the DoG filters with the image is the same as convolving Dx and Dy filters with the blurred image.