🖼️ Image Compression Techniques

Learn how digital images are compressed using mathematical and information-theoretic techniques such as RLE, Huffman Coding, DCT, Quantization and JPEG.

1️⃣ Upload Your Image

📁 Choose Image

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2️⃣ Image for Compression Study

🖼️ Original Image

Upload an image to begin.

⚫ Grayscale Version

3️⃣ What is Image Compression?

Image compression reduces the number of bits required to represent an image while attempting to preserve the important visual information.

🟢 Lossless Compression

The reconstructed image is exactly identical to the original image. No information is permanently lost.

Examples: RLE, Huffman, LZW, PNG.

🟠 Lossy Compression

Some information is discarded to obtain a much smaller file. The reconstructed image is usually an approximation.

Example: JPEG.

🔵 Redundancy

Compression removes different forms of redundancy:

• Spatial redundancy
• Statistical redundancy
• Psychovisual redundancy

🟣 Main Goal

Reduce storage and transmission requirements while maintaining acceptable image quality.

4️⃣ Major Compression Techniques

Technique	Type	Main Idea	Typical Use
RLE	Lossless	Encode repeated values	Simple images
Huffman	Lossless	Short codes for frequent symbols	JPEG / general coding
LZW	Lossless	Dictionary-based coding	GIF / TIFF
DPCM	Predictive	Encode prediction error	Image signals
DCT	Transform	Convert spatial data to frequency coefficients	JPEG
DWT	Transform	Wavelet decomposition	JPEG 2000
Quantization	Lossy	Reduce coefficient precision	JPEG

5️⃣ Compression Ratio

Compression ratio compares the original size with the compressed size.

CR = Original Size / Compressed Size

Percentage reduction:

Reduction = [(Original − Compressed) / Original] × 100%

Original Size

Compressed Size

Click Calculate Ratio.

6️⃣ Run-Length Encoding (RLE)

RLE is a simple lossless compression technique. Instead of storing every repeated pixel separately, it stores the value and the number of consecutive repetitions.

AAAAABBBCCAAAA

becomes:

A5 B3 C2 A4

🔬 Interactive RLE Demonstration

Enter a sequence and click Compress.

7️⃣ Entropy and Image Compression

Entropy measures the average information contained in the image intensity distribution.

H = −Σ pᵢ log₂(pᵢ)

For an 8-bit grayscale image:

0 ≤ H ≤ 8 bits/pixel

Important: Lower statistical redundancy generally provides less opportunity for lossless compression, while predictable/repetitive data is often more compressible. Entropy provides a theoretical lower bound for average lossless coding length under the appropriate source model.

8️⃣ DCT — Discrete Cosine Transform

JPEG divides an image into 8×8 blocks and applies the Discrete Cosine Transform to represent spatial intensity variations as frequency coefficients.

F(u,v) = (1/4) C(u)C(v) ΣΣ f(x,y) cos[(2x+1)uπ/16] cos[(2y+1)vπ/16]

where:

f(x,y)

Original 8×8 image block.

F(u,v)

DCT frequency coefficient.

u,v

Frequency coordinates.

C(u), C(v)

Normalization factors.

8×8 Image Block

The upper-left coefficient is called the DC coefficient. Other coefficients represent increasing spatial frequencies.

9️⃣ Quantization

Quantization reduces the precision of DCT coefficients. This is the major stage responsible for information loss in typical JPEG compression.

Q(u,v) = round[F(u,v) / Q_table(u,v)]

Larger quantization values produce stronger compression but usually lower image quality.

Small Quantization

More coefficients are retained.

Higher quality → Larger file

Large Quantization

More coefficients become zero or smaller.

Lower quality → Smaller file

🔟 JPEG Compression Pipeline

🖼️
Image

➜

🌈
RGB → YCbCr

➜

⬛
8×8 Blocks

➜

📐
DCT

➜

➗
Quantization

➜

↗️
Zig-Zag

➜

🔢
RLE

➜

🌳
Huffman

➜

📦
Compressed

Click Start JPEG Animation.

1️⃣1️⃣ Measuring Compression Quality

Mean Squared Error — MSE

MSE = (1/MN) ΣΣ [I(i,j) − K(i,j)]²

where I is the original image and K is the reconstructed image.

Peak Signal-to-Noise Ratio — PSNR

PSNR = 10 log₁₀(MAX²/MSE)

For an 8-bit image:

MAX = 255

Generally: Lower MSE means less pixel-wise error. Higher PSNR generally indicates better reconstruction quality.

1️⃣2️⃣ Lossless vs Lossy Compression

Feature	Lossless	Lossy
Information loss	No	Yes
Reconstruction	Exactly original	Approximation
Compression ratio	Usually lower	Usually higher
Quality degradation	None	Possible
Examples	PNG, RLE, Huffman, LZW	JPEG
Best suited for	Medical/technical graphics, text-like images	Photographs and natural scenes

1️⃣3️⃣ Three Types of Redundancy

1. Statistical Redundancy

Some symbols occur much more frequently than others. Huffman coding can exploit this redundancy.

2. Spatial Redundancy

Neighboring pixels often have similar values. Predictive and transform techniques can exploit this property.

3. Psychovisual Redundancy

Human vision does not perceive all image information equally. Lossy techniques can discard some less perceptually important information.

1️⃣4️⃣ Applications

📱 Mobile Applications

Reducing image size saves storage and network bandwidth.

🌐 Web Images

Compressed images improve page loading and reduce bandwidth usage.

🛰️ Satellite Images

Compression reduces the amount of data that must be transmitted.

🏥 Medical Imaging

Lossless methods are particularly important when exact pixel information must be preserved.

📹 Video Processing

Image compression principles form an important foundation for video compression systems.

☁️ Cloud Storage

Compression can reduce storage requirements for large image collections.

🎯 Complete Compression Flow

Image → Remove Redundancy → Transform / Predict → Quantize → Entropy Coding → Compressed Image

Important Formulas

Compression Ratio = Original Size / Compressed Size

H = −Σpᵢlog₂(pᵢ)

MSE = (1/MN)ΣΣ[I(i,j)−K(i,j)]²

PSNR = 10log₁₀(255²/MSE)

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