Unveiling the Mystery: Why Your Sobel Filter Only Detects Horizontal Edges in Pygame
You're on the right track with your Sobel filter implementation in Pygame, but it seems there's a slight hiccup in the logic causing it to favor horizontal edges. Let's break down the issue and craft a solution.
Understanding the Sobel Filter
The Sobel filter is a fundamental edge detection algorithm in image processing. It works by calculating the gradient of the image intensity in both horizontal (Gx) and vertical (Gy) directions. Edges are typically found where these gradients are high.
The Bug in Your Code
The core issue lies in the calculation of Gx and Gy within your sobel function:
Gx = (imgmap[x-1][y + 1] + 2 * imgmap[x-1][y] * imgmap[x-1][y - 1]) - (imgmap[x+1][y + 1] + 2 * imgmap[x+1][y] * imgmap[x+1][y - 1])
Gy = (imgmap[x+1][y - 1] + 2 * imgmap[x+1][y] * imgmap[x+1][y + 1]) - (imgmap[x-1][y - 1] + 2 * imgmap[x-1][y] * imgmap[x-1][y + 1])
The problem is in the multiplication terms: 2 * imgmap[x-1][y] * imgmap[x-1][y - 1] and 2 * imgmap[x+1][y] * imgmap[x+1][y + 1]. This multiplication is not part of the standard Sobel operator. Instead, the Sobel filter uses weighted sums of neighboring pixel values.
The Correct Implementation
Here's the corrected sobel function with the standard Sobel operator applied:
def sobel(path: str, n: int): # path to image, image scale
img = pygame.image.load(path)
img = pygame.transform.scale_by(img, n)
img = greyscale(img)
imgmap = [[] for _ in range(img.width)]
for x in range(img.width):
for y in range(img.height):
imgmap[x].append(img.get_at((x, y)).b)
for x in range(1, img.width - 1):
for y in range(1, img.height - 1):
Gx = (imgmap[x + 1][y - 1] + 2 * imgmap[x + 1][y] + imgmap[x + 1][y + 1]) - \
(imgmap[x - 1][y - 1] + 2 * imgmap[x - 1][y] + imgmap[x - 1][y + 1])
Gy = (imgmap[x - 1][y + 1] + 2 * imgmap[x][y + 1] + imgmap[x + 1][y + 1]) - \
(imgmap[x - 1][y - 1] + 2 * imgmap[x][y - 1] + imgmap[x + 1][y - 1])
# Calculate the magnitude of the gradient
gradient_magnitude = np.sqrt(Gx**2 + Gy**2)
# Normalize the gradient magnitude to 0-255
gradient_magnitude = int(gradient_magnitude * 255 / np.max(gradient_magnitude))
if gradient_magnitude > 128:
pygame.draw.rect(img, "#FF0000", (x, y, 1, 1))
return img
Explanation:
- Correct Sobel Operator: The code now accurately calculates Gx and Gy using the standard Sobel kernel.
- Gradient Magnitude: We calculate the magnitude of the gradient using the Pythagorean theorem (
gradient_magnitude = np.sqrt(Gx**2 + Gy**2)) to combine both horizontal and vertical contributions. - Thresholding: To visually highlight edges, we apply a threshold. Any pixel with a gradient magnitude above 128 will be drawn in red, indicating a strong edge.
Key Improvements:
- Accurate Gradient Calculation: The code now correctly computes the Sobel filter's gradient in both directions.
- Robust Edge Detection: By using the gradient magnitude, the filter can detect edges regardless of their orientation.
- Clearer Output: The thresholding ensures that only significant edges are marked, making the output easier to interpret.
Further Refinements:
- Noise Reduction: Consider using a Gaussian blur before applying the Sobel filter to smooth out noise in your input image, leading to cleaner edge detection results.
- Adaptive Threshold: Instead of a fixed threshold, you can use an adaptive thresholding technique, which adjusts the threshold based on local image characteristics.
- Non-Maximum Suppression: This technique can further refine the edge map by thinning out spurious edges and enhancing the prominent ones.
Remember, edge detection is a versatile technique, and experimentation with different filters and parameters is key to achieving optimal results for your specific application.
