Edge Detection

Detect edges in a grayscale image using simple gradient-based edge detection:

$$G_x[i][j] = \frac{\text{Input}[i][j+1] - \text{Input}[i][j-1]}{2}$$ $$G_y[i][j] = \frac{\text{Input}[i+1][j] - \text{Input}[i-1][j]}{2}$$ $$\text{Output}[i][j] = \sqrt{G_x[i][j]^2 + G_y[i][j]^2}$$

The result is normalized to the range [0, 255].

This algorithm computes horizontal and vertical gradients, then combines them to find edge strength at each pixel.

Input:

• Grayscale image of size $\text{height} \times \text{width}$

Output:

• Edge detected image of size $\text{height} \times \text{width}$

Notes:

• The input tensor is a single-channel grayscale image
• Only compute gradients for interior pixels (ignore 1-pixel border)
• Border pixels remain zero in the output