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Image Histogram Equalization

Implement histogram equalization to enhance image contrast using NumPy.

Histogram equalization redistributes pixel intensities to achieve a more uniform histogram, improving contrast in images with concentrated intensity ranges.

Algorithm:

Compute histogram $h[i]$ = count of pixels with intensity $i$
Compute cumulative distribution function: $CDF[i] = \sum_{j=0}^{i} h[j]$
Normalize CDF to range [0, 255]: $CDF_{norm}[i] = \frac{CDF[i] - CDF_{min}}{(M \times N) - CDF_{min}} \times 255$
Map each pixel: $output[x,y] = CDF_{norm}[input[x,y]]$

Where $M \times N$ is the total number of pixels and $CDF_{min}$ is the minimum non-zero CDF value.

Example:

Input:

image = [[50, 50], [50, 50]]

Output:

[[255, 255], [255, 255]]

Reasoning:

Step 1: Histogram Only intensity 50 appears, count = 4

Step 2: CDF CDF[50] = 4, all others = 0 or 4

Step 3: Normalize CDF_min = 4, total pixels = 4 CDF_norm[50] = (4-4)/(4-4) × 255 = undefined → use 255 when all same

Step 4: Map All pixels map to 255 (maximum) since they all have the same value.

When all pixels are identical, equalization maps them to maximum intensity.

Constraints:

image: 2D numpy array with values in [0, 255]
Return: Equalized image with same shape, values in [0, 255]
Output values should be integers

Editor

Python 3.13.1

Test Results

0/0

Run code to see test results.

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