JPEG стандарт Лекц-15. МУИС ХШУИС МКУТийн багш П.Гантуяа

Transcription

1 JPEG стандарт Лекц-15 МУИС ХШУИС МКУТийн багш П.Гантуяа

2 What is JPEG? JPEG: Joint Photographic Expert Group an international standard in Works for both color and grayscale images. Targets at natural images. Applications include satellite, medical imaging, general photography...

3 Color Space Conversion JPEG first converts RGB to YUV or YCrCb. Y is the luminance component (brightness). Y = R G B U and V are color components U = B Y V = R - Y Y U V

4 Color Subsampling JPEG down-samples-дээж the color channels by half-хагас and partitions-хуваах,тусгаарлах images into-руу 8x8 small blocks. Y 1 Y 2 U V Y 3 Y 4 Intensity-эрч Component-бүрэлдэхүүн Color components

5 DCT (Discrete Cosine Transform) DCT converts each image 8x8 block into another 8x8 block. The energy in DCT domain is concentrated into very few coefficients. Image block DCT DCT coefficients

6 Grayscale Level DCT Coefficients row Image block 4 col row DCT Coefficients 4 col 2 0

7 Definition of DCT A linear transfrom F(u,v) = x=07 y=0 7 h(u,v,x,y) f(x,y) where h(u,v,x,y) is the linear weighting-нэмэгдэл function. DCT: The inverse transform IDCT recovers the original data from DCT coefficients.

8 For DCT, h(u,v,x,y) can be decomposed-задрах into g(u,x) * g(v,y) F(u,v) = x=07 y=0 7 h(u,v,x,y) f(x,y) = y=07 g(v,y) [ x=0 7 g(u,x) f(x,y)] followed by Horizontal 1D DCT Vertical 1D DCT

9 Given u and v, h can be viewed as an image of x and y. u v DCT coefficients are projection of image block into these patterns.

10 Quantization Recall that quantization can be used to collapseнурах the input into smaller number of values.- эрхэм For DCT coefficients,- we quantize different coefficients in different details: DC coefficient should have the most quantization levels. Quantization for AC coefficients can be coarser and coarser as the frequency increases.

11 Y quantization table U, V quantization table Quantization: De-quantization: F q (u,v) = round(f(u,v)/q(u,v)) F r (u,v) = F q (u,v) * Q(u,v)

12 quantization dequantization

13 The Quality Factor For most-ихэнх current-урсгал JPEG encoders, we can choose a quality-чанар factor-хүчин зүйл from 1 to 100. The method-арга of controlling the compressionшахах quality is by scaling- the quantization table. For example,-жишээ F q (u,v) = round(f(u,v)* (quality) / Q(u,v))

14 DC Coefficients Encoding D(m,n) D(m,n+1) D(m,n+2) D(m,n+3) We compute the difference of each two successive quantized coefficients D(m,n) 0 => d(m,n) D(m,n+1) D(m,n) => d(m,n+1) D(m,n+2) D(m,n+1) => d(m,n+2) D(m,n+3) D(m,n+2) => d(m,n+3)

15 DC Coefficients Encoding Then, we encode each DC difference value by (size, coefficient) 1-1, 1 2-3, -2, 2, , 4,, ,,-1024,1024,, will be coded as (3, 7) The first number 3 is Huffman - coded. The second 7 is encoded as 1 s complement 111. (-7 will be 000) The Size Table Can we encode the dc difference value directly?

16 AC Coefficients Encoding AC coefficients are not differentially encoded. Instead, we first do run-length coding. The run length code: (0,11), (0,-12), (1, -12), (0, 10), (0,16), (0, 0) Zig-zag scanning Indicates all are 0 from here

17 AC Coefficients Encoding (cont) For AC coefficients, we now have a bunch-баглаа of symbols-тэмдэг like (zero-run length, value) The value -үнэ цэнэ has large number of possible-боломжтой values in [-1023, 1023]. Direct Huffman coding is infeasible.- Instead, we generate-гаргах symbols like ( zero-run length, size, value) Huffman coded 1 s complement

18 JPEG File Format Start of image Frame End of image Tables Header Scan Scan Scan Tables Header Segment Restart Segment. Block Block Block

19 JPEG Extensions The basic mode of JPEG supports-дэмжлэг sequential дараалсан coding (the order-дэс дараа is from top-оройгоос to bottom төгсгөл and left to right-зүүнээс баруун). JPEG extensions support progressive-аажим, дэвшилтэт modes-төрөлүүд*(jpeg өрөгтгөлийг дэмждэг дэвшилтэт төрөлүүд) Spectrum selection.-спектер сонголт Successive approximation.-дараалсан утга Hierarchical mode.-шаталсан төлөв

20 JPEG 2000 JPEG 2000 is a new standard-стандарт based on wavelet- transform.-өөрчлөн хувиргах JPEG2000 does not partition-хуваах, хуваагдал, тусгаарлах an image into-руу small blocks. Wavelet decomposes-зардал the whole-бүхэл image into different-ялгаатай bands and thenтэгээд дараа нь encodes-кодолсон the coefficients in different-ялгаатай bands smartly.

21 LL LH HL HH The wavelet decomposition of Lena image using Haar Wavelet.