Learn how convolutional filters in CNNs detect edges in grayscale images. Understand why a specific filter detects 45-degree edges and its role in image processing for CNN certification exams.
Table of Contents
Question
What do you think applying this filter to a grayscale image will do?
A. Detect vertical edges.
B. Detect 45-degree edges.
C. Detecting image contrast.
D. Detect horizontal edges.
Answer
B. Detect 45-degree edges.
Explanation
Notice that there is a high delta between the values in the top left part and the ones in the bottom right part. When convolving this filter on a grayscale image, the edges forming a 45-degree angle with the horizontal will be detected.
The given filter matrix is designed to amplify pixel intensity changes along a diagonal (45-degree) direction. Here’s why this filter detects 45-degree edges:
Structure of the Filter:
- The weights in the matrix are asymmetric, emphasizing differences along a diagonal orientation.
- Positive values (e.g., 2) are concentrated on the bottom-right diagonal, while negative values (e.g., -1) are on the top-left diagonal.
- This structure highlights transitions from dark to light or light to dark along a 45-degree angle.
Edge Detection Mechanism:
- Convolution involves sliding this filter across the image and computing the weighted sum of pixel intensities.
- The filter responds strongly to patterns matching its diagonal orientation, effectively detecting edges at 45 degrees.
Comparison with Other Filters:
- Filters for vertical or horizontal edges (like Sobel or Prewitt) have symmetric structures emphasizing changes in x or y directions.
- The unique asymmetry of this filter makes it specialized for detecting diagonal edges.
Why Not Other Options?
A. Detect vertical edges: Vertical edge detection requires symmetric filters emphasizing changes along the x-axis, such as Sobel’s vertical kernel.
C. Detecting image contrast: Contrast detection typically involves filters like Laplacian, which highlight all abrupt intensity changes without directional specificity.
D. Detect horizontal edges: Horizontal edge detection requires symmetric filters emphasizing changes along the y-axis.
This filter is specifically tailored for detecting edges at a 45-degree angle, making B the correct answer.
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