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# M19 Past Exam Problems

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# Question 1

📗 [2 points] Given the following image gradient, suppose gradient vectors are put into one of the four bins according to the gradient direction: bin 1:

(0, \frac{π}{2}]

, bin 2:

(\frac{π}{2}, π]

, bin 3:

[- \frac{π}{2}, - π)

, bin 4:

[0, - \frac{π}{2})

, which bin does the gradient of the center element (pixel) fall into?

\nabla_{x}

[\begin{matrix} 8 & - 2 & 10 \\ - 4 & - 3 & - 5 \\ - 1 & - 8 & 5 \end{matrix}]

\nabla_{y}

[\begin{matrix} - 2 & 0 & 9 \\ 9 & - 10 & 6 \\ 10 & - 2 & - 10 \end{matrix}]

.
Enter the bin number (1, 2, 3, or 4), not the direction.

📗 Calculator (you can use the function atan2(y, x)): .

📗 Answer: .

📗

# Question 2

📗 [4 points] What is the gradient magnitude of the center element (pixel) of the image

[\begin{matrix} 8 & - 2 & 10 \\ - 4 & - 3 & - 5 \\ - 1 & - 8 & 5 \end{matrix}]

. Use the x gradient filter:

[\begin{matrix} - 1 & 0 & 1 \end{matrix}]

, and the y gradient filter:

[\begin{matrix} - 1 \\ 0 \\ 1 \end{matrix}]

. Remember to flip the filters.

📗 Answer: .

📗

# Question 3

📗 [4 points] What is the gradient magnitude of the center element (pixel) of the image

[\begin{matrix} 8 & - 2 & 10 \\ - 4 & - 3 & - 5 \\ - 1 & - 8 & 5 \end{matrix}]

. Use the x gradient filter:

[\begin{matrix} - 1 & 0 & 1 \\ - 2 & 0 & 2 \\ - 1 & 0 & 1 \end{matrix}]

, and the y gradient filter:

[\begin{matrix} - 1 & - 2 & - 1 \\ 0 & 0 & 0 \\ 1 & 2 & 1 \end{matrix}]

. Remember to flip the filters.

📗 Answer: .

📗

# Question 4

📗 [4 points] What is the gradient magnitude of the center element (pixel) of the image

[\begin{matrix} 8 & - 2 & 10 \\ - 4 & - 3 & - 5 \\ - 1 & - 8 & 5 \end{matrix}]

. Use the x gradient filter:

[\begin{matrix} - 1 & 0 & 1 \\ - 2 & 0 & 2 \\ - 1 & 0 & 1 \end{matrix}]

* * * * *

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📗 You can find videos going through the questions on Link.

Last Updated: February 23, 2025 at 5:49 AM