Assignment 3:
Submission Instructions: Please submit a .zip file named <your name.zip containing 1) report
named report.pdf including your answers to all required questions with images and/or plots showing
your results, and 2) the python notebook provided, with the cells run and the relevant source code. If
you include other source code files for a given exercise, please indicate it in the report.
Problem 1. Separable Convolution (20%)
Separable Convolution refers to breaking down the convolution kernel into lower dimension kernels.
Show that convolution with a 2D Gaussian kernel is a spatially separable convolution, i.e. there are two
1D kernels if applied to the image row-wise and column-wise in sequence, it is equivalent to convolving
that image with the 2D Gaussian kernel. Is Sobel kernel spatially separable? Why separable convolutions
are preferred?
Problem 2. Edge Detection (50%)
Implement Canny Edge Detection algorithm as described in the class. Apply your program to detect
edges in image 1. Your program will take as an input a grayscale image, the sigma of the Gaussian filter
and the two low and high thresholds. The output of your program is a binary image. Implement gaussian
convolution as a separable sequence of horizontal and vertical convolutions.
Problem 3. Corner Detection (30%)
Implement Harris Corner Detection algorithm described in the class. Apply your program to detect
corners in image 1.
