Corner detection (Harris) in Computer Vision - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

What does the Harris corner detector primarily measure?

The Harris corner detector is used in computer vision to find corners in images. What is the main quantity it measures to detect corners?

A The change in intensity in all directions around a pixel

B The average color value of a pixel neighborhood

C The distance between edges in the image

D The brightness of the pixel compared to the image mean

💡 Hint

Think about what makes a corner different from an edge or flat area.

The Harris corner detector measures how much the intensity changes in all directions around a pixel. Corners have large changes in intensity in multiple directions.

❓ Predict Output

intermediate

Output of Harris response matrix calculation

Given the following code snippet that computes the Harris response matrix R for a pixel, what is the value of R?

Computer Vision

import numpy as np
Ix = 2
Iy = 3
Ixx = Ix * Ix
Iyy = Iy * Iy
Ixy = Ix * Iy
k = 0.04
M = np.array([[Ixx, Ixy], [Ixy, Iyy]])
R = np.linalg.det(M) - k * (np.trace(M) ** 2)
print(round(R, 2))

A 0.44

B 1.44

C 0.0

D -6.76

💡 Hint

Calculate determinant and trace carefully.

M = [[4,6],[6,9]]; det(M) = 4*9 - 6*6 = 36 - 36 = 0; trace(M) = 4 + 9 = 13; R = 0 - 0.04*(13**2) = -6.76; round(-6.76, 2) = -6.76.

❓ Model Choice

advanced

Choosing parameters for Harris corner detection

Which parameter adjustment will increase the sensitivity of the Harris corner detector to detect more corners in an image?

A Increase the threshold for corner response R

B Increase the value of the Harris detector free parameter k

C Decrease the window size used for gradient summation

D Use a larger Gaussian smoothing before computing gradients

💡 Hint

Think about how window size affects local detail detection.

A smaller window size focuses on smaller neighborhoods, making the detector more sensitive to small corners and details.

❓ Metrics

advanced

Evaluating Harris corner detection results

After running Harris corner detection, you get a set of corner points. Which metric best describes the quality of detected corners compared to ground truth corners?

A Recall (ratio of detected corners to total ground truth corners)

B Precision (ratio of correctly detected corners to all detected corners)

C Accuracy (ratio of correct detections to total image pixels)

D Mean squared error between detected corner coordinates and ground truth

💡 Hint

Consider how many detected corners are actually correct.

Precision measures how many detected corners are true corners, reflecting detection quality.

🔧 Debug

expert

Debugging incorrect Harris corner detection output

You implemented Harris corner detection but the output shows no corners detected. Which of the following code mistakes would cause this issue?

Computer Vision

import cv2
import numpy as np
img = cv2.imread('image.jpg', 0)
Ix = cv2.Sobel(img, cv2.CV_64F, 1, 0, ksize=3)
Iy = cv2.Sobel(img, cv2.CV_64F, 0, 1, ksize=3)
Ixx = Ix * Ix
Iyy = Iy * Iy
Ixy = Ix * Iy
k = 0.04
window_size = 3
height, width = img.shape
R = np.zeros((height, width))
for y in range(window_size, height - window_size):
    for x in range(window_size, width - window_size):
        Sxx = np.sum(Ixx[y - window_size:y + window_size + 1, x - window_size:x + window_size + 1])
        Syy = np.sum(Iyy[y - window_size:y + window_size + 1, x - window_size:x + window_size + 1])
        Sxy = np.sum(Ixy[y - window_size:y + window_size + 1, x - window_size:x + window_size + 1])
        M = np.array([[Sxx, Sxy], [Sxy, Syy]])
        R[y, x] = np.linalg.det(M) - k * (np.trace(M) ** 2)
threshold = 0.01 * R.max()
corners = np.where(R > threshold)
print(len(corners[0]))

A The threshold is set too high, filtering out all corners

B The image is read in color mode instead of grayscale

C The Sobel operator is applied with wrong kernel size

D The window size is too large, causing sums to be zero

💡 Hint

Check the threshold relative to the maximum R value.

If the threshold is too high, no R values exceed it, so no corners are detected.