Data and information. Image Codning and Compression. Image compression and decompression. Definitions. Images can contain three types of redundancy
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1 Image Codning and Compression data redundancy, Huffman coding, image formats Lecture 7 Gonzalez-Woods: , , , 8.6 Carolina Wählby carolina@cb.uu.se Data and information 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 codning or compression has as a goal to reduce the amount of data by reducing the amount of redundancy. Definitions n =data n 2 =data-redundancy (i.e. data after compression) Compression ratio = C R = Relative redundancy = R D = Images can contain three types of redundancy. Coding Redundancy 2. Interpixel Redundancy 3. Psycho-Visual Redundancy CR: some graylevels are more common than others IR: the same graylevel covers large areas PVR: the eye can only resolve 32 graylevels locally Image compression and decompression original image (loss less compression) (lossy compression) compression decompression approximation of the original image compact information (for storage or transmission) Image compression can be Reversible (loss less) -no loss of information. New image is identical to original image (after decoding). Neccessary in most image analysis. Compression ratio typically 2-0x. Non reversibel (lossy) - loss of some information Often used in image communication, video, www. Important: that the image visually nice. Compression ratio typically 0-30x.
2 Objective measures of image quality error e(x,y)=f approx (x,y)-f original (x,y) total e tot = M N x = 0 y = 0 app rox f orig inal ) How much information is present in the image? If p(e) is the probability of an event, then I(E)=-logp(E) is a measure of the information that the event provides. root-men-square e RMS = a p p ro x f o rig in a l ) M N 2 M N x = 0 y = 0 The average information is called entropy (Shannon entropy) signal-to-noice ratio SNR RMS = M N M x = 0 y = 0 N x = 0 y = 0 approx ) app rox f original ) 2 2 Subjektive measures of image quality -Let a number of test persons grade the images as bad/ok/good etc. Basic idea: different gray levels occur with different probability (non uniform histogram). Use shorter code words for the more common gray levels and longer code words for the less common gray levels. This is called Variable Length Coding. The amount of data in an MxN image with L gray levels =MxNxL avg where L avg =. Coding redundancy l(r k ) is the number of bits used to represent gray level r k p(r k ) is the probability of gray level r k in the image Example 3-bit image: gray level r k probability p(r k ) source code L L avg = k = 0 l( r ) p( r ) k k source : L avg =(constant l(r k )=3)=3*=3 code: L avg =0.*2+0.4*+ =.32 This will however NOT work since the code is not unambiguous. What does for example the code 00 mean? Use Hoffman coding! The Huffman code: -yields the smallest possible number of unique code symbols per source symbol. Step. sort the gray levels by decreasing probability 2. add the two smallest probabilities 3. sort the new value into the list 3. repeat until only two probabilities remain Step 2. give the code 0 to the highest probability, and the code to the lowest probability in the present node 2. go backwards through the tree and add 0 to the highest and to the lowest probability in each node until all gray levels have a unique code Example of Huffman coding graylevel rk p(rk) node node 2 node 3 node 4 node 5 node 6 0,4 4 0,3 0 0, 5 0, 3 0,05 2 0,03 6 0,0 7 0,0 Lavg=3 graylevel rk code node node 2 node 3 node 4 node 5 node Lavg= C R =n /n 2 = R D =-/C R =(n -n 2 )/n =
3 The Huffman code (continued) The Huffman code results in an unambiguous code, i.e. no code can be created by combining other codes. The code is reversible without loss. The table for the translation of the code has to be stored together with the coded image. The Huffman code does not take correlation between adejacent pixels into consideration. 2. Interpixel Redundancy (also called spatial or geometric redundancy) There is often correlation between adjacent pixels, i.e. the value of the neighbours of an observed pixel can often be predicted from the value of the observed pixel. Coding methods: Run-length coding Difference coding. Run-length coding Every code word is made upp of a pair (g,l) where g is the graylevel and l is the number of pixels with that graylevel (length, or run ). Ex creates the runlength code (56,3) (82,3) (83,) (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 Difference coding f(x i )= { x i if i=0, x i -x i- if i>0 Ex original: code f(x i ) : The code is calculated row by row. Both Run-length coding och Difference coding are reversible and can be combined with for example Huffman coding. Exemple of combined Difference and Huffman coding Huffman code of original image original image difference image L avg =3.
4 Huffman code of difference image Bitplane coding Divide the grayscale/color image into a series of binary images (one image per bit). Code each image separately using the above described methods. An 8-bit image will be represented by 8 coded binary images. L avg =2 2. Psycho-Visual Redundancy If the image will only be used for visual observation (i.e. illustrations on the web etc), a lot of the information is usually psycho-visually redundant. It can be removed without changing the visual quality of the image. This kind of compression is usually irreversible. 0.5kB 0.05kB Psycho-visual redundancy is often reduced by quantifiacation: Example: Uniform quantification of graylevels - remove the least significant bits of the data - causes edge effects The edge effects can be reduced by "Improved Gray Scale", IGS - Remove the least significant bits and add a random number based on the sum of the least significant bits of the present and the previous pixel. - special case if the graylevel of a pixel in an 8-bit image is xxxx, addera IGS reduces edge effects but will at the same time unsharpen true edges. IGS More quantification methods: Motion pictures method :. transfere the first image to the observer 2. find the changes from the previous image 3. transfere only the changes method 2:. transfere the most important information (e.g. the lowest frequencies) first 2. send the less important information later
5 Transform coding. Divide the image into nxn subimages 2. Transform each subimage using a reversible transform (e.g. the Hotellingtransform, the Diskreta Fourier Transform (DFT), the Diskreta Cosinus Transform (DCT)). 3. Quantify, i.e. truncate the transformed image, (for example with DFT and DCT frequencies with small amplitude can be removed without much information loss).the quantification can be either image dependent (IDP) or image independent (IIP). 4. Code the resulting data, normally using some kind of "variable length coding", for example Huffman code. - The coding is not reversible (unless step 3 is skipped) Some common image formats JPEG (Joint Photographic Experts Group) exists in many different versions but is always some kind of transform coding. JPEG is not reversible due to quantification. MPEG (Motion Pictures Experts Group) - Similar to JPEG, but the motion in comparison to the previous image is calculated and used in the compression. Example: JPEG compression 75% 27 kb 50% 7 kb 25% kb 0% 6 kb Some more common image formats LZW-kodning (Lempel-Ziv-Welch) A "word-based" code. The data is represented by pointers to a library of symbols (see Huffman code). LZW compression is loss less and can often be choosen when TIFF (Tagged Image File Format) images are stored. The result is a smaller file which usually takes a bit longer to decode. An Image File Directory (set of symbols) is included in the header. GIF (Graphics Interchange Format) Creates a coding for color images where each color is coded by only one bit (usually 3). GIF also uses LZW compression for storage and transfere. GIF is fully reversible (lossless) if less than 256 colors are present in the original image. Remember that the TIME used for coding and decoding is important when choosing coding method! Choice of image format Images to be used for image analysis should always be saved in a loss less format! Example of losses at compression Images for the WWW have to be either GIF or JPEG Chose GIF for graphs and hand drawn figures with few color shades (JPEG transform coding and truncation can cause artefacts around sharp edges) coded as jpeg: 64kb Chose JPEG for photos and figures with many colors and smooth transitions between colors (GIF reduces the number of colors to 256). original: 259 kb tif coded as gif: 22kb
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