Presentation on theme: "Time Frequency Analysis and Wavelet Transforms Oral Presentation"— Presentation transcript:
1 Time Frequency Analysis and Wavelet Transforms Oral Presentation Image CompressionJPEG and JPEG 2000Presenter：許銘宸November 9,2017
2 GoalSave the memoriesReduce the transmission time
3 HowLow frequency parts correlation between pixels→high sensitive for the human eyes ex：large area with the same colorHigh frequency parts correlation between pixel→low insensitive for the human eyes ex：edge、cornerHigh frequency parts are the information that we are uninterested
4 Evaluation Mean Square Error (MSE): 𝑀𝑆𝐸= 𝑥=0 𝑊−1 𝑦=0 𝐻−1 𝐼 𝑥,𝑦 −𝐾 𝑥,𝑦 𝑊𝐻I(x,y): original image K(x,y): reconstructed imag H: height of image W: width of imagePeak signal-to-noise ratio (PSNR):𝑃𝑆𝑁𝑅=10 log 𝑀𝐴𝑋 𝐼 2 𝑀𝑆𝐸𝑀𝐴𝑋 𝐼 :the maximum possible pixel value of the image
7 RGB to YCbCr Sensitivity for human eyes: Red(R) > Green(G) > Blue(B)Luminance(Y) > Chrominance(Cb, Cr)𝑌 =+0.299×𝑅+0.587×𝐺+0.114×𝐵𝐶 𝑏 =−0.169×𝑅−0.331×𝐺+0.500×𝐵𝐶 𝑟 =+0.500×𝑅−0.419×𝐺−0.081×𝐵
8 Downsampling Y Cb Cr Y Cb Cr Y Cb Cr or Y Cb Cr 4:4:4 (No downsampling)4:2:2 (Downsampling every 2 pixels in vertical or horizontal direction.)4:2:0(Downsampling every 2 pixels in both vertical and horizontal direction.)YCbCrYCbCrYCbCrorYCbCr
9 KL Transform & DCT Transform Fourier Transform & Fourier Series (1-Dimension):combination of sines and cosines.KL Transform & DCT Transform (2-Dimension):combination of many kinds of simple pattern (i.e. bases).
10 KLT & DCTKarhunen-Loeve Transform (KLT): Every image has its own basesAdvantage:Minimums the Mean Square Error(MSE).Disadvantage:We need to find the bases information → Computationally expensive.We need to save the bases information → More data.Discrete Cosine Transform (DCT):Compress different image by the “same” basesComputationally efficient.The performance of MSE is not as well as KL TransformBut it’s good enough.
11 Formulas of DCT:DCT 𝐹 𝑢,𝑣 = 2𝐶 𝑢 𝐶 𝑣 𝑁 𝑖=0 𝑁−1 𝑗=0 𝑁−1 𝑓 𝑖,𝑗 cos 2𝑖+1 𝑢𝜋 2𝑁 cos 2𝑗+1 𝑣𝜋 2𝑁 Inverse-DCT 𝑓 𝑖,𝑗 = 2 𝑁 𝑢=0 𝑁−1 𝑣=0 𝑁−1 𝐶 𝑢 𝐶 𝑣 𝐹 𝑢,𝑣 cos 2𝑖+1 𝑢𝜋 2𝑁 cos 2𝑗+1 𝑣𝜋 2𝑁 Where 0≤𝑖,𝑗,𝑢,𝑣≤𝑁−1, 𝐶 𝑛 = 1 2 𝑛=0 1 𝑛≠0 For JPEG N=8
20 For high compression ratio For JPEG 2000, there is no need to divide the image into many 8x8 blocksJPEG both has Strong block effect and blurJPEG-2000 only has blur
21 Forward Multicomponent Transformation Irreversible component transform (ICT) ICT is used in the lossy compression , which is same as JPEGReversible component transform (RCT) RCT is used in the lossy and lossless compressionY= R+2G+B 4C b =B−GC r =R−G
22 Tiles Size：tile >> block 重點區塊處理（Region of Interest）：不同的區域可以挑選不同的壓縮品質
33 Arithmetic coding-range encoding where C and b are integers (b is as small as possible), then the data X can be encoded bywhere means that using k-ary (k 進位) and b bits to express C.0.4375所以編碼的結果為
34 Rate control and Tier-2 encoder Rate Control： Maintain the minimum distortion for the best image quality with the optimal bitrate to specify the image data sizeTier-2 encoder： Packages the output of the Tier-1 encoder into the bit-stream.
35 Conclusion for JPEGWe transfer RGB to YCbCr since the luminance is sensitive to the human eyesWe reduce the correlation between pixels by applying DCT to concentrate the energy in DC termWe quantize the DCT blocks to reduce the high frequency components (i.e.AC terms).We transfer the 8x8 blocks into sequence for purpose of run-length-codingWe encode the sequences by Huffman-coding to minimize code length
36 Conclusion for JPEG-2000We transfer RGB to YCbCr by ICT or RCT to choose lossy or lossless compressionWe perform DWT to split each tile into several subbands to reduce the correlation between pixelsWe quantize the DWT coefficients by adjusting the quantization step to achieve lossy or lossless compressionWe encode the quantized DWT coefficients by Tier-1 encoder, Tier-2 encoder and Rate Control with arithmetic coding to get a compressed image.
37 JPEG 2000 is not as popular as JPEG For JPEG We have to input the entire image into the memory buffer of hardware.For JPEG It divides the image into several 8x8 blocks during the compression. The cost of memory for JPEG is small.JPEG 2000是基於小波變換的圖像壓縮標準。JPEG 2000的壓縮比更高，而且不會產生原先的基於離散餘弦變換的JPEG標準產 生的塊狀模糊瑕疵。JPEG 2000同時支持破壞性資料壓縮和非破壞性資料壓縮。 另外，JPEG 2000也支持更複雜的漸進式顯示和下載。 由於JPEG 2000在非破壞性壓縮下仍然能有比較好的壓縮率，所以JPEG 2000在圖 像品質要求比較高的醫學圖像的分析和處理中已經有了一定程度的廣泛應用。
38 Reference 酒井善則、吉田俊之 共著，白執善 編譯，影像壓縮技術 映像情報符号化， 全華科技圖書股份有限公司, Oct. 2004 Discrete Wavelet Transform for JPEG 2000 Tier 1 and Tier 2 Encoding Techniques for JPEG 2000 WIKIPEDIA, “JPEG”, WIKIPEDIA, “JPEG2000”,