📘

Implement Prewitt Edge Detector

Implement the Prewitt edge detector, one of the earliest edge detection methods (1970).

The Prewitt operator uses two 3×3 kernels to compute horizontal and vertical gradients:

$G_x = \begin{pmatrix} -1 & 0 & 1 \\ -1 & 0 & 1 \\ -1 & 0 & 1 \end{pmatrix} * I, \quad G_y = \begin{pmatrix} -1 & -1 & -1 \\ 0 & 0 & 0 \\ 1 & 1 & 1 \end{pmatrix} * I$

The edge magnitude and direction are: $G = \sqrt{G_x^2 + G_y^2}, \quad \theta = \arctan\left(\frac{G_y}{G_x}\right)$

Return both the magnitude map and the edge direction map (in degrees, 0-360).

Example:

Input:

image = [[0, 0, 0],
         [0, 255, 0],
         [0, 0, 0]]

Output:

{'magnitude': [[..], [..], [..]], 'direction': [[..], [..], [..]]}

Reasoning:

Applying Prewitt kernels to center pixel (1,1):

$G_x$ convolution at (1,1): $-1(0) + 0(0) + 1(0) + -1(0) + 0(255) + 1(0) + -1(0) + 0(0) + 1(0) = 0$

$G_y$ convolution at (1,1): $-1(0) + -1(0) + -1(0) + 0(0) + 0(255) + 0(0) + 1(0) + 1(0) + 1(0) = 0$

Center has no edge (surrounded by zeros).

At (1,0): $G_x = 255$ , $G_y = 0$ → magnitude = 255, direction = 0°

Constraints:

image: 2D grayscale array
Return: Dict with 'magnitude' and 'direction' arrays
Use zero-padding for borders
Direction in degrees [0, 360), rounded to 1 decimal
Magnitude rounded to 2 decimals

Editor

Python 3.13.1

Test Results

0/0

Run code to see test results.