Reading Ma 4.3 and 4.A

Warning The textbook starts Chapter 4 by discussing tracking, which means that motion as a function of time is considered as well as the image as a funciton of spatial co-ordinates. This is a lot of concepts and quantities to process at the same time. We will instead start by discussing features in a still image. When we have a good idea of what features are and how they behave, we shall introduce motion.

Briefing Corner Lecture

Exercises

Learning Objectives

1. What makes a feature in visual terms?
2. What makes a feature in mathematical terms?
3. How do we differentiate a sampled signal?
4. How does the Harris corner detector work?

Setup

We will be using opencv for today’s exercises, you can install it with pip install opencv-python. We might also use scipy, which can be downloaded the same way (pip install scipy)

We will also be working on a image, e.g. the valve image from https://upload.wikimedia.org/wikipedia/commons/f/f0/Valve_original_%281%29.PNG . Load the image and convert it to grayscale with:

import cv2 as cv

# Load image, replace "path" with the image path
img = cv.imread("path", 1)
# Convert img to BGR, then to grayscale
img = cv.cvtColor(img, cv.COLOR_RGB2BGR)
img_gray = cv.cvtColor(img, cv.COLOR_BGR2GRAY)

Exercise 1

Learning goal: 1D derivatives and 1D convolutions

Part 1
Extract one row from the grayscale image, and visualize it (e.g. with matplotlib.pyplot).
Does the values correspond to what you would expect from the row?

Part 2
Convolve the row with a \([1/2,-1/2]\) kernel, using numpy, and visualize.
Does the values make sense?

(Optional, if you have time) Part 3
Repeat part 2 with an image column (instead of row) and the transpose of the kernel.

Exercise 2

Learning goals: Blur filters

Part 1

\[1/16 \begin{bmatrix} 1 & 2 & 1 \\ 2 & 4 & 2 \\ 1 & 2 & 1 \\ \end{bmatrix} \]

Works as an approximation of a \(3x3\) gaussian blur filter.
Using scipy.signal.convolve2d, scipy.signal.correlate2d or cv.filter2d, apply the filter to the entire grayscale image and either show the image or write it to file with cv.imwrite.   How does the filter affect the image?

Part 2
Compare the above result with the result from cv.GaussianBlur(img_gray, (3, 3), -1)

(Optional) Part 3
Using the function from part 2, test out different kernel sizes and compare the difference.

Exercise 3

Learning goals: 2D Derivatives

Part 1
Apply the sobel operator \[G_x = 1/8 \begin{bmatrix} 1 & 0 & -1 \\ 2 & 0 & -2 \\ 1 & 0 & -1 \\ \end{bmatrix} \]

as you did in exercise 2.1.
How does this relate to the 1D derivative you did in exercise 1.2?

Part 2
Repeat part 1 with \(G_y\) \[G_y = 1/8 \begin{bmatrix} 1 & 2 & 1 \\ 0 & 0 & 0 \\ -1 & -2 & -1 \\ \end{bmatrix} \]

Part 3
Compute and visualize the gradient magnitude of the image, using the results from part 1 and 2.

(Optional, only if you have time) Part 4

Using the same method as in exercise 1.2 and 1.3, compute the gradient of all rows and columns, and compute the magnitude (as in exercise 3.3), compare with the magnitude from 3.3.

Exercise 4

Learning goals: Introduction to harris corner detector

Part 1

Consider the grayscale image we have been working with, and the gradient magnitude from 3.3.
Where do you expect to find corners?

Apply opencv’s built in harris-detector.
E.g. cv.cornerHarris(img_gray, block_size, kernel_size, k) with block_size = 2, kernel_size = 5 and k = 0.06.
Here, block_size is the size of neighbourhood considered for corner detection, kernel_size is the size of the sobel derivative kernel, while k is the harris free parameter.

Make a copy of the original image (with colors) and make circles around any corners found by the harris-detector.
Example code for drawing circles is added below.

Save/visualize the result, how does it compare with your expectations?

Part 2
Adjust the threshold T when drawing circles, what does this do?

(Optional) Part 3
Adjust the kernel_size (must be positive and odd), block_size and/or k, and observe how they change the result.