JPEG和BMP格式转换源码

A note about the JPEG decoding algorithm. Copyright 1999 Cristi Cuturicu. DISCLAIMER ........... You get this file for free, so you cannot have any legal requests from me. If you don't agree, read no more. No warranty is provided with this doc, there might be bugs or errors in it (although I've tried to avoid them), so use the information contained in this file at your own risk. This is NOT an official documentation, for further information please refer to the JPEG ISO standard. All product names mentioned in this file are trademarks or registered trademarks of their respective owners. You are free to distribute it, as long as you do not modify it. First, a word about this doc ............................ This doc tries to explain the JPEG compression algorithm. I'm not an expert in this field, I just needed this info for my own JPEG decoder. Long ago, I wanted to write my own JPEG decoder, so I've been looking on the net a good doc which could have explained to me the JPEG compression, and particularly the JPG file format. And except the standard I couldn't find one. The ISO-ITU JPEG standard = ISO standard 10918-1 or CCITT standard recommendation T.81: "Information Technology - Digital compression and coding of continuous-tone still images - Requirements and guidelines") Though this standard is quite complete, it has a lot of not interesting parts in its 186 pages, and I had to dig in it, and then write my own JPG viewer, to get from this standard the main stuff I needed : The Baseline Sequential DCT JPG compression. So I thought that a short (but with enough details) doc might be useful to others. Mainly because of the fact that the majority of the JPG files are Baseline Sequential JPGS, this doc concerns only the Baseline Sequential JPG compression and particularly the JFIF implementation of it. It DOES NOT cover the JPG Progresive or Hierarchical compression. (For more details about these read the itu-1150 standard. It can be found at www.wotsit.org or somewhere at www.jpeg.org/jpeg) I've thought that it would be easier for the reader to understand the JPG compression if I'll explain the steps of the JPG encoder. (The decoder steps will be the inverse of the encoder's steps, but in reverse order, of course) THE JPEG ENCODER STEPS ---------------------- 1) The afine transformation in colour space : [R G B] -> [Y Cb Cr] --------------------------------------------------------------------- (It is defined in the CCIR Recommendation 601) (R,G,B are 8-bit unsigned values) | Y | | 0.299 0.587 0.114 | | R | | 0 | | Cb | = |- 0.1687 - 0.3313 0.5 | * | G | + |128| | Cr | | 0.5 - 0.4187 - 0.0813| | B | |128| The new value Y = 0.299*R + 0.587*G + 0.114*B is called the luminance. It is the value used by the monochrome monitors to represent an RGB colour. Physiologically, it represents the intensity of an RGB colour perceived by the eye. You see that the formula for Y it's like a weighted-filter with different weights for each spectral component: the eye is most sensitive to the Green component then it follows the Red component and the last is the Blue component. The values Cb = - 0.1687*R - 0.3313*G + 0.5 *B + 128 Cr = 0.5 *R - 0.4187*G - 0.0813*B + 128 are called the chromimance values and represent 2 coordinates in a system which measures the nuance and saturation of the colour ([Approximately], these values indicate how much blue and how much red is in that colour). These 2 coordinates are called shortly the chrominance. [Y,Cb,Cr] to [R,G,B] Conversion (The inverse of the previous transform) -------------------------------- RGB can be computed directly from YCbCr ( 8-bit unsigned values) as follows: R = Y + 1.402 *(Cr-128) G = Y - 0.34414*(Cb-128) - 0.71414*(Cr-128) B = Y + 1.772 *(Cb-128) A note relating Y,Cb,Cr to the human visual system --------------------------------------------------- The eye, particulary the retina, has as visual analyzers two kind of cells : Cells for night view which perceive only nuances of gray ranging from intense white to the darkest black and cells for the day view which perceive the color nuance. The first cells, given an RGB colour, detect a gray level similar to that given by the luminance value. The second cells, responsible for the perception of the colour nuance, are the cells which detects a value related to that of the chrominance. 2) Sampling ------------ The JPEG standard takes into account the fact that the eye seems to be more sensitive at the luminance of a colour than at the nuance of that colour. (the white-black view cells have more influence than the day view cells) So, on most JPGS, luminance is taken in every pixel while the chrominance is taken as a medium value for a 2x2 block of pixels. Note that it is not neccessarily that the chrominance to be taken as a medium value for a 2x2 block , it could be taken in every pixel, but good compression results are achieved this way, with almost no loss in visual perception of the new sampled image. A note : The JPEG standard specifies that for every image component (like, for example Y) must be defined 2 sampling coefficients: one for the horizontal sampling and one for vertical sampling. These sampling coefficients are defined in the JPG file as relative to the maximum sampling coefficient (more on this later). 3) Level shift -------------- All 8-bit unsigned values (Y,Cb,Cr) in the image are "level shifted": they are converted to an 8-bit signed representation, by subtracting 128 from their value. 4) The 8x8 Discrete Cosine Transform (DCT) ------------------------------------------ The image is break into 8x8 blocks of pixels, then for each 8x8 block is applied the DCT transform. Note that if the X dimension of the original image is not divisible by 8, the encoder should make it divisible, by completing the remaining right columns (until X becomes a multiple of 8) with the right-most column of the original image. Similar, if the Y dimension is not divisible by 8, the encoder should complete the remaining lines with the bottom-most line of the original image. The 8x8 blocks are processed from left to right and from top to bottom. A note: Since a pixel in the 8x8 block has 3 components (Y,Cb,Cr) the DCT is applied separately to 3 blocks 8x8: The first 8x8 block is the block which contains the luminance of the pixels in the original 8x8 block The second 8x8 block is the block which contains the Cb value of the pixels in the original 8x8 block And, similar, the third 8x8 block contains the Cr values. The purpose of the DCT transform is that instead of processing the original samples, you work with the spatial frequencies present in the original image. These spatial frequencies are very related to the level of detail present in an image. High spatial frequencies corresponds to high levels of detail, while lower frequencies corresponds to lower levels of detail. The DCT transform is very similar to the 2D Fourier transform which shifts from the time domain (the original 8x8 block) to the frequency domain (the new 8x8= 64 coefficients which represents the amplitudes of the spatial frequencies analyzed) The mathematical definition of Forward DCT (FDCT) and Inverse DCT (IDCT) is : FDCT: c(u,v) 7 7 2*x+1 2*y+1 F(u,v) = --------- * sum sum f(x,y) * cos (------- *u*PI)* cos (------ *v*PI) 4 x=0 y=0 16 16 u,v = 0,1,...,7 { 1/2 when u=v=0 c(u,v) = { 1/sqrt(2) when u=0, v!=0 { 1/sqrt(2) when u!=0, v=0 { 1 otherwise IDCT: 1 7 7 2*x+1 2*y+1 f(x,y) = --- * sum sum c(u,v)*F(u,v)*cos (------- *u*PI)* cos (------ *v*PI)