Comparison between JPEG(DCT) and JPEG 2000(DWT) compression standards
- 1. IMAGE COMPRESSION Comparison between JPEG(DCT) and JPEG 2000(DWT) compression standards Presented by Rishab Shah (1313048 )
- 2. Introduction Need of Compression Image compression is done to reduce the number of bits required to store the same image Lesser the number of bits per pixel, lesser is the space consumed to store the Image Example, 256X256, 8 bpp image Before Compression: Space consumed= (28x28x8 / 23x210 ) = 64KB After Compression (assuming 5bpp) Space consumed= (28x28x5 / 23x210 ) = 40KB Space saved = 24KB
- 3. Compression Ratio It is defined in 2 ways Definition 1: It is defined as the ratio of number of bits required after compression to the number of bits required before compression Used by MATLAB software Definition 2: It is defined as the ratio of number of bits saved after compression to the number of bits required before compression Theoretical definition Previous example, Definition 1 Definition 2 Compression ratio= 0.625(40/64) Compression Ratio =0.375(24/64)
- 4. Types of Compression Lossy Compression: When the image is uncompressed, some part of the original data is completely lost A redundant information is eliminated Lossless compression: When the image is uncompressed, every single bit of data is restoredLossless Compression Lossy Compression No loss of information Some loss of information MSE =0 MSE ≠0 PSNR =∞ PSNR ‹∞ Different methods 1)Run Length Encoding 2)Huffman codes 3)Arithmetic codes 4)Dictionary(LZW) Different methods 1)Improved Grey Scale Quantization (IGS) 2)DPCM 3)Transform coding
- 5. General Block Diagram for compression • Transformer: It transforms the input data into a format to reduce inter-pixel redundancies in the input image • Higher the capability of compressing information in fewer coefficients, better the transform. Hence, DCT and DWT are used • Quantizer: operation is not reversible and must be omitted if lossless compression is desired • Reduces the psych visual redundancies of the input image • Symbol (entropy) encoder: It creates a fixed or variable-length code to represent the quantizer’s output and maps the output in accordance with the
- 6. Compression process for JPEG Original image is divided into blocks of 8 x 8. Pixel values of a black and white image range from 0- 255 but DCT is designed to work on pixel values ranging from -128 to 127. Therefore each block is modified to work in the range Equation is used to calculate DCT matrix. DCT is applied to each block by multiplying the modified block with DCT matrix on the left and transpose of DCT matrix on its right. Each block is then compressed through quantization. Quantized matrix is then entropy encoded. Compressed image is reconstructed through reverse process. Inverse DCT is used for decompression
- 7. Mathematical expression for DCT
- 8. Results of DCT Original Image After 8X8 DCT After 4X4 DCT
- 9. As the number of coefficients increases quality of the image decreases whereas compression ratio continues to increase
- 10. SNR value increases with number of coefficients.
- 11. Advantages of DCT It has been implemented in single integrated circuit It has the ability to pack most information in fewest coefficients It minimizes the block like appearance called blocking artifact that results when boundaries between sub-images become visible
- 12. JPEG 2000 Addresses the problems like Low bit rate compression Large images Single Decompression Architecture Transmission in Noisy Environment Computer generated imaginary Compound Documents
- 13. Compression steps for JPEG 2000 Digitize the source image into a signal s, which is a string of numbers. Characterized by its intensity levels or scales of gray which range from 0(black) to 255(white) Decompose the signal into a sequence of wavelet coefficients w. Use threshold to modify the wavelet coefficients from w to w’. Use quantization to convert w’ to a sequence q. Entropy encoding is applied to convert q into a sequence e.
- 14. Mathematical expression for DWT The two-dimensional DWT of an image function of size may be expressed as The image function is obtained through the 2-D IDWT, as given below
- 15. Results of DWT As threshold value increases blurring of image continues to
- 16. Advantages of JPEG 2000 Reduced costs for storage and maintenance Smaller file size compared to uncompressed TIFF One master replaces multiple derivatives Enhanced handling of large images Fast access to image subsets Intelligent metadata support Enables new opportunities
- 17. Comparison of JPEG and JPEG2000 Performance Original Image JPEG JPEG2000 Compressed images at 1bpp
- 18. Comparison between DCT and DWT based on various performance parameters The above Graphs shows that for DCT based image compression ,as the window size increases MSE increases proportionately whereas for DWT based image compression shows that MSE first decreases with increase in window size and then starts to increase slowly with finally attaining a constant value. A) Mean Squared Error vs Window Size
- 19. Compression increases with increase in window size for DCT and decreases with increase in window size for DWT. B) Compression vs Window Size
- 20. Results and Conclusion DCT is used for transformation in JPEG standard. DCT performs efficiently at medium bit rates. Disadvantage with DCT is that only spatial correlation of the pixels inside the single 2-D block is considered and the correlation from the pixels of the neighboring blocks is neglected. Blocks cannot be decorrelated at their boundaries using DCT. DWT is used as basis for transformation in JPEG 2000 standard. DWT provides high quality compression at low bit rates. The use of larger DWT basis functions or wavelet filters produces blurring near edges in images. DWT performs better than DCT in the context that it avoids blocking artifacts which degrade the reconstructed images. However, DWT provides lower quality than JPEG at the Low compression rates. DWT requires longer compression time
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