Edge detection filters - ML & AI Coding

176. Edge detection filters

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General

senior

Implement a simple edge-detection filter for grayscale images by convolving the image with horizontal and vertical Sobel kernels and combining their responses into an edge-magnitude map.

The edge strength $G$ at each pixel is computed from the horizontal gradient $G_x$ and vertical gradient $G_y$ as:

G = \sqrt{G_x^2 + G_y^2}

Requirements

Implement the function

python

Rules:

Use the Sobel kernels:
- (K_x=\begin{bmatrix}-1&0&1\-2&0&2\-1&0&1\end{bmatrix}), (K_y=\begin{bmatrix}-1&-2&-1\0&0&0\1&2&1\end{bmatrix})
Compute (G_x) and (G_y) by 2D convolution with zero padding so the output stays shape ((H, W)).
Compute edge magnitude per pixel as (G=\sqrt{G_x^2+G_y^2}).
Return the output as np.ndarray of float type.
Use only NumPy (and Python built-ins); don’t use OpenCV/SciPy convolution helpers.

Example

python

Output:

python

Input Signature

Argument	Type
image	np.ndarray

Output Signature

Return Name	Type
value	np.ndarray

Constraints

Use NumPy only; no SciPy/OpenCV.
Zero padding; output shape equals input.
Return np.ndarray of shape (H, W).

Hint 1

Ensure image is a float NumPy array first; it simplifies padding and 3×3 window math.

Hint 2

Use np.pad(img, ((1,1),(1,1)), mode='constant') so every output pixel corresponds to a 3×3 neighborhood centered on the original pixel.

Hint 3

For each (i,j), slice region = padded[i:i+3, j:j+3], compute gx = (region*kx).sum(), gy = (region*ky).sum(), then magnitude sqrt(gx**2 + gy**2).

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Levels

senior

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