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# Interpixel redundancy

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This presentation briefly explain various methods used to predict neighbors of observed pixel.

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### Interpixel redundancy

1. 1. SUBMITTED BY :NAVEEN KUMARM.E.(ECE), 2011(REGULAR)ROLL NO. : 112610
2. 2.  Data is not the same thing as information. Data is the means with which information is expressed. The amount of data can be much larger than the amount of information. Data that provide no relevant information = redundant data or redundancy. Image coding or compression has a goal to reduce the amount of data by reducing the amount of redundancy
3. 3.  n1 = data. n2 = data − redundancy (i.e., data after compression). Compression ratio = CR = n1/n2Relative redundancy = RD = 1 − 1/CR
4. 4. CR Coding Redundancy.IR Interpixel Redundancy.PVR Psycho-Visual Redundancy
5. 5. Image compression can be: Reversible (loss less), with no loss of information.  A new image is identical to the original image (after decompression).  Reversibility is necessary in most image analysis applications.  The compression ratio is typically 2 to 10 times.  Examples are Huffman coding and run-length coding. Non reversible (lossy), with loss of some information.  Lossy compression is often used in image communication, video,WWW, etc.  It is usually important that the image visually is still nice.  The compression ratio is typically 10 to 30 times.
6. 6.  There is often correlation between adjacent pixels, i.e., the value of the neighbors of an observed pixel can often be predicted from the value of the observed pixel. Coding methods:  Run-Length coding.  Difference coding
7. 7.  Every code word is made up of a pair (g, l) where g is the gray level, and l is the number of pixels with that gray level (length, or “run”). E.g., 56 56 56 82 82 82 83 80 56 56 56 56 56 80 80 80 creates the run-length code (56, 3)(82, 3)(83, 1)(80, 4)(56, 5). The code is calculated row by row. Very efficient coding for binary data. Important to know position, and the image dimensions must be stored with the coded image. Used in most fax machines.la University) Image Coding an
8. 8. Compression AchievedOriginal image requires 3 bits per pixel (in total - 8x8x3=192 bits).Compressed image has 29 runs and needs 3+3=6 bits perrun (in total - 174 bits or 2.72 bits per pixel).
9. 9.  f (xi ) = Xi if i = 0, xi − xi-1 if i > 0 E.g., original 56 56 56 82 82 82 83 80 80 80 80 Code f(xi ) 56 0 0 26 0 0 1 −3 0 0 0 The code is calculated rob by row. Both run-length coding, and difference coding are reversible, and can be combined with, e.g., Huffman coding
10. 10.  Requires no priori knowledge of pixel probability distribution values. Assigns fixed length code words to variable length sequences. Patented Algorithm US 4,558,302 Included in GIF and TIFF and PDF file formats
11. 11. 39 39 126 126 As the encoder examines image pixels,39 39 126 126 gray level sequences (i.e., blocks) that are not in the dictionary are assigned to a new39 39 126 126 entry.39 39 126 126 Dictionary Location Entry 0 0 - Is 39 in the dictionary……..Yes 1 1 - What about 39-39………….No . . - Then add 39-39 in entry 256 255 255 256 - 39-39 511 -
12. 12.  A predictive coding approach. Each pixel value (except at the boundaries) is predicted based on its neighbors (e.g., linear combination) to get a predicted image. The difference between the original and predicted images yields a differential or residual image.  i.e., has much less dynamic range of pixel values. The differential image is encoded using Huffman coding.
13. 13.  Digital Image Processing by Gonzalez & Woods web.uettaxila.edu.pk/CMS/.../notes/Image %20Compression.ppt hpourreza.profcms.um.ac.ir/imagesm/196/.../c h08-compression.ppt discovery.bits- pilani.ac.in/discipline/physics/.../compression- II.ppt