Transform_coding_2005 - Lecture notes of Image Compression...

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Lecture notes of Image Compression and Video Compression 2. Transform Coding
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#2 Topics z Introduction to Image Compression z Transform Coding z Subband Coding, Filter Banks z Haar Wavelet Transform z SPIHT, EZW, JPEG 2000 z Motion Compensation z Wireless Video Compression
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#3 Transform Coding z Why transform Coding? z Purpose of transformation is to convert the data into a form where compression is easier. This transformation will transform the pixels which are correlated into a representation where they are decorrelated. The new values are usually smaller on average than the original values. The net effect is to reduce the redundancy of representation. z For lossy compression, the transform coefficients can now be quantized according to their statistical properties, producing a much compressed representation of the original image data.
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#4 Transform Coding Block Diagram z Transmitter z Receiver Segment into n*n Blocks Forward Transform Quantization and Coder Original Image f(j,k) F(u,v) F*(uv) Channel Combine n*n Blocks Inverse Transform Decoder Reconstructed Image f(j,k) F(u,v) F*(uv)
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#5 How Transform Coders Work z Divide the image into 1x2 blocks z Typical transforms are 8x8 or 16x16 x 1 x 1 x 2 x 2
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#6 Joint Probability Distribution z Observe the Joint Probability Distribution or the Joint Histogram. x 1 x 2 Probability
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#7 Pixel Correlation in Image[Amar] z Rotate 45 o clockwise Source Image: Amar Before Rotation After Rotation = = 2 1 2 1 45 cos 45 sin 45 sin 45 cos X X Y Y Y o o o o
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#8 Pixel Correlation Map in [Amar] -- coordinate distribution z Upper: Before Rotation z Lower: After Rotation z Notice the variance of Y 2 is smaller than the variance of X 2 . z Compression: apply entropy coder on Y 2.
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#9 Pixel Correlation in Image[Lenna] z Let’s look at another example Before Rotation After Rotation Source Image: Lenna = = 2 1 2 1 45 cos 45 sin 45 sin 45 cos X X Y Y Y o o o o
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#10 Pixel Correlation Map in [Lenna] -- coordinate distribution z Upper: Before Rotation z Lower: After Rotation z Notice the variance of Y 2 is smaller than the variance of X 2 . z Compression: apply entropy coder on Y 2.
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#11 Rotation Matrix z Rotated 45 degrees clockwise z Rotation matrix A = = = = 2 1 2 1 2 1 2 2 2 2 2 2 2 2 45 cos 45 sin 45 sin 45 cos X X X X AX Y Y Y o o o o = = = 1 1 1 1 2 2 2 2 2 2 2 2 2 2 45 cos 45 sin 45 sin 45 cos o o o o A
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#12 Orthogonal/orthonormal Matrix z Rotation matrix is orthogonal . z The dot product of a row with itself is nonzero .
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This note was uploaded on 06/09/2011 for the course CAP 5015 taught by Professor Mukherjee during the Spring '11 term at University of Central Florida.

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Transform_coding_2005 - Lecture notes of Image Compression...

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