Linear and Non-linear Filtering

The two following labs deal with filtration of images, which can be used for smoothing, deblurring, denoising and other applications.

The theory behind the labs can be found in the lectures:

Start by downloading the template of the assignment.

Use test_script.m to check your solution.

Brute-force convolution and simple kernels

1a: implement brute-force convolution using loops (convolution_2D.m) - 2 points

Note that the input kernels can have general 2D shape (not just square matrices).
Use “DC” padding, i.e., clip the pixel coordinates just to the area of the original image. For the pixels in areas, where the kernel would look outside of the original image, use the nearest image pixel.
A nice visualization of 2D convolution with simple kernels: https://setosa.io/ev/image-kernels/.

1b: implement the generator for specified kernels (get_kernel.m): - 0.2 point / kernel - 1 point total

Implement the following kernels: average, Sobel, Gauss, Gauss derivation, Laplacian of Gaussian
Note that there are many other commonly used simple kernels. Check, e.g., Wikipedia for few examples.
If your Sobel operator is mirrored relative to the reference solution, it is OK. You can find both definitions in literature.