Method of recognition of human motion, vector sequences and speech

• US 20030208289A1
• Filed: 05/01/2003
• Published: 11/06/2003
• Est. Priority Date: 05/06/2002
• Status: Active Grant

• Current Assignee: Jezekiel Ben-Arie
• Original Assignee: Jezekiel Ben-Arie
• Inventors: Ben-Arie, Jezekiel
• Granted Patent: US 7,366,645 B2
• Time in Patent Office: Days
• US Class Current: 700/61
• CPC Class Codes: G06F 3/011 Arrangements for interaction with the human body, e.g. for user immersion in virtual reality blind teaching G09B21/00
• CPC Class Codes: G06V 40/20 Movements or behaviour, e.g. gesture recognition recognition of facial expressions G06V40/16
• CPC Class Codes: G10L 15/142 Hidden Markov Models [HMMs]

Abstract

A method for recognition of an input human motion as being the most similar to one model human motion out of a collection of stored model human motions. In the preferred method, both the input and the model human motions are represented by vector sequences that are derived from samples of angular poses of body parts. The input and model motions are sampled at substantially different rates. A special optimization algorithm that employs sequencing constraints and dynamic programming, is used for finding the optimal input-model matching scores. When only partial body pose information is available, candidate matching vector pairs for the optimization are found by indexing into a set of hash tables, where each table pertains to a sub-set of body parts. The invention also includes methods for recognition of vector sequences and for speech recognition.

Claims

1. A method for recognizing an input human motion as most similar to a model human motion, which is a member of a stored collection of model human motions, comprising the steps of:

a. Creating a collection of model human motions by measuring and recording the model trajectories of body parts that pertain to human performances of such collection of model human motions;

b. sampling at a model-rate of sampling, one recorded model trajectories of body parts;

c. repeating step b each time with another recorded model trajectories of body parts, until all the recorded model trajectories of body parts included in the collection of model human motions, have been sampled;

d. representing each sample of the recorded model trajectories of body parts by a model vector m_rj;

wherein each component of such model vector is derived from a sample of a recorded model trajectory of one body part;

e. representing each member of the collection of model human motions by a model vectors sequence M_j=(m_1j . . . m_rj . . . m_qj);

wherein the subscript q denotes the total number of model vectors in the model vectors sequence M_j;

wherein the subscript r denotes the location of the model vector m_rj within the model vectors sequence M_j;

wherein the subscript j denotes the serial number of the model vectors sequence M_j within the collection of model vectors sequences {M_j} that represents the corresponding collection of model human motions;

f. storing in a hash table, the entire collection of model vectors sequences {M_j} by storing each of the model vectors m_rj that belongs to the collection of model vectors sequences {M_j}, in a hash table bin whose address is the nearest to the model vector m_rj;

g. Acquiring an input human motion by measuring and recording the input trajectories of body parts that pertain to a human performance of such input human motion;

h. sampling at an input-rate of sampling, the recorded input trajectories of body parts;

wherein the input-rate of sampling is set to be substantially different from the model-rate of sampling;

i. representing each sample of the recorded input trajectories of body parts by an input vector t_nk;

wherein each component of such an input vector is derived from a sample of a recorded input trajectory of the same body part that pertains to the corresponding component of the model vector m_rj;

j. representing the sampled input human motion by an input vectors sequence T_k=(t_1k . . . t_nk . . . t_pk);

wherein the subscript p denotes the total number of input vectors in the input vectors sequence;

wherein the subscript n denotes the location of the input vector t_nk within the input vectors sequence T_k;

wherein the subscript k denotes the serial number of the input vectors sequence;

k. employing an optimal matching algorithm to find the optimal matching score between the input vectors sequence T_k and one model vectors sequence M_j, which is one of the members of the collection of model vectors sequences {M_j};

l. repeating step k until all the optimal matching scores that pertain to all the model vectors sequences M_j, which are members of the collection of model vectors sequences {M_j} are found;

m. comparing all the optimal matching scores that pertain to all the model vectors sequences M_j, which are members of the collection of model vectors sequences {M_j} and finding one model vectors sequence M_o that has the highest optimal matching score;

recognizing the input human motion as most similar to the model human motion that pertains to the model vectors sequence M_o with the highest optimal matching score;

2. The method of claim 1 wherein employing the optimal matching algorithm for finding the optimal matching score between the input vectors sequence T_k and one model vectors sequence M_j, which is one of the members of the collection of model vectors sequences {M_j}, comprising of the steps:

a. indexing into a hash table, each input vector t_nk that belongs to the input vectors sequence T_k, and retrieving all the model vectors m_rj that are near to each input vector t_nk;

using the model vectors retrieved to construct all the vector pairs (t_nk, m_rj) composed of vectors that are near to one another;

b. computing for each vector pair (t_nk, m_rj) retrieved in step a, a pair matching score that reflects the vector pair'"'"'s matching quality;

c. removing from all the vector pairs retrieved all the vector pairs that have a pair matching score equal or below a predetermined threshold and retaining the remaining vector pairs and naming these remaining vector pairs as matching vector pairs;

d. employing an optimization algorithm to find the valid pair sequence with the highest sequence matching score;

wherein a sequence matching score of a valid pair sequence is defined as the sum of all the pair matching scores that pertain to the matching vector pairs that are components of the valid pair sequence;

wherein the valid pair sequence is constructed only from sequences of matching vector pairs that have mutual sequential relation;

wherein the mutual sequential relation between any two matching vector pairs . . . (t_nk, m_rj) . . . (t_ck, m_ej) . . . included in the valid pair sequence has to fulfill the following 3 conditions;

(I) c is not equal to n (II) if c>

n, then r≦

e;

(III) if c<

n then e≦

r;

e. naming the valid pair sequence with the highest sequence matching score as the optimal pair sequence with the optimal matching score;

3. The method of claim 2 wherein the recorded trajectories of human body parts are equivalent to recorded poses of human body parts;

wherein both the collection of model vectors sequences {M_j } and the input vectors sequence T_k are derived from samples of recorded poses of human body parts and from temporal derivatives of samples of recorded poses of human body parts.

4. The method of claim 3 wherein the samples of recorded poses of human body parts and the temporal derivatives of samples of recorded poses of human body parts, correspond to samples of recorded angular poses of body parts and to temporal derivatives of samples of recorded angular poses of human body parts.

5. The method of claim 4 wherein the input vectors sequence T_k is acquired by a sparse-slow input-rate of sampling and acquiring by a fast model-rate of sampling each of the model vectors sequences M_j, which are members of the collection of model vectors sequences {M_j}.

6. The method of claim 5 wherein the optimal matching scores are obtained by a special optimization algorithm that employs principles of dynamic programming.

7. The method of claim 4 wherein the input vectors sequence T_k is acquired by a fast input-rate of sampling and each model vectors sequence M_j, which is a member of the collection of model vectors sequences {M_j} is acquired by slow-sparse model-rate of sampling.

8. The method of claim 7 wherein the optimal matching scores are obtained by a special optimization algorithm that employs principles of dynamic programming.

9. The method of claim 1 wherein employing the optimal matching algorithm for finding the optimal matching score between the input vectors sequence T_k and one model vectors sequence M_j, which is one of the members of the collection of model vectors sequences {M_j}, comprising of the steps:

a. indexing into a hash table, each input vector t_nk that belongs to the input vectors sequence T_nk, and retrieving all the model vectors m_rj that are near to each input vector t_nk;

using the model vectors retrieved to construct all the vector pairs (t_nk, m_rj) composed of vectors that are near to one another;

b. computing for each vector pair (t_nk, m_rj) retrieved in step a, a pair matching score that reflects the vector pair'"'"'s matching quality;

c. removing from all the vector pairs retrieved all the vector pairs that have a pair matching score equal or below a predetermined threshold and retaining the remaining vector pairs and naming these remaining vector pairs as matching vector pairs;

d. employing an optimization algorithm to find the valid pair sequence with the highest sequence matching score;

wherein a sequence matching score of a valid pair sequence is defined as the sum of all the pair matching scores that pertain to the matching vector pairs that are components of the valid pair sequence;

wherein the valid pair sequence is constructed only from sequences of matching vector pairs that have mutual sequential relation;

wherein the mutual sequential relation between any two matching vector pairs . . . (t_nk, m_rj) . . . (t_ck, M_ej) . . . included in the valid pair sequence has to fulfill the following 3 conditions;

(I) r is not equal to e;

(II) if e>

r, then n≦

c;

(III) if e<

r then c≦

n;

e. naming the valid pair sequence with the highest sequence matching score as the optimal pair sequence with the optimal matching score;

10. The method of claim 9 wherein the recorded trajectories of human body parts are equivalent to recorded poses of human body parts;

wherein both the collection of model vectors sequences {M_j} and the input vectors sequence T_k are derived from samples of recorded poses of human body parts and from temporal derivatives of samples of recorded poses of human body parts.

11. The method of claim 10 wherein the samples of recorded poses of human body parts and the temporal derivatives of samples of recorded poses of human body parts, correspond to samples of recorded angular poses of body parts and to temporal derivatives of samples of recorded angular poses of human body parts.

12. The method of claim 11 wherein the input vectors sequence T_k is acquired by a sparse-slow input-rate of sampling and acquiring by a fast model-rate of sampling each of the model vectors sequences M_j, which are members of the collection of model vectors sequences {M_j}.

13. The method of claim 12 wherein the optimal matching scores are obtained by a special optimization algorithm that employs principles of dynamic programming.

14. The method of claim 11 wherein the input vectors sequence T_k is acquired by a fast input-rate of sampling and each model vectors sequence M_j, which is a member of the collection of model vectors sequences {M_j} is acquired by slow-sparse model-rate of sampling.

15. The method of claim 14 wherein the optimal matching scores are obtained by a special optimization algorithm that employs principles of dynamic programming.

16. A method for recognizing an input vectors sequence T_k as most similar to a model vectors sequence M_j, which is a member of a stored collection of model vectors sequences {M_j}, comprising the steps of:

a. Creating a collection of model signal sets by measuring and recording all the model signal sets of a collection of model signal sets;

b. sampling at a model-rate of sampling, one model signal set;

c. repeating step b each time with another model signal set, until all the recorded model signal sets included in the collection of model signal sets, have been sampled;

d. representing each sample of the model signal set by a model sample vector w_rj;

wherein each component of such model sample vector is derived from one sample of one recorded model signal that belongs to the model signal set;

e. transforming each model sample vector w_rj into a model vector m_rj using a pre-specified transformation;

f. representing each member of the collection of model vectors sequences by a model vectors sequence M_j=(m_1j . . . m_rj . . . m_qj);

wherein the subscript q denotes the total number of model vectors in the model vectors sequence M_j;

wherein the subscript r denotes the location of the model vector m_rj within the model vectors sequence M_j;

wherein the subscript j denotes the serial number of the model vectors sequence M_j within the collection of model vectors sequences {M_j};

g. storing in a hash table, the entire collection of model vectors sequences {M_j} by storing each of the model vectors m_rj that belongs to the collection of model vectors sequences {M_j}, in a hash table bin whose address is the nearest to the model vector m_rj;

h. Acquiring an input signal set by measuring and recording an input signal set;

wherein each input signal of the input signal set corresponds to a model signal of the model signal set;

i. sampling at an input-rate of sampling, the recorded input signal set;

wherein the input-rate of sampling is adjusted to be substantially different from the model-rate of sampling;

j. representing each sample of the recorded input signal set by an input sample vector v_nk;

wherein each component of such an input sample vector is derived from one sample of a recorded input signal that belongs to the input signal set;

k. transforming each input sample vector v_nk into an input vector t_rj using a pre-specified transformation;

l. representing the sampled input signal set by an input vectors sequence T_k=(t_1k . . . t_nk . . . t_pk);

wherein the subscript p denotes the total number of input vectors in the input vectors sequence;

wherein the subscript n denotes the location of the input vector t_nk within the input vectors sequence T_k;

wherein the subscript k denotes the serial number of the input vectors sequence;

m. employing an optimal matching algorithm to find the optimal matching score between the input vectors sequence T_k and one model vectors sequence M_j, which is one of the members of the collection of model vectors sequences {M_j};

n. repeating step k until all the optimal matching scores that pertain to all the model vectors sequences M_j, which are members of the collection of model vectors sequences {M_j} are found;

o. comparing all the optimal matching scores that pertain to all the model vectors sequences M_j, which are members of the collection of model vectors sequences {M_j} and finding one model vectors sequence M_o that has the highest optimal matching score;

recognizing the input signal set as most similar to the model signal set that pertains to the model vectors sequence M_o with the highest optimal matching score;

17. The method of claim 16 wherein employing the optimal matching algorithm for finding the optimal matching score between the input vectors sequence T_k and one model vectors sequence M_j, which is one of the members of the collection of model vectors sequences {M_j}, comprising of the steps:

a. indexing into a hash table, each input vector t_nk that belongs to the input vectors sequence T_k, and retrieving all the model vectors m_rj that are near to each input vector t_nk using the model vectors retrieved to construct all the vector pairs (t_nk, m_rj) composed of vectors that are near to one another;

b. computing for each vector pair (t_nk, m_rj) retrieved in step a, a pair matching score that reflects the vector pair'"'"'s matching quality;

c. removing from all the vector pairs retrieved all the vector pairs that have a pair matching score equal or below a predetermined threshold and retaining the remaining vector pairs and naming these remaining vector pairs as matching vector pairs;

d. employing an optimization algorithm to find the valid pair sequence with the highest sequence matching score;

wherein a sequence matching score of a valid pair sequence is defined as the sum of all the pair matching scores that pertain to the matching vector pairs that are components of the valid pair sequence;

wherein the valid pair sequence is constructed only from sequences of matching vector pairs that have mutual sequential relation;

wherein the mutual sequential relation between any two matching vector pairs . . . (t_nk, m_rj) . . . (t_ck, M_ej) . . . included in the valid pair sequence has to fulfill the following 3 conditions;

(I) c is not equal to n (II) if c>

n, then r≦

e;

(III) if c<

n then e≦

r

e. naming the valid pair sequence with the highest sequence matching score as the optimal pair sequence with the optimal matching score;

18. The method of claim 17 wherein the input vectors sequence T_k is acquired by a sparse-slow input-rate of sampling and acquiring by a fast model-rate of sampling each of the model vectors sequences M_j, which are members of the collection of model vectors sequences {M_j}.

19. The method of claim 18 wherein the optimal matching scores are obtained by a special optimization algorithm that employs principles of dynamic programming.

20. The method of claim 19 wherein both the input vectors sequence T_k and the collection of model vectors sequences {M_j} represent speech utterances and both the collection of model vectors sequences {M_j} and the input vectors sequence T_k are derived from values of sampled speech signals, discrete transforms of sampled speech signals and their temporal derivatives.

21. The method of claim 17 wherein the input vectors sequence T_k is acquired by a fast input-rate of sampling and acquiring by a slow-sparse model-rate of sampling each of the model vectors sequences M_j, which are members of the collection of model vectors sequences {M_j}.

22. The method of claim 21 wherein the highest sequence matching scores are obtained by a special optimization algorithm that employs principles of dynamic programming.

23. The method of claim 22 wherein both the input vectors sequence T_k and the collection of model vectors sequences {M_j} represent speech utterances and both the collection of model vectors sequences {M_j} and the input vectors sequence T_k are derived from values of sampled speech signals, discrete transforms of sampled speech signals and their temporal derivatives.

24. The method of claim 16 wherein employing the optimal matching algorithm for finding the optimal matching score between the input vectors sequence T_k and one model vectors sequence M_j, which is one of the members of the collection of model vectors sequences {M_j}, comprising of the steps:

a. indexing into a hash table, each input vector t_nk that belongs to the input vectors sequence T_k, and retrieving all the model vectors m_rj that are near to each input vector t_nk;

using the model vectors retrieved to construct all the vector pairs (t_nk, m_rj) composed of vectors that are near to one another;

b. computing for each vector pair (t_nk, m_rj) retrieved in step a, a pair matching score that reflects the vector pair'"'"'s matching quality;

c. removing from all the vector pairs retrieved all the vector pairs that have a pair matching score equal or below a predetermined threshold and retaining the remaining vector pairs and naming these remaining vector pairs as matching vector pairs;

d. employing an optimization algorithm to find the valid pair sequence with the highest sequence matching score;

wherein a sequence matching score of a valid pair sequence is defined as the sum of all the pair matching scores that pertain to the matching vector pairs that are components of the valid pair sequence;

wherein the valid pair sequence is constructed only from sequences of matching vector pairs that have mutual sequential relation;

wherein the mutual sequential relation between any two matching vector pairs . . . (t_nk, m_rj) . . . (t_ck, m_ej) . . . included in the valid pair sequence has to fulfill the following 3 conditions;

(I) r is not equal to e;

(II) if e>

r, then n≦

c;

(III) if e<

r then c≦

n;

e. naming the valid pair sequence with the highest sequence matching score as the optimal pair sequence with the optimal matching score;

25. The method of claim 24 wherein the input vectors sequence T_k is acquired by a sparse-slow input-rate of sampling and acquiring by a fast model-rate of sampling each of the model vectors sequences M_j, which are members of the collection of model vectors sequences {M_j}.

26. The method of claim 25 wherein the optimal matching scores are obtained by a special optimization algorithm that employs principles of dynamic programming.

27. The method of claim 26 wherein both the input vectors sequence T_k and the collection of model vectors sequences {M_j} represent speech utterances and both the collection of model vectors sequences {M_j} and the input vectors sequence T_k are derived from values of sampled speech signals, discrete transforms of sampled speech signals and their temporal derivatives.

28. The method of claim 24 wherein the input vectors sequence T_k is acquired by a fast input-rate of sampling and acquiring by a slow-sparse model-rate of sampling each of the model vectors sequences M_j, which are members of the collection of model vectors sequences {M_j}.

29. The method of claim 28 wherein the highest sequence matching scores are obtained by a special optimization algorithm that employs principles of dynamic programming.

30. The method of claim 29 wherein both the input vectors sequence T_k and the collection of model vectors sequences {M_j} represent speech utterances and both the collection of model vectors sequences {M_j} and the input vectors sequence T_k are derived from values of sampled speech signals, discrete transforms of sampled speech signals and their temporal derivatives.

31. A method for recognizing an input human motion as most similar to a model human motion, which is a member of a stored collection of model human motions, comprising the steps of:

a. Creating a collection of model human motions by measuring and recording the model trajectories of body parts that pertain to human performances of such collection of model human motions;

b. sampling at a model-rate of sampling, one recorded model trajectories of body parts;

c. repeating step b each time with another recorded model trajectories of body parts, until all the recorded model trajectories of body parts included in the collection of model human motions, have been sampled;

d. representing each sample of the recorded model trajectories of body parts by a model vector m_rj;

wherein each component of such model vector is derived from a sample of a recorded model trajectory of one body part;

e. representing each member of the collection of model human motions by a model vectors sequence M_j=(m_1j . . . m_rj . . . m_qj);

wherein the subscript q denotes the total number of model vectors in the model vectors sequence M_j;

wherein the subscript r denotes the location of the model vector m_rj within the model vectors sequence M_j;

wherein the subscript j denotes the serial number of the model vectors sequence M_j within the collection of model vectors sequences {M_j} that represents the corresponding collection of model human motions;

f. Acquiring an input human motion by measuring and recording the input trajectories of body parts that pertain to a human performance of such input human motion;

g. sampling at an input-rate of sampling, the recorded input trajectories of body parts;

wherein the input-rate of sampling is set to be substantially different from the model-rate of sampling;

h. representing each sample of the recorded input trajectories of body parts by an input vector t_nk;

wherein each component of such an input vector is derived from a sample of a recorded input trajectory of the same body part that pertains to the corresponding component of the model vector m_rj;

i. representing the sampled input human motion by an input vectors sequence T_k=(t_1k . . . t_nk . . . t_pk);

wherein the subscript p denotes the total number of input vectors in the input vectors sequence;

wherein the subscript n denotes the location of the input vector t_nk within the input vectors sequence T_k;

wherein the subscript k denotes the serial number of the input vectors sequence;

j. dividing the full set of human body parts into several groups of human body parts;

k. in complete correspondence to the division into groups of human body parts, also dividing each of the input vectors and each of the model vectors into input sub-vectors and corresponding model sub-vectors;

wherein each sub-vector pertains to another group of human body parts;

l. storing each division of model sub-vectors, which corresponds to the same group of body parts, in a separate hash sub-table;

wherein the hash sub-table has addressing sub-vectors that correspond in their dimensions to the dimensions of the model sub-vectors stored;

wherein each model sub-vector is stored in a hash sub-table bin whose address sub-vector is the nearest to the model sub-vector;

wherein the bins have address sub-vectors that are determined by a process of vector quantization;

m. indexing each of the input vectors t_nk within the input vectors sequence T_k by using each of its input sub-vectors to index separately into the corresponding hash sub-table;

n. for each input vector t_nk within the input vectors sequence T_k, retrieving the corresponding model sub-vectors extracted by separately indexing with input sub-vectors that are parts of the same input vector t_nk and merging them back into model vectors m_rj;

creating from each retrieved and merged model vector m_rj a vector pair (t_nk, m_rj);

o. computing for each vector pair (t_nk, m_rj) created in step n, a pair matching score that reflects the vector pair'"'"'s matching quality;

p. removing from all the vector pairs created in step n, all the vector pairs that have a pair matching score equal or below a predetermined threshold and retaining the remaining vector pairs and naming these vector pairs as matching vector pairs;

q. employing an optimal matching algorithm to find the optimal matching score between the input vectors sequence T_k and one model vectors sequence M_j which is one of the members of the collection of model vectors sequences {M_j};

r. repeating step q until all the optimal matching scores that pertain to all the model vectors sequences M_j, which are members of the collection of model vectors sequences {M_j} are found;

s. comparing all the optimal matching scores that pertain to all the model vectors sequences M_j, which are members of the collection of model vectors sequences {M_j} and finding one model vectors sequence M_n that has the highest optimal matching score;

recognizing the input human motion as most similar to the model human motion that pertains to the model vectors sequence M_n with the highest optimal matching score;

32. The method of claim 31 wherein finding the optimal matching score between the input vectors sequence T_k and one model vectors sequence M_j, which is one of the members of the collection of model vectors sequences {M_j}, comprising of the steps:

a. constructing from the matching vector pairs, all the permutations of valid pair sequences;

wherein all the valid pair sequences are constructed only from sequences of matching vector pairs that have mutual sequential relation;

wherein the mutual sequential relation between any two matching vector pairs . . . (t_nk, m_rj) . . . (t_ck, m_ej) . . . included in the valid pair sequence has to fulfill the following 3 conditions;

(I) c is not equal to n (II) if c>

n, then r≦

e;

(III) if c<

n then e≦

r;

b. employing an optimization algorithm to find the valid pair sequence with the highest sequence matching score;

wherein a sequence matching score of a valid pair sequence is defined as the sum of all the pair matching scores that pertain to the matching vector pairs that are components of the valid pair sequence;

c. naming the valid pair sequence with the highest sequence matching score as the optimal pair sequence with the optimal matching score;

33. The method of claim 32 wherein the recorded trajectories of human body parts are equivalent to recorded poses of human body parts;

wherein both the collection of model vectors sequences {M_j} and the input vectors sequence T_k are derived from samples of recorded poses of human body parts and from temporal derivatives of samples of recorded poses of human body parts.

34. The method of claim 33 wherein the samples of recorded poses of human body parts and the temporal derivatives of samples of recorded poses of human body parts, correspond to samples of recorded angular poses of body parts and to temporal derivatives of samples of recorded angular poses of human body parts.

35. The method of claim 34 wherein the input vectors sequence T_k is acquired by a sparse-slow input-rate of sampling and acquiring by a fast model-rate of sampling each of the model vectors sequences M_j, which are members of the collection of model vectors sequences {M_j}.

36. The method of claim 35 wherein the optimal matching scores are obtained by a special optimization algorithm that employs principles of dynamic programming.

37. The method of claim 34 wherein the input vectors sequence T_k is acquired by a fast input-rate of sampling and acquiring by a slow-sparse model-rate of sampling each of the model vectors sequences M_j, which are members of the collection of model vectors sequences {M_j}.

38. The method of claim 37 wherein the optimal matching scores are obtained by a special optimization algorithm that employs principles of dynamic programming.

39. The method of claim 31 wherein finding the optimal matching score between the input vectors sequence T_k and one model vectors sequence M_j, which is one of the members of the collection of model vectors sequences {M_j}, comprising of the steps:

a. constructing from the matching vector pairs, all the permutations of valid pair sequences;

wherein all the valid pair sequences are constructed only from sequences of matching vector pairs that have mutual sequential relation;

wherein the mutual sequential relation between any two matching vector pairs . . . (t_nk, m_rj) . . . (t_ck, m_ej) . . . included in the valid pair sequence has to fulfill the following 3 conditions;

(I) r is not equal to e;

(II) if e>

r, then n≦

c;

(III) if e<

r then c≦

n;

b. employing an optimization algorithm to find the valid pair sequence with the highest sequence matching score;

wherein a sequence matching score of a valid pair sequence is defined as the sum of all the pair matching scores that pertain to the matching vector pairs that are components of the valid pair sequence;

c. naming the valid pair sequence with the highest sequence matching score as the optimal pair sequence with the optimal matching score;

40. The method of claim 39 wherein the recorded trajectories of human body parts are equivalent to recorded poses of human body parts;

wherein both the collection of model vectors sequences {M_j} and the input vectors sequence T_k are derived from samples of recorded poses of human body parts and from temporal derivatives of samples of recorded poses of human body parts.

41. The method of claim 40 wherein the samples of recorded poses of human body parts and the temporal derivatives of samples of recorded poses of human body parts, correspond to samples of recorded angular poses of body parts and to temporal derivatives of samples of recorded angular poses of human body parts.

42. The method of claim 41 wherein the input vectors sequence T_k is acquired by a sparse-slow input-rate of sampling and acquiring by a fast model-rate of sampling each of the model vectors sequences M_j, which are members of the collection of model vectors sequences {M_j}.

43. The method of claim 42 wherein the optimal matching scores are obtained by a special optimization algorithm that employs principles of dynamic programming.

44. The method of claim 41 wherein the input vectors sequence T_k is acquired by a fast input-rate of sampling and acquiring by a slow-sparse model-rate of sampling each of the model vectors sequences M_j, which are members of the collection of model vectors sequences {M_j}.

45. The method of claim 44 wherein the optimal matching scores are obtained by a special optimization algorithm that employs principles of dynamic programming.