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The scalable video coding (SVC) amendment of H.264/AVC offers three scalability dimensions: spatial, temporal, and quality scalabilities. Since these three dimensions can be easily combined, a single SVC bit stream has various extraction points, providing many sub-streams. When a specific bit rate is given, finding an optimal extraction point among various extraction points is a difficult problem due to the difference in the metric of each scalability dimension. We develop a method to efficiently transform three scalability dimensions into utility functions and propose an algorithm to find an efficient extraction path by using the points of inflection. Experimental results show that our approach can find a better extraction path as compared to the Joint Scalable Video Model (JSVM) basic extractor. Moreover, using the determined extraction path for an SVC bit stream is less complex owing to its monotonically increasing property.