This interpretation gives us a way to think about multiplying an image by a scalar and adding two images. For example, suppose we start with the three images (A, B , and C) below. M_A = M_B = M_C = Now below are four images (1-4), some of which can be written as a linear combination of the matrices for the images \( \mathrm{A}, \mathrm{B} \), and C . Others are impossible to obtain from such a linear combination.
Exercise 1 First try to guess a combination of \( M_{A}, M_{B} \), and \( M_{C} \) that could yield image 1 and image 2. How close can you get? Write some code to check your conjectures. Print your code and submit it with this lab.
Excrcise 2 Do the same for image 3 and image 4. How close can you get? Write some code to check your conjectures. Print your code and submit it with this lab. You may find this more difficult.
Exercise 3: To determine how to combine images \( \mathrm{A}, \mathrm{B} \), and C with either scalar multiplication or addition to obtain image 3 , write the matrices for each image, then form the matrix equation:
\[
M_{3}=\alpha M_{A}+\beta M_{B}+\gamma M_{C} .
\]
Use this equation to find the values of \( \alpha, \beta \), and \( \gamma \).
Excrcise 4: Do the same for image 4.
Exercise 5: Please give your thoughts on the following questions.
i. What happens when pixel intensities in an image exceed the display range as input into the imshow function?
ii. How should we interpret pixel intensities that lie outside our specified range?
iii. How should we interpret the difference between two images? Give an example.
iv. What algebraic properties does the set of all images have in common with the set of real numbers? There are more than one shared properties.
