📊 Histogram Specification / Matching

Match the histogram of an input image with a target image

📁 Select Input Image 🎯 Select Target Image

Upload an input image and a target image.

1. Input Image

2. Target Image

3. Input Histogram

4. Target Histogram

5. Input CDF

6. Target CDF

7. Gray-Level Mapping

Input Gray	Input H	Input CDF	Target Gray	Target CDF	New Map

8. New Mapped Image

9. Histogram After Mapping

10. Mapping Result

Waiting for histogram matching...

🧮 Histogram Matching Mathematics

Step 1 — Convert image to grayscale

For an RGB pixel:

Gray = 0.299R + 0.587G + 0.114B

Step 2 — Calculate histogram

For each gray level r_k, count the number of pixels.

H(r_k) = n_k

Step 3 — Calculate probability

If N is the total number of pixels:

P(r_k) = n_k / N

Step 4 — Calculate input CDF

C_input(r_k) = Σ P(r_j)

where j = 0 to k.

Step 5 — Calculate target CDF

C_target(z_q) = Σ P(z_j)

Step 6 — Find the matching gray level

For every input gray level, find the target gray level whose CDF is closest to the input CDF.

Find z such that C_target(z) ≈ C_input(r)

Step 7 — Create the mapping

r → z

Every pixel having gray level r is replaced with the mapped gray level z.

Example

Input CDF = 0.60

Suppose the target histogram has:

Target CDF at gray 150 = 0.58 Target CDF at gray 151 = 0.61

The closest target CDF is 0.61, therefore:

Input gray level → Target gray level r → 151

Complete process

Input Image → Grayscale → Input Histogram → Input CDF → Target Histogram → Target CDF → Mapping → New Image

Interactive Digital Image Processing — Histogram Specification / Histogram Matching