### Table 1. The proposed fast motion estimation algorithm.

"... In PAGE 2: ... In the following stages, CX BP C2 are used for computing BW CX . The proposed multiresolution motion estimation method algo- rithm is shown is Table1... In PAGE 4: ...0000 4. EXPERIMENTAL RESULTS The two-dimensional version of algorithm of Table1 was used for finding the best match for each block in each frame of video se- quences, from a search conducted in its neighborhood in the pre- vious frame. For the first 30 frames of the gray-scale, 8 bit-per-pixel, BFBIBCA2 BEBKBK , salesman video sequence, with blocks of size BDBI A2 BDBI,and search area of BFBF A2 BFBF (W=16), and D4 BPBE, the proposed method gives an speed up of more than 36 compared to a full search.... ..."

### Table 2. Fast full search algorithms. Motion estimation algorithm Savings

in A New Algorithm for Fast Full Search Block Motion Estimation Based on Number Theoretic Transforms

"... In PAGE 4: ... In the Table 1 the algorithmic operation counts (indexing is not accounted) and the time used are shown for the estimation of one motion vector. Table2 compares the NTT-based motion estimation algorithm to results reported in the literature for other fast full search algorithms. In the soft- ware implementation, the NTT algorithm do not appear to surpass other fast full search algorithms.... ..."

Cited by 1

### Table 1: Computational complexities of the fast motion estimation algorithms described.

"... In PAGE 21: ... To perform a direct comparison among the computational e ciencies of the fast search methods, the computational complexity of each method has been formulated for a motion displacement of size w. Table1 shows the computational complexities of the methods when w is a power of 2. Some logarithmic searches may not be able to search all the positions at the boundaries of the search window.... ..."

### Table 12. Fast full search motion estimation algorithms Algorithm Savings NTT Algorithm Savings

2002

"... In PAGE 66: ... The 48-point algorithm minimizes the count of general multiplications, where nei- ther of the multiplicands is a constant, but nonetheless it does not perform well, since the congruent reduction after a multiplication in that case is so slow operation. The approximative comparison between different fast full search algorithms is given in Table12 , where higher percentage means higher computation savings, as compared to ESA, and thus faster algorithm. However, it should be noted that there are much more considerations than just the plain execution speed given in the table: many papers benchmark motion estimation methods with good-quality video sequences with little noise and often with little motion.... In PAGE 69: ... Unlike other fast full search algorithms, or even conventional search strategies such as Three Step Search, correlation-based algorithms (as NTT) have absolutely regular data flow, and they are therefore most suitable for ASIC implementation in this aspect. The rough comparison between different fast full search algorithms is given in Table12 , but in many applications the savings will be less for methods which are not based on corre- lation. Additionally, from many papers it is not clear how the algorithms were implemented.... ..."

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### Table 3: The experimental result of applying the AEJO technique to several fast motion estimation algorithms.

1997

"... In PAGE 10: ... In all algorithms used here the EJOfactor value is set to 16, and the spiral search order and the random match order are used. Table3 illustrates the experimental results. The video quality degradation due to applying the AEJO technique is usually within 0.... ..."

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### Table 2. Motion Estimation Results for CIF sequences Sequence Algorithm Quality

2001

"... In PAGE 21: ... We have implemented the full search algorithm with the mrMAD as a matching criterion and the results are included in the following table. Table2 . Bit rate with different block matching criteria for full search Sequence Error bits with MAD as matching criterion Error bits with mrMAD as matching criterion Akiyo 3.... ..."

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### Table 5: Average relative overhead in % for implementing rate constrained motion estimation in MPEG-4.

"... In PAGE 8: ... Using an instruction profiler, the number of necessary instructions was measured for common block matching as well rate constrained motion estimation and averaged over the set of sequences coded. These results were obtained separately for frame as well as object-based coding and are listed in Table5 . As can be seen, the total... In PAGE 9: ... While the expense for SAD calculation is proportional to the number of image pixels coded, the complexity for calculating the Lagrangian term is constant and thus - based on the number of pixels as reference - higher for boundary blocks than for full image blocks, as boundary blocks are only partially filled with image data. Speaking in absolute terms, arithmetic instructions and memory operations are prevailing and the corresponding figures are thus listed separately in Table5 . It can be seen that similar relations hold for all different instruction types measured, i.... In PAGE 9: ...The values given in Table5 are basically independent of the specific search method used for motion estimation and thus also valid for fast estimation methods, as long as they are based on a subsampling of the motion vector field such as three step search or spiral search. As mentioned in section 2, spiral search was actually used in combination with the triangle inequality in our experiments.... ..."

### Table 7. Results for the Full Search motion estimation algorithm Full Search (Orig.) Full Search (Transf.)

### Table 3: Comparison between the TMN4 motion estimation algorithm and the proposed optimal motion estimator on an average basis. The comparison uses the luminance values of the the QCIF sequences quot;Miss America quot;, \Mother and Daughter quot; and quot;Foreman quot; at three di erent frame rates, 7.5, 10 and 15 frames/second and the table displays the average rate distortion performance for the TMN4 run and the matched rate and the matched distortion run of the optimal QT based motion estimator

1996

"... In PAGE 25: ... Having this rate distortion pair for every frame in the temporally downsampled sequence, we then run the optimal QT based motion estimator, in the matched rate and the matched distortion mode. Doing this for all the sequences at all the frame rates results in Table3 . Clearly the proposed motion estimator outperforms the TMN4 block matching algorithm in the rate distortion sense.... In PAGE 25: ...ense. For the matched rate case, the average increase in PSNR (decrease in DFD energy) is about 0.4 dB and for the matched distortion case the average decrease in rate is about 25%. Note that Table3 also shows that we have very good control over the rate distortion tradeo with the proposed scheme, since we can hit any given rate distortion pair with very high accuracy. We have discussed the time complexity... ..."

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### Table 1. Tradeoff between motion estimation

"... In PAGE 6: ... The bit rate (number of bytes per frame in the encoded video) is also calculated to get an idea of the compression achieved by encoding. Table1 represents tradeoffs of image quality, execution time (power consumption) and bit rate between motion esti- mation algorithm. We use full search, diamond search, three step search, one at a time search, two dimensional logarith- mic search, motion estimation without half-pel search and no motion estimation.... ..."