🖼️ Image Entropy Calculator

Upload any image and calculate its grayscale histogram, probability distribution and Shannon entropy automatically.

1️⃣ Upload an Image

📁 Choose Image

No image selected.

2️⃣ Image Processing

🖼️ Original Image

⚫ Grayscale Image

3️⃣ Image Statistics

Total Pixels

0

Used Gray Levels

0

Entropy

0

Maximum Entropy

8 bits

Upload an image and click Analyze Image.

4️⃣ Mathematical Calculation

pᵢ = nᵢ / N

where:

• nᵢ = number of pixels having intensity i
• N = total number of pixels

I(i) = −log₂(pᵢ)

Information associated with intensity i.

H = − Σ pᵢ log₂(pᵢ)

This is the Shannon entropy of the grayscale image.

0 ≤ H ≤ 8 bits/pixel

for an 8-bit grayscale image.

5️⃣ Grayscale Histogram

The histogram shows how frequently each gray level occurs in the uploaded image.

6️⃣ Probability Distribution

Only gray levels actually present in the image are displayed below.

Gray Level	Pixel Count	Probability pᵢ	Information −log₂(pᵢ)	Contribution pᵢI(i)
Upload and analyze an image.

7️⃣ Entropy Calculation Animation

🖼️ Image
Pixels

➜

⚫ Grayscale
Image

➜

📊 Histogram
nᵢ

➜

📐 Probability
pᵢ=nᵢ/N

➜

🧮 Information
−log₂(pᵢ)

➜

📈 Entropy
H

Click Start Animation

8️⃣ Interpretation

Entropy	Interpretation
Near 0	Very uniform image / little intensity variation
Low	Few dominant intensity values
Medium	Moderate intensity variation
High	Large variety of intensity values
Near 8	Intensity distribution approaches uniformity

🎯 Important Concept

Image → Grayscale → Histogram → Probability → Information → Entropy

Image entropy is the average amount of information carried by the intensity distribution of the image.

For an 8-bit grayscale image, the theoretical maximum is:

H_max = log₂(256) = 8 bits/pixel

Created by Bijan Krishna Paul
B.K.PAUL Bhairab Ganguly College