1.
a. JPEG2000 achieves spatial scalability by using wavelet transform. Suppose you want to enable 3 spatial layers,
show the wavelet decomposition structure (i.e. how is the image decomposed into different subbands) and specify which band(s) each spatial layer includes. If the original image has a size of MxN, what is the spatial resolution of each layer?
b. H.264/SVC achieves temporal scalability by using hierarchical temporal prediction structure. Suppose you want to code a video into a temporal scalable video stream with 3 temporal layers. Illustrate the temporal prediction structure that you would use. If the original video has a frame rate of 30 Hz, what is the frame rate of your layer 1, layer1+ layer 2 and layer 1+layer2+layer 3?

2.Suppose you are given a sequence of video frames taken when the cameraman's hand was not stable, so that successive video frames have some small global shift between each frame. You would like to stabilize this video by finding the shift between each frame and a center frame, and compensate the shift of each frame so that it is aligned with the center frame. (a ) Write a MATLAB program that can estimate the global shift between two frames (f1 and f2), with the following syntax: [vx,vy]=EstiamteShift(f1, f2). (b) Write a MATLAB function for stabilizing 3 frames, which calls your EstimateShift( ) function. Your proposed should have a syntax: [g1,g2,g3]=stabilize(f1,f2,f3), where fi are original i-th frame, gi are stabilized i-th frame.

3.(a) Write a MATLAB script for coding a video frame f2 as a B-frame, using f1 and f3 as two reference frames. For each block, it finds the best intra-prediction, uni-directional inter-prediction (f2 from f1), and bi-directional inter-prediction (f2 from f1 and f3), and use the prediction that has the smallest prediction error (in terms of sum of absolute difference). It then form the prediction error block, and applies DCT transform on the prediction error (same transform block size as the prediction block), quantize the transform coefficients using a uniform quantizer centered at 0 with a constant quantization stepsize QS. The program should have the following syntax:
[f2q]=BframeCoding(f2,f1,f3,QS,fp)
where f2q is the decoded frame for f2, fp is the pointer to the file storing the encoded bits for this frame. Assume the following functions are given to you. Write all other operations that are necessary, including deciding which
mode to use, performing DCT, quantization, inverse DCT. However, you can call dct2( ) and idct2( ) functiona of MATLAB.
• [IntraDirection, PredBlock,]=IntraPred(f, x0,y0,B), where f is the frame being coded, and x0, y0 is the top-left pixel coordinate of the block, and BxB is the block size; IntraMode is the best intra mode found, PredBlock is the best prediction block.
• [vx,vy,PredBlock]=MotionEstimation(f1,f2,x0,y0,B), where f1 is the frame being coded, f2 is the reference frame for motion estimation, vx,vy is the motion vector found, PredBlock is the prediction block
• [ModeBits]=BinaryEncodingMode(BestMode,IntraDirection,vx1,vy1,vx2,vy2); where BestMode is the chosen mode ("0"=intra, "1"=uni-directional inter, "2"=bi-directional inter), IntraDirection is the best intra-prediction direction returned by IntraPred( ), (vx1,vy1) is the motion vector of the current block in f2 with respect to f1, and the (vx2,vy2) is the motion vector of the current block in f2 with respect to f3, both are returned by the MotionEstimation( ) function; ModeBits are the binary bits generated for the mode information.
• [CoeffBits]=BinaryEncodingCoef(QDCTIndics); where QDCTIndics include the blocks of quantized DCT coefficient indices, CoeffBits are the binary bits generated for QDCTIndics.
• AppendBits(Bits, fp): append Bits to the compressed file
(b) Write a main function for coding frames f1, f2, f3, f4, f5 as I-, B-, P-, B-, P-frames. Assume the following functions are available:
[fq]=IframeCoding(f,QS,fp): coding frame f using intra-mode only
[f2q]=PframeCoding(f2,f1,QS,fp): coding frame f2 using either intra-mode or uni-directional prediction from f1 [f2q]=BframeCoding(f2,f1,f3,QS,fp): coding frame f2 using either intra-mode or uni-directional prediction from f1 or bi-directional prediction from f1 and f3.