Interactive Image Processing Lab • PNG • RLE • Huffman • LZW
Lossless compression reduces the size of an image without permanently removing image information.
Upload an image to analyse its dimensions, raw grayscale size and PNG lossless representation.
| Parameter | Value |
|---|---|
| Dimensions | - |
| Total Pixels | - |
| Raw Grayscale Size | - |
| PNG Lossless Size | - |
| Measurement | Result |
|---|---|
| Original File | - |
| Lossless PNG | - |
| Compression Ratio | - |
| Size Reduction | - |
| Pixel Verification | - |
In lossless compression, decompression must reproduce the same pixel values.
RLE replaces consecutive repeated values with a value and its repetition count.
Huffman coding assigns shorter binary codes to frequently occurring symbols and longer codes to less frequent symbols.
| Symbol | Frequency | Example Code |
|---|---|---|
| A | 50% | 0 |
| B | 25% | 10 |
| C | 15% | 110 |
| D | 10% | 111 |
LZW is a dictionary-based lossless compression technique. Repeated patterns are represented by dictionary codes.
| Redundancy | Meaning | Technique |
|---|---|---|
| Coding Redundancy | Inefficient representation of symbols | Huffman Coding |
| Spatial Redundancy | Neighbouring pixels are similar | RLE / Prediction |
| Statistical Redundancy | Some values occur more frequently | Entropy Coding |
| Feature | Lossless | Lossy |
|---|---|---|
| Information Loss | ❌ No | ✅ Yes |
| Exact Recovery | ✅ Yes | ❌ No |
| Compression | Moderate | High |
| Quality | Original | May decrease |
| Examples | PNG, GIF, RLE, LZW | JPEG |
Interactive JPEG Compression • DCT • Quantization • MSE • PSNR
Lossy compression reduces the size of an image by permanently removing some information that is less important to human visual perception.
Upload a photograph or other image to demonstrate lossy JPEG compression.
Move the slider to change JPEG compression quality.
Higher quality → larger file → less information loss
Lower quality → smaller file → more information loss
| Parameter | Result |
|---|---|
| Image Dimensions | - |
| JPEG Quality | - |
| Original File Size | - |
| Compressed File Size | - |
| Compression Ratio | - |
| Size Reduction | - |
| MSE | - |
| PSNR | - |
DCT transforms pixel information from the spatial domain into the frequency domain.
This is the main lossy operation in JPEG.
Suppose a DCT coefficient is:
During reconstruction:
Lower MSE means the compressed image is closer to the original image.
For an 8-bit image:
| Feature | Lossless | Lossy |
|---|---|---|
| Information Loss | No | Yes |
| Original Recovery | Exact | Not exact |
| File Size | Moderate | Usually smaller |
| Quality | Original quality | Depends on compression |
| Examples | PNG, RLE, Huffman | JPEG |
Learn how digital images are compressed using mathematical and information-theoretic techniques such as RLE, Huffman Coding, DCT, Quantization and JPEG.
Upload an image to begin.
Image compression reduces the number of bits required to represent an image while attempting to preserve the important visual information.
The reconstructed image is exactly identical to the original image. No information is permanently lost.
Examples: RLE, Huffman, LZW, PNG.
Some information is discarded to obtain a much smaller file. The reconstructed image is usually an approximation.
Example: JPEG.
Compression removes different forms of redundancy:
Reduce storage and transmission requirements while maintaining acceptable image quality.
| 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 |
Compression ratio compares the original size with the compressed size.
Percentage reduction:
RLE is a simple lossless compression technique. Instead of storing every repeated pixel separately, it stores the value and the number of consecutive repetitions.
Entropy measures the average information contained in the image intensity distribution.
For an 8-bit grayscale image:
JPEG divides an image into 8×8 blocks and applies the Discrete Cosine Transform to represent spatial intensity variations as frequency coefficients.
Original 8×8 image block.
DCT frequency coefficient.
Frequency coordinates.
Normalization factors.
Quantization reduces the precision of DCT coefficients. This is the major stage responsible for information loss in typical JPEG compression.
Larger quantization values produce stronger compression but usually lower image quality.
More coefficients are retained.
Higher quality → Larger fileMore coefficients become zero or smaller.
Lower quality → Smaller filewhere I is the original image and K is the reconstructed image.
For an 8-bit image:
| 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 |
Some symbols occur much more frequently than others. Huffman coding can exploit this redundancy.
Neighboring pixels often have similar values. Predictive and transform techniques can exploit this property.
Human vision does not perceive all image information equally. Lossy techniques can discard some less perceptually important information.
Reducing image size saves storage and network bandwidth.
Compressed images improve page loading and reduce bandwidth usage.
Compression reduces the amount of data that must be transmitted.
Lossless methods are particularly important when exact pixel information must be preserved.
Image compression principles form an important foundation for video compression systems.
Compression can reduce storage requirements for large image collections.
Noiseless Coding Theorem — Fundamental Limit of Lossless Source Coding
Shannon's First Theorem is also known as the Noiseless Coding Theorem or Shannon's Source Coding Theorem.
It describes the theoretical limit for lossless compression of data generated by an information source.
where:
For a discrete memoryless source and a suitable binary prefix code, there exists a code whose average codeword length satisfies:
Suppose a source produces symbols:
with probabilities:
The entropy is:
where:
Suppose each symbol xįµ¢ is represented by a codeword of length lįµ¢.
Thus the average number of bits per source symbol is the probability weighted average of codeword lengths.
| Symbol | Probability | Code | Length | pįµ¢lįµ¢ |
|---|---|---|---|---|
| A | 0.50 | 0 | 1 | 0.50 |
| B | 0.25 | 10 | 2 | 0.50 |
| C | 0.125 | 110 | 3 | 0.375 |
| D | 0.125 | 111 | 3 | 0.375 |
| Symbol | Probability | Code | Length |
|---|---|---|---|
| A | 0.50 | 0 | 1 |
| B | 0.25 | 10 | 2 |
| C | 0.125 | 110 | 3 |
| D | 0.125 | 111 | 3 |
Therefore, the code reaches the entropy bound exactly.
Entropy represents the average information generated by the source. Lossless coding cannot represent that information using fewer average bits than its information content.
A compression algorithm may reduce the average code length, but it cannot continuously beat the entropy limit for a source without losing information.
Entropy helps estimate how efficiently source data can theoretically be stored.
It provides a fundamental limit for lossless transmission of source information.
Shannon-Fano coding assigns shorter codes to more probable symbols and longer codes to less probable symbols.
| Symbol | Probability | Possible Code |
|---|---|---|
| A | 0.40 | 0 |
| B | 0.30 | 10 |
| C | 0.20 | 110 |
| D | 0.10 | 111 |
Huffman coding is another important lossless source coding technique. It constructs a prefix code with minimum average codeword length among binary prefix codes for a given symbol distribution.
For some probability distributions, Huffman coding can achieve entropy exactly. For others, it produces an average length slightly above entropy.
| No. | Source Probabilities | Entropy | Observation |
|---|---|---|---|
| 1 | 0.5, 0.5 | 1.000 | Maximum for 2 symbols |
| 2 | 0.8, 0.2 | 0.722 | Biased source |
| 3 | 0.9, 0.1 | 0.469 | Highly biased |
| 4 | 0.25,0.25,0.25,0.25 | 2.000 | Uniform 4-symbol source |
| 5 | 0.5,0.25,0.125,0.125 | 1.750 | Non-uniform source |
| 6 | 0.4,0.3,0.2,0.1 | 1.846 | Four-symbol source |
| 7 | 0.7,0.1,0.1,0.1 | 1.357 | One dominant symbol |
| 8 | 0.6,0.2,0.1,0.1 | 1.571 | Moderate uncertainty |
| 9 | 0.5,0.3,0.2 | 1.485 | Three-symbol source |
| 10 | 0.25,0.5,0.125,0.125 | 1.750 | Reordered probabilities |
Enter four probabilities and four codeword lengths. The probabilities should add up to approximately 1.
Suppose:
and
Then:
The code is optimal with respect to the entropy bound.
For a general code, if:
the average code length is within one bit per symbol of the theoretical entropy limit.
Used to understand the fundamental limit of lossless compression.
The principle is relevant to compression techniques such as Huffman coding and related statistical coding methods.
Provides the source-coding limit before considering transmission noise.
Helps determine how efficiently information can theoretically be represented.
Measuring the information, randomness and complexity present in an image using probability and information theory.
Image entropy is a numerical measure of the amount of information or uncertainty contained in an image.
It is calculated from the probability distribution of the image's intensity values.
Most pixels have similar intensity values. The image is relatively uniform.
Example: A plain white wall.
Many different intensity values occur with significant probabilities.
Example: A detailed natural scene.
When logarithm base 2 is used, entropy is measured in:
bits/pixel
An 8-bit grayscale image contains 256 possible intensity values.
Suppose an image contains N pixels and has L possible gray levels. Let nįµ¢ be the number of pixels having gray level i.
The information associated with gray level i is:
The average information is obtained by multiplying each information value by its probability:
Therefore:
Consider a small grayscale image whose pixels contain four intensity levels.
| Gray Level | Number of Pixels | Probability pįµ¢ |
|---|---|---|
| 0 | 4 | 4/16 = 0.25 |
| 85 | 4 | 4/16 = 0.25 |
| 170 | 4 | 4/16 = 0.25 |
| 255 | 4 | 4/16 = 0.25 |
Therefore:
Since:
Therefore:
Enter probabilities for four intensity groups. The probabilities should approximately add up to 1.
The histogram represents the distribution of intensity values. Entropy is calculated from the normalized histogram.
| Property | Low Entropy | High Entropy |
|---|---|---|
| Intensity variation | Low | High |
| Image complexity | Low | High |
| Uniformity | High | Low |
| Information content | Low | High |
| Typical histogram | Concentrated | Spread out |
| Example | Plain background | Detailed texture |
For a completely uniform image, suppose every pixel has intensity 128.
Then:
Maximum entropy occurs when all possible intensity values are equally likely.
For an 8-bit grayscale image:
Entropy can help identify regions containing different levels of texture and information.
Entropy gives an estimate of the theoretical lower bound of average bits needed to represent image information.
Highly textured regions generally contain greater intensity variation and may have higher entropy.
Entropy can be used as one statistical feature when comparing images or image-processing results.
Entropy is commonly considered when evaluating randomness in image-encryption results.
Entropy can be used as a feature for classification and region analysis.
Suppose:
Because one intensity dominates, the entropy is lower than the 50%-50% case.
The following animation shows how image pixels are converted into probabilities and finally into entropy.
Higher entropy generally means a more varied and information-rich intensity distribution, while lower entropy indicates a more predictable or uniform distribution.