Complexity can be discussed in two different ways: time and space. Both complex-ities of the proposed and optimal methods are discussed.
The complexity of Farins’ optimal method is divided into two parts: the build-ing of codbuild-ing cost matrix described in Sec. 2.1, and the optimal partition algorithm described in Sec. 2.2. While building the cost matrix, the coding cost of all subse-quences beginning at frame i and ending at frame k with reference frame r must be computed. Suppose that the sequence has N frames, the time and space complexity of building a cost matrix will be N3. However, a method was developed to reduce the space required for N2. The optimal partition algorithm using Eq. (4) to find the best partition frame-by-frame takes N2time.
The proposed method calculates the accumulated translation and scaling first, and both of them take linear time. The finding of candidate partition points also requires linear time because it only observes the changes of accumulated transla-tion and scaling once. Let M be the number of candidate partitransla-tion points found in Sec. 4.1, finding reference frame for all possible subsequences takes M2× N time.
Finally, the Farins’ optimal partition is applied. Since only M candidate partition points are involved, it takes only M2time. The accumulated translations and scal-ings must be held in memory and the coding-cost matrix must be generated. These will need 2N + M2space.
Table 5 shows the complexity of both methods. The proposed method takes N + N + M2× N + M2time, i.e. O(M2× N) in time and O(M2) + O(N ) in space.
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Table 5. Complexity comparison.
Time Space
Farin et al.’s optimal method O(N3) O(N2) Proposed method O(M2N) O(M2)+O(N)
Since M is usually very small in contrast to N in practice, for example, M = 6 and N = 300 in the sequence “stefan”, this makes the complexity of the proposed method better than the optimal method.
7. Conclusions
An efficient and fast method for generating multiple sprites is proposed. In contrast to the conventional sprite generating method that uses a single sprite, using multiple sprites reduces the storage space of sprites. Conventional multiple sprite generation method uses an exhaustive search to find the optimal subsequence partition and optimal reference frame of each partition. However, the exhaustive search costs a lot of time. The proposed method consists of a subsequence partition algorithm and a fast reference frame selection algorithm, which are developed based on the frame accumulated translations and scalings. By using the proposed methods, a video sequence can be partitioned and reference frame can be selected in a very short time. In order to increase the performance of the selected reference frames, two reference frame validation methods are also proposed. The proposed validation methods searches frames close to the result of the fast reference frame selection method and checks if better reference frame exists. The experimental results also show that the proposed method greatly increases the executing speed from 10 to 190 times in contrast to the Farins’ optimal method, the total sprite size is slightly higher and the qualities of generated sprites are preserved.
Acknowledgments
This work is supported in part by National Science Council under the contract number NSC-96-2221-E-009-201-. The authors would like to thank the anonymous reviewers for their many valuable suggestions which have greatly improved the presentation of the paper.
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MPEG-4, World Multiconference on Systemics, Proc. Cybernetics and Informatics (SCI)XIII (July 2001) 420–425. currently a Ph.D. student in the Institute of Computer Science and Engineering at National Chiao Tung University, Hsinchu, Tung University, Hsinchu, Taiwan in 1987.
From August 1977 to April 1979 she worked as a research assistant in the Chung-Shan Institute of Science and Technology, Taoyan, Taiwan. From May 1979 to February 1981 she worked as a research associate in the Electronic Research and Service Organi-zation, Industry Technology Research Insti-tute, Hsinchu, Taiwan. From March 1981 to August 1983 she worked as an engineer in the Institute of Information Industry, Taipei, Tai-wan. She is now a Professor in the Depart-ment of Computer Science at the National Chiao Tung University.
Her current research interests include image processing, pattern recognition, mul-timedia compression, content-based retrieval and multimedia steganography.
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1. Walid Barhoumi, Mohammed Chafik Bakkay, Ezzeddine Zagrouba. 2013. An online approach for multi-sprite generation based on camera parameters estimation. Signal, Image and Video Processing 7:5, 843-853. [CrossRef]
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