📊 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

📊 Histogram Equalization Visualizer

Upload an image and explore grayscale conversion, histogram analysis, histogram equalization and its mathematics.

📁 Upload Image

Please upload an image to begin.

1. Original Image

2. Grayscale Image

3. Grayscale Histogram

4. Histogram Values

Gray Level	Frequency	Probability	CDF	New Gray Level

5. Equalized Image

6. Histogram After Equalization

🧮 Histogram Equalization Mathematics

Step 1: Find the frequency

For every grayscale intensity r_k, count how many pixels have that intensity.

n_k = Number of pixels having intensity r_k

Step 2: Calculate probability

Let n be the total number of pixels.

p(r_k) = n_k / n

Step 3: Calculate cumulative distribution function (CDF)

CDF(r_k) = Σ p(r_j) for j = 0 to k

The CDF adds the probabilities from the first gray level up to the current gray level.

Step 4: Histogram equalization formula

s_k = (L - 1) × CDF(r_k)

Where:

L = number of possible gray levels
For an 8-bit image, L = 256
Therefore L − 1 = 255
r_k = original gray level
s_k = new equalized gray level

Step 5: Example calculation

Suppose an intensity level has:

CDF = 0.60

For an 8-bit image:

s = 255 × 0.60

s = 153

Therefore, the original gray level is mapped to approximately gray level 153.