7.11 Problems

1.	In MPEG-1, with the group of picture structure of N = 12 and M = 3, the maximum motion speed is assumed to be 15.5 pixels/frame (half pixel precision), calculate the number of search operations required to estimate the motion in P-pictures with: telescopic method direct on the P-pictures
2.	In an MPEG-1 encoder, for head-and-shoulders-type pictures, the maximum motion speed for P-pictures is set to 13 pixels and those of the forward and backward for the first B-picture in the subgroup are set to five pixels and nine pixels, respectively. explain why the search range for the B-picture is smaller than that of the P-picture what would be the forward and backward search ranges for the second B-picture in the subgroup? calculate the number of search operations with half pixel precision for the P and B-pictures
3.	An I-picture is coded at 50 kbits. If the quantiser step size is linearly distributed between 10 and 16, find the complexity index for this picture.
4.	In coding of SIF-625 video at 1.2 Mbit/s, with a group of pictures (GOP) structure N = 12, M = 3, the ratios of complexity indices of I, P and B are 20: 10: 7, respectively. Calculate the target bit rate for coding of each frame in the next GOP.
5.	If in problem 4 the allocated bits to B-pictures were reduced by a factor of 1.4, find the new complexity indices and the target bits to each picture type.
6.	In problem 4 if due to scene change the average quantiser step size in the last P-picture of the GOP was doubled, but those of other pictures did not change significantly: how do the complexity index ratios change? what is the new target bit rate for each picture type?
7.	If in problem 4 the complexity indices ratios were wrongly set to 1:1:1, but after coding the average quantiser step sizes for I, P and B were 60, 20 and 15 respectively, find: the target bit rate for each picture type before coding the target bit rate for each picture type of the next GOP.

Answers

1.	each operation = (2 × l5 + 1)² + 8 = 969, total operations = 3 × 969 = 2907 ω = 3 × 15 = 45, total no of operations = (2 x 45 + 1)² + 8 = 8289
2.	the first B-picture is closer to its forward prediction than its backward prediction picture. for the second B-picture, FWD = 9 and BWD = 5 for P-picture (2 × 13 + 1)² + 8 = 737, and for each B-picture (2 × 5 + 1)² + 8 + (2 x 9 + 1)² + 8 = 498
3.	Average and the complexity index is 50 × 1000 × 13 = 65 × 10⁴.
4.	(8 × 7) + (3 × 10) + 20 = 106 for I-pictures: for P = 54.3 kbits and for B = 38 kbits.
5.	The new index ratio for B becomes 7/1.4 = 5 (8 × 5) + (3 × 10) + 20 = 90, and bits for I = 128 kbits, for P = 64 and for B = 32 kbits
6.	20 + 10 + 10 + 20 + 8 × 7=116 for P, the average index of (10 + 10 + 20)/3 = 13.3 should be used, hence the target bit rates for I = 99.3 kbits, for P = 66.2 kbits and for B = 34.75 kbits.
7.	all equal to 48 kbit/s 60 + 3 × 20+8 × 15 = 240 For for P = 48 kbits and for B = 36 kbits