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Mathematical Methods For Image Compression

Mathematical Methods For Image Compression. what does compression mean?.

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Mathematical Methods For Image Compression

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  1. Mathematical Methods For Image Compression

  2. what does compression mean? • Compression is the reduction in size of data in order to save space or transmission time. And its used just about everywhere. All the images you get on the web are compressed, typically in the JPEG (Joint Photographic Experts Group ), Medical Images , Libraries and Video Conferences, ….etc.

  3. what does Image Compression mean? • Image compression is the application of data compression. The objective is to reduce redundancy of the image data in order to be able to store or transmit data in an efficient form. The reduction in file size allows more images to be stored in a given amount of disk or memory space. It also reduces the time required for images to be sent over the Internet or downloaded from Web pages.

  4. ♣The two fundamental principles used in image compression are redundancy and irrelevancy. ☻Redundancy removes redundancy from the image. ☻irrelevancy omits pixel values which are not noticeable by human eye. ♣ The information in an image can be minimized by removing the redundancy present in it.

  5. ♣ There are three types of redundancies: • spatial redundancy, which is due to the correlation or dependence between neighboring pixel values • spectral redundancy, which is due to the correlation between different color planes or spectral bands. • temporal redundancy, which is present because of correlation between different frames in images. Image compression aims to reduce the number of bits required to represent an image by removing the spatial and spectral redundancies as much as possible. ♣ JPEG and JPEG 2000 are two important techniques used for image compression

  6. Why Image Compression ( Motivation) • The need to efficiently store, manipulate, and transmit large masses of information is growing more rapidly than the capacity of systems to handle it. • Uncompressed images take too much space, require larger bandwidth for transmission and longer time to transmit. • easier exchange of image files between different devices and applications.

  7. Encoder and Decoder Compression system consists of two components which are encoder and decoder.

  8. Pre processing Symbol encoder quantizer Compressed Image Input Image Source Encoder Symbol encoder Compressed Image Inverse DCT Dequantizer Reconstructed Image Source Decoder JPEG block diagram

  9. 8x8 block extraction DCT Symbol encoder quantizer Compressed Image Input Image Source Encoder 8x8 block mersor Inverse DCT Symbol encoder Dequant-izer Compressed Image Reconstructed Image Source Decoder JPEG block diagram

  10. Fourier transform DCT transform Wavelet transform Or any linear transform Original Lena image 8x8 blockdivided used Quantizer Decoding processing Symbol encoder compressed Lena Image With 4 coefficients

  11. Original Lena image For examplelet the input pixel matrix is The coefficient of DCT can be compute as follow:

  12. Output DCT matrix DC coefficient is at position 0,0 in the upper left corner of the matrix.

  13. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 Zigzag sequence

  14. Original Lena image Compressed Lena image with 4 coefficients Compressed image with 16 coefficients Compressed image with 25 coefficients Compressed image with 40 coefficients Compressedimage with 50 coefficients

  15. Types of Techniques Used in Image Compression • There are two important compression schemes which are lossy and lossless compression

  16. Lossy compression • is a type of data compression in which actual information is lost. the goal is to use lossy compression such that there is not much observable loss in the final product, while saving enormously on file size over lossless compression. In a lossy compression scheme, some of the original information is discarded when it is compressed. Therefore, it is impossible to produce an exact replica of the original image when the image is reconstruct.

  17. Medium compression 92% less information Orginal image High compression 98% less information

  18. Lossless Compression • Lossless compressors produce an exact replica of the original image. • Lossless compression is a compression technique that does not lose any data in the compression process. It assumes you want to get everything back that you put in.

  19. Difference Between Lossless &Lossy Schemes

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