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Algorithm Reference: Difference of Gaussians (DoG)

Type: Feature Enhancement / Band-Pass Filter
Library: OpenCV (cv2.subtract)
Application: Edge & Blob Detection

The Difference of Gaussians (DoG) is a feature enhancement algorithm that involves the subtraction of one blurred version of an original image from another, less blurred version of the original. This mimics how the human retina processes visual information to extract edges.

1. Mathematical Formulation

The DoG function is obtained by subtracting two Gaussian kernels with different standard deviations, σ₁ and σ₂.

DoG(x,y) = G(x,y, σ₁) - G(x,y, σ₂)

Where σ₁ < σ₂. This operation acts as a band-pass filter, removing high-frequency noise (via the blurring) and low-frequency uniform backgrounds (via the subtraction), leaving only the structural edges and blobs.

2. Python Backend Logic (Snippet)

On the ImageStylo server, we process this using matrix subtraction. We allow the user to define independent sigma values for the X and Y axes, enabling the detection of directional features.

Note: We normalize the result to the 0-255 range to ensure the output is visible as an image.

def apply_dog_filter(image, s1_x, s1_y, s2_x, s2_y):
    # 1. Apply First Gaussian Blur (Fine details)
    g1 = cv2.GaussianBlur(image, (0, 0), sigmaX=s1_x, sigmaY=s1_y)

    # 2. Apply Second Gaussian Blur (Coarse details)
    g2 = cv2.GaussianBlur(image, (0, 0), sigmaX=s2_x, sigmaY=s2_y)

    # 3. Compute Difference
    # We use cv2.subtract to handle saturation arithmetic safely
    dog = cv2.subtract(g1, g2)

    return dog

3. Computational Efficiency

DoG is computationally efficient because the Gaussian blur operation is separable. A 2D Gaussian convolution can be performed as two 1D convolutions (one horizontal, one vertical).

This makes DoG a much faster alternative to the "Laplacian of Gaussian" (LoG) operator while providing nearly identical results for blob detection tasks.

Try the DoG Tool:

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