![Arithmetic Coding
Arithmetic Coding is a form of entropy encoding used in lossless data compression. normally , a
string of characters such as the words is represented using a fixed number of bits per character, as
in the ASCII code.In general, each step of the encoding process, except for the very last, is the same; the
encoder has basically just three pieces of data to consider:
● The next symbol that needs to be encoded
● The current interval (at the very start of the encoding process, the interval is set to [0,1], but that will change)
● The probabilities the model assigns to each of the various symbols that are possible at this stage (as mentioned
earlier, higher-order or adaptive models mean that these probabilities are not necessarily the same in each step.)
The encoder divides the current interval into sub-intervals, each representing a fraction of the current interval proportional to
the probability of that symbol in the current context. Whichever interval corresponds to the actual symbol that is next to be
encoded becomes the interval used in the next step.](https://image.slidesharecdn.com/losslessimagecompression-200611082125/85/Lossless-image-compression-1-10-320.jpg)
Lossless image compression.(1)
- 1. Lossless Image Compression. By Group 7 Roll no : 1806037 , 1806040 , 1806044 , 1806046.
- 2. Image Compression Image compression is the process of encoding or converting an image file in such a way that it consumes less space than the original file. It is a type of compression technique that reduces the size of an image file without affecting or degrading its quality to a greater extent. Types of Image compression techniques: ● Lossy compression ● Lossless compression Size of the second image is reduced with great extent.
- 3. Lossless Image Compression The goal of lossless image compression is to represent an image signal with the smallest possible number of bits without loss of any information, thereby speeding up transmission and minimizing storage requirements.
- 4. Lossless Image Compression Techniques. Huffman Coding Shannon Fano Coding Arithmetic Coding.
- 5. Huffman Coding Huffman code is a technique for compressing data. Huffman’s greedy algorithm looks at the occurrence of each character and it as a binary string in an optimal way. Huffman coding is a form of statistical coding which attempts to reduce the amount of bits required a string of symbols. Algorithmic steps for Huffman Coding : 1. Create a leaf node for each unique character and build a min heap of all leaf node. 2. Extract two nodes with the minimum frequency from the min heap. 3. Create a new internal node with a frequency equal to the sum of the two nodes frequencies. Make the first extracted node as its left child and the other extracted node as its right child. Add this node to the min heap. 4. Repeat steps#2 and #3 until the heap contains only one node. The remaining node is the root node and the tree is complete.
- 6. Example of Binary Huffman Coding.
- 7. Example of Non-Binary Huffman Coding. Note:- The only difference between binary and non binary huffman coding is that every node except root of the tree must have more than two children. That is at least k children. Where in case of ternary Tree k=3 (figure).
- 8. Shannon Fano Coding. Shannon Fano Algorithm is a entropy encoding technique for lossless data compression of multimedia. The steps of the algorithm are as follows: 1. Create a list of probabilities or frequency counts for the given set of symbols so that the relative frequency of occurrence of each symbol is known. 2. Sort the list of symbols in decreasing order of probability, the most probable ones to the left and least probable to the right. 3. Split the list into two parts, with the total probability of both the parts being as close to each other as possible. 4. Assign the value 0 to the left part and 1 to the right part. 5. Repeat the steps 3 and 4 for each part, until all the symbols are split into individual subgroups.
- 9. Example of Shannon Fano Coding.
- 10. Arithmetic Coding Arithmetic Coding is a form of entropy encoding used in lossless data compression. normally , a string of characters such as the words is represented using a fixed number of bits per character, as in the ASCII code.In general, each step of the encoding process, except for the very last, is the same; the encoder has basically just three pieces of data to consider: ● The next symbol that needs to be encoded ● The current interval (at the very start of the encoding process, the interval is set to [0,1], but that will change) ● The probabilities the model assigns to each of the various symbols that are possible at this stage (as mentioned earlier, higher-order or adaptive models mean that these probabilities are not necessarily the same in each step.) The encoder divides the current interval into sub-intervals, each representing a fraction of the current interval proportional to the probability of that symbol in the current context. Whichever interval corresponds to the actual symbol that is next to be encoded becomes the interval used in the next step.
- 11. Example of Arithmetic Coding Tag Value=(lower limit+upper Limit)/2 Tag Value=(0.14432+0.1456)/2 =0.1449
- 12. Merits and Demerits of Lossless Image Compression Merits 1) Useful for large files 2) Exact data is restored after re-compression 3) High-quality data 4) No loss of quality, slight decreases in image file sizes. Demerits 1) Compression ratio is low 2) Transfer time is high 3) Decoding is difficult 4) Less browser support, slightly larger file sizes than lossy.
- 13. Summary 1) Lossless Compression is a class of data compression algorithms that allows the original data to be perfectly reconstructed from the compressed data. 2) Lossless compression is used in cases where it is important that the original and the decompressed data be identical, or where deviations from the original data would be unfavourable. 3) Typical examples are executable programs, text documents, and source code. Some image file formats, like PNG or GIF, use only lossless compression, while others like TIFF and MNG may use either lossless or lossy methods. 4) Lossless audio formats are most often used for archiving or production purposes, while smaller lossy audio files are typically used on portable players and in other cases where storage space is limited or exact replication of the audio is unnecessary.
- 14. References 1. Lossy vs Lossless image compression - A guide to the trade-off between image size and quality - UpdraftPlus 2. Merits of lossless image compression - Google Search 3. Lossy vs Lossless Compression - KeyCDN Support 4. Lossless_Image_Compression_Techniques_A_State-of-t.pdf ‘ 5. Non Binary Huffman coding image - Google Search 6. Image Processing, 2nd Edition.pdf - Google Drive 7. (1) (PDF) New Image Compression/Decompression Technique Using Arithmetic Coding Algorithm 8. Lossless_Image_Compression_Techniques_A_State-of-t.pdf