CV-1.md

CV-1 Assignment: CNN Basics

Made by: Pranjal Gulati

1. Do you really understand the convolution operation?

Implement the convolution operation and image processing kernels from scratch. The following three kernels need to implemented:

• Sobel X Kernel: for gradients in X direction

$$\begin{bmatrix} -1 & 0 & 1 \\ -2 & 0 & 2 \\ -1 & 0 & 1 \\ \end{bmatrix}$$

• Sobel Y Kernel: for gradients in Y direction

$$\begin{bmatrix} -1 & -2 & -1 \\ 0 & 0 & 0 \\ 1 & 2 & 1 \\ \end{bmatrix}$$

• Gaussian Kernel (with $\sigma = 1.4$): for smoothing

$$\frac{1}{159} \begin{bmatrix} 2 & 4 & 5 & 4 & 2 \\ 4 & 9 & 12 & 9 & 4 \\ 5 & 12 & 15 & 12 & 5 \\ 4 & 9 & 12 & 9 & 4 \\ 2 & 4 & 5 & 4 & 2 \\ \end{bmatrix}$$

The code skeleton is as below:

def conv(image, kernel):
    # implement conv operation here
    raise NotImplementedError
    
def get_kernel(name):
    # return the kernel based on the name
    raise NotImplementedError

2. Check your implementation

Use this image for the following steps:

• Apply the Gaussian filter on the image. Call the output smoothened
• Apply the Sobel X and Sobel Y filters on smoothened. Call them sobel_x and sobel_y respectively.
• Calculate the gradient magnitude: $I_{xy} = \sqrt{I_x(x,y)^2 + I_y(x,y)^2}$ where $I_x$ is sobel_x, $I_y$ is sobel_y and $(x, y)$ represents a particular pixel.
• Display this gradient magnitude

3. Do you really understand conv backprop?

Read this article to understand how we backprop through conv layers efficiently.