Mapping Analysis Between Viterbi and DTW Algorithms—Application to the Identification of Signer Independent Sign Language

In classical pattern classification theory, Viterbi algorithm represents pattern matching algorithm of statistic probability. However, DTW algorithm represents pattern matching algorithm of template matching algorithm. Whether there is any relationship between them have not been presented clearly. Aiming at this problem, the authors set up relationship between Viterbi algorithm and DTW algorithm based on application of fuzzy math theory under the premise that “the category of fuzzy math membership is the general probability”. Firstly, they propose the common closeness degree expression transferring “distance” of DTW algorithm to “probability” of Viterbi algorithm making use of closeness degree in fuzzy math and prove the common closeness degree expression theoretically. Secondly, the HMM parameters are re-estimated with the common closeness degree of DTW to set up fuzzy closeness degree relationship between DTW algorithm and Viterbi algorithm, for which the δ-ε algorithm is presented to obtain parameter re-estimating form similar to HMM based on data frame. Then, in order to ensure correctness of the fuzzy closeness relationship between DTW algorithm and Viterbi algorithm, corresponding proof is given as a theorem. Thirdly, during the HMM parameter re-estimation with the decided DTW closeness degree expression, it is found that there exists fuzzy relationship between the DTW closeness degree re-estimating parameters and the HMM re-estimating parameters and it is proved as a theorem. Finally, the authors propose Dtw-ViterbiⅠ,Ⅱ,Ⅲ based on the above theorem, prove the correctness of them as a theorem and implement them in signer-independent sign language recognition. Experiment results show that introducing the path searching strategy of DTW algorithm in Viterbi algorithm in the form of probability can partly reduce the failures in signer-independent sign language recognition by reducing candidate vocabulary thus improving the signer-independent sign language recognition rate and speed in case of large vocabulary.