JPH0449954B2 - - Google Patents

Description

[Detailed description of the invention]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a pattern comparison device that automatically recognizes continuous speech patterns as a series of patterns. Conventional configuration and its problems The general configuration of a speech recognition device using pattern matching is as follows. Input audio signal, filter bank, frequency analysis
Feature extraction means for converting into a series of feature vectors by LPC analysis etc., and standard pattern storage means for registering the series of feature vectors uttered in advance and extracted by the feature extraction means as standard patterns for all recognized words. pattern comparison means for calculating the similarity or distance as a series of feature vectors between the input pattern extracted by the feature extraction means and all standard patterns stored in the standard pattern storage means; and a determining means for determining and outputting a word corresponding to the standard pattern having the highest degree of similarity (smallest distance) as a recognition result as a result of pattern comparison. At this time, even if the same speaker utters the same word, the duration of the utterance differs each time, so when comparing the standard pattern and the input pattern using the pattern comparison means, the time axis of both It is necessary to expand and contract the pattern lengths of the two to make them the same and compare them. At this time, since the change in utterance time length does not occur uniformly in each part of the uttered word, it is necessary to expand and contract each part non-uniformly. The best results have been obtained when the expansion/contraction is performed in a way that maximizes the similarity between the two patterns to be compared (minimizes the distance), as explained below using distance. (hereinafter, this matching is referred to as DP matching).The DP matching method can be explained using a lattice graph.Figure 1 is a lattice graph, and The horizontal axis is the i coordinate corresponding to the input pattern T = a ₁ , a ₂ ...a _I ,
The vertical axis represents the j coordinate corresponding to the standard pattern R ⁿ =b ⁿ ₁ , b ⁿ ₂ . . . b ⁿ _Jo . Matching the input pattern T and the standard pattern by non-linearly expanding and contracting the time axis involves determining the path (1) showing the correspondence between the feature vectors of both patterns on this lattice graph using some price standard. , to evaluate the distance between both patterns with respect to this path. When determining this route, limiting conditions are set in consideration of the nature of the voice. FIG. 2a shows an example of restrictive conditions for route selection. That is, in this example, the path to point (i, j) is from point (i-2, j-1) to point (i-1, j)
Path (2) passing through, path (3) coming from point (i-1, j-1), or path (3) from point (i-1, j-2) to point (i, j
This means that only one of the routes (4) passing through -1) can be taken. At this time, if we set the condition that the start and end of the input pattern and standard pattern must correspond,
The matching path is limited to the shaded area in FIG. This restriction is made to prevent extreme correspondences from occurring due to the fact that no matter how much the time axis expands or contracts, it is unlikely that the same word will expand or contract so drastically. If the distance between the vectors a _i and b ⁿ _J is d ⁿ (i, j), the distance along the path between the input pattern T and the standard pattern R ⁿ is d ⁿ along that path.
It is defined as the weighted average of (i,j). The a, b, c, and d on the route in Figure 2 are the loads when the corresponding route is selected.In order to apply DP matching, the method of determining this load is to No matter what route is selected below, it should be determined so that the sum of the loads along that route will be constant. a=c=e=2, b=d=1
Then, the sum of this load is I+J ⁿ , a=b=c=
1, d=e=0.5, the sum of this load is I,
If a=b=0.5, c=d=e=1, the sum of these loads will be J ⁿ and will be constant regardless of how the path is selected. Both of these are commonly used. Furthermore, by making this load a function of j under the condition that the sum of the loads is constant, it is also possible to perform operations such as increasing the load on a portion of the path that is to be matched with greater emphasis. The distance between the input pattern T and the standard pattern R ⁿ is
is defined as the minimum value of the weighted average under the limiting conditions. That is, by solving the following recurrence formula, the minimum value of the weighted average and the path that provides the minimum value can be determined. g ⁿ (i, j) = mimg ⁿ (i-2, j-1) + ad ⁿ (
i-1, j) + bd ⁿ (i, j) g ⁿ (i-1, j-1) + cd ⁿ (i, j) g ⁿ (i-1, j-1) + cd ⁿ (i, j) g ⁿ (i-1, j-2)+ed ⁿ (i, j-1)+dd ⁿ (i,
j)...(1) Initial condition g ⁿ (1, 1) = d ⁿ (1, 1) D (T, R ⁿ ) = g ⁿ (I, J ⁿ )/sum of loads Here, D (T, R ⁿ ) is the distance between the input pattern T and the standard pattern _Ro . There are various other possible route selection conditions, such as those shown in FIGS. 2b to 2j, which are other examples. In addition to this, various other modifications can be considered. Of course, the recurrence formula can be rewritten into a corresponding one depending on the selection conditions of these routes. DP matching has achieved good results not only when recognizing isolated words but also when recognizing consecutively uttered sounds (uttered without any breaks between words). The problem of continuous word speech recognition is formulated as follows. The number of frames of the input pattern is I, the feature vector of the i-th frame is a _i , the number of frames of the standard pattern of word n is J ⁿ , the feature vector of the j-th frame is b ⁿ _j
Then, the standard pattern R ⁿ of word n is expressed as follows. R ⁿ = b ⁿ ₁ b ⁿ ₂ …b ⁿ _j …b ⁿ _j n Then, the combination of standard patterns corresponding to x word strings, R = R ^q(1) R ^q(2) …R ^q(x) ＝b ^q(1) ₁ b ^q(1) ₂ …b ^q(1) _Jq(1) b ^q(2) ₁ b ^q(2) ₂ …b ^q(x) _Jq(
2) Vector sequence of …b ^q(x) ₁ b ^q(x) ₂ …b ^q(x) _Jq(x) …(2) and input pattern T=a ₁ , a ₂ …a _i …a _I Word sequence q(1)q(2)…q with the minimum distance between
Find (x). If we try to solve the above calculation using DP matching in the same way as in the case of isolated words, for example, when we have a word with 10 digits as a standard pattern, we can recognize the sound of 3 digits uttered consecutively. 10 ³ = Must be matched with 1000 different standard patterns. As the number of standard patterns increases, the number of combinations quickly becomes prohibitive. Therefore, in order to apply DP matching to continuous word recognition, we set the conditions for path selection so that the normalization coefficient of the cumulative distance of matching (the sum of the weights mentioned above) depends only on the number of input frames. Then, as shown below, dynamic programming can be applied to word combinations of standard patterns, and the amount of calculation can be significantly reduced. The route selection conditions generally include those shown in FIGS. 3a to 3e. The numerical value shown on the route is the load factor when that route is selected. The j-th continuous standard pattern R consisting of the i-th frame (feature vent of the input pattern T, hereinafter referred to simply as frame) a _i and the connection of X standard patterns
The interframe distance (vector distance) of frame b ^R _j is
Let d _R (i, j) be the time function that matches the input pattern with the continuous standard pattern (the matching path) as u(i), and let the next cumulative distance (frame It is assumed that R (denoted as R^) that minimizes D (T, R) (sum of loads of distances) is to be sought. That is, D (T, R) = min u (i) [ _I 〓 ⁱ⁼¹ d _R (i, u (i))] ... (3) R^ = argmjn R [D (T, R)] here So, for the path shown in Figure 3a, 0<u(i)-u(i-1)<2, u(1)=1, u(I
)
= ^JR . Further, min[f(z)] means f(z) minimized with respect to z, and argmin[f(z)] means the value of z that minimizes f(z). Equation (3) can be solved when the number of words is known, when it is unknown, or when automaton control is incorporated. Various methods have already been proposed, and some examples have been commercialized. Among these, the present application relates to a device that recognizes continuously uttered speech by solving equation (3) in a form that incorporates automaton control. Next, formula (3) incorporating automaton control is expressed as
We will explain the conventional method for solving the problem. If we actually say the words in succession,
In many cases, their order is fixed. Therefore,
The input pattern (input sentence) is a sentence generated by a regular grammar equivalent to the finite state automaton α, and the word sequence that minimizes equation (3) among all word sequences accepted by the automaton α. (q(1), q
(2),...,q(x)), the recognition rate can be improved. Here, if the word string (q(1), q(2), ..., q(x)) is accepted by the automaton α, Δ(q _p , q(1)) = q _i
CS, Δ(q _i , q(2)=q _j CS, …, Δ(q _k , q(x−
This is a case where there is a state transition such that 1))=q _l CS, Δ(q _l , q(x))=q _f CFCS. The meaning of each symbol is that S is a finite set of states q {q∈q ₀ , q ₁ ,...,
q| _S | _-1 }, 〓 is a finite set of input words n {n∈1,
2,...,N}, Δ is the state transition function, S×〓→S,
{Δ(q ₁ , n)=q _j }, q _p is an initial state, q _p ∈S, F is a set of final states FCS. Here q(1),…q
(x)∈{1, 2,...N}. The difference from normal automaton recognition problems is that the frame number representing time is also included as a variable, and it is not just an output of acceptance or rejection.
This is the point where the degree of acceptability (cumulative distance) is output. Let D _qj (i) be the minimum cumulative distance among all word strings assuming that it ends at the input i frame in state q _j , and N _qj (i) be the last word name of the word string corresponding to D _qj (i). , B _qj (i) is the starting point position of N _qj (i) minus 1 (the last frame of the word before N _qj (i),
), Q _qj (i) is the state name that satisfies D _qj (i) by state transition to q _j , that is, Δ(Q _qj (i), N _qj (i)) = q _j . Then, by solving the following recurrence equation, the solution to equation (3) by automaton control can be obtained. That is, with the initial conditions D _qj (o)=O, B _qj (o)=0, D _q (i)=min [D _qj (m)+D ⁿ (m+1: ⁱ )], q=Δ(q _k , n ₎ ... ₍ 4) for q = q ₁ , q _{2 ,} ..., q| _{S |} ) = n^, B _q (i) = m, Q _q (i) = q _k . If this calculation is performed until i=I, words can be found in reverse order starting from the last word as follows. That is, if i=I, q=a _g ming _f D _qf (i), q _f ∈F, then n^=N _q (i) B _q (i)≠, then i=B _q (i), q=Q _q As (i), if B _q (i)=0, the process ends. FIG. 6 is a flowchart. Note that D ⁿ (m+1:i) is defined by the following equation, and is obtained using the same method as the DP matching of isolated words described above. D ⁿ (m+1:i)= min u(i) [ _i 〓 ^k=m+1 d ⁿ (k, u(k))]
...(5) Here, for the route shown in Figure 3a, ou(k)-u(k-1)2, u(m+1)=1,
u(i)=J ⁿ . Equation (3) calculates D ⁿ (m+1:i) for a predetermined range of m from i ₁ to i ₂ , and calculates D _qk (m) and D ⁿ (m+1: i) that have already been calculated for each m. m and q _k ∈ {q ₀ , q ₁ , ..., q|s|−
1} (however, q _k satisfies q = Δ(q _k , n)) and n, and use this as D _q (i). As a way to reduce this amount of calculation, after i = m + 1, is word n and the next state is q, then
(i, j) = (1, 1) to (i, j) = (i', j')
Let D ⁿ _q (i′, j′) be the cumulative distance to D ⁿ _q (i, j′).
D _q (i) as the minimum value of n, q _k of J ⁿ )
A method has been proposed to find the . The problem with these methods is that although the amount of calculation can be further reduced depending on the structure of the automaton, this point has not been taken into consideration in the past. OBJECT OF THE INVENTION It is an object of the invention to propose a pattern comparison device that significantly reduces the amount of calculation in continuous speech recognition using automaton control. Structure of the Invention The present invention provides continuous pattern DP matching using automaton control, when the automaton control rule is q=Δ(q _k , n), pattern n
On the other hand, when there are multiple states q _k , if the minimum cumulative distance to each state is q^ _k , then the cumulative distance to the last pattern n to state q is is calculated assuming that the immediately preceding state is only q^ _k , thereby reducing the cumulative distance calculation that was conventionally performed for all q _k . DESCRIPTION OF EMBODIMENTS The principle and embodiments of the present invention will be described below. FIG. 5 is a diagram for explaining the principle of the present invention,
Figure 5a is a finite automaton representation for the word written in b. For simplicity, the explanation here uses monosyllables instead of the words. In the calculations in the conventional example described above, calculations had to be performed for all state transitions (the number of which is 22 in FIG. 7). However, in the example in Figure 7,
The same "O" has entered state _S12 from states _S6 , _S7 , and _S8 . In such a case, states S ₆ , S ₇ , S ₈
If we temporarily degenerate, we get “O” in state S ₁₂ .
It only needs to be calculated once. This also applies to “YA” in state _S14 . The present invention
This is a pattern comparison device that utilizes this principle to reduce the amount of calculation. In the example of Figure 7, q=S ₁₂ , n _p =n _p (n _p is
number attached to the syllable “O”), then q=S ₁₂
^The _{meaning of equation} ^{( 3} ₎ ^for m) D ^no _S8(n) +D ^no (m+1:i) ...(7). In other words, in FIG. 5, S ₆ , S ₇ ,
When issuing “O” from S ₈ and transitioning to S ₁₂ , D _s
In order to minimize (i), D _S6 (m), D _S7 (m),
This means that the transition will start from the minimum state of D _S8 (m). If you multiply this in general,
With q _p as the initial state, D _qp (o) = 0, B _qp (o) D _q (i) = min n, m [min qk [D _qk (m)] + D ⁿ (m+1:
i)] ...(8) However, q=Δ(q _k , q) N _q (i)=n^, B _q (i)=m^, Q _q (i)=argmin [D _qk
(m^)]. That is, among the states immediately before becoming state q in frame i, the same syllable (or word) n
If something is connected, it means that it is connected from the state where the cumulative distance to reach those states is the minimum. By utilizing this fact, in the case of the example shown in FIG. 5, the above can be said about "O" and "YA", so the calculation of equation (3) becomes 19 times, which is reduced by 3 times. D ⁿ (m+
1:i) and directly solves equation (3), this quantity can be almost ignored, but when the above-mentioned high-speed calculation method is used, it becomes a big difference. Also, depending on the task, a significant reduction in the amount of calculation is expected. An embodiment in which the present invention is applied to one of the above-mentioned high-speed calculation methods will be described. According to the path restriction conditions shown in Figure 3b, D ⁿ (m+
1:i) is from (i,j)=(m,1) to (i,j)=(i,
j ⁿ ). Here, (6) has a slope of 1/2,
(7) is a straight line with a slope of 2. Now, the path (5) is (i,
j) = (1, 1) to (i, j) = (i, j ⁿ ), then according to the principles of dynamic programming, (i, j) = The path that minimizes the cumulative distance from (1, 1) to the point (i, j) = (i', j') on path (5) is (i, j) = (i ′、
j'). Therefore, D ⁿ (m
+1:i) does not need to be specifically determined, but D ⁿ _q (i, j) can be calculated using the recurrence formula D ⁿ _q (i, j) = mimD ⁿ _q (i-2, j-1) + d ⁿ
(i-1, j)+d ⁿ (i, j)...(1) D ⁿ _q (i-1, j-1)+d ⁿ (i, j)...(2) D ⁿ _q (i-1, j −2)+d ⁿ (i, j)...(3)...(9), and can be obtained as D ⁿ _q (i)=D ⁿ _q (i, j ⁿ ). However, the initial value of recurrence formula (9) is D ⁿ _q (-1, j) = ∞ (J = 0, 1, ..., J ⁿ ) D ⁿ _q (0, 0) = 0 D ⁿ _q (0 , j)=∞ (J=-1, 1, 2,...,
J ⁿ ) D ⁿ _q (i, -1) = ∞ (i = 1, 2, ..., I) D ⁿ _q (i, 0) = D _qk (i - 1) (q _k is q = U (q _k ,
q _k ) that satisfies n, and the back pointer corresponding to D ⁿ _q (i, j)
B ⁿ _q (i, ^j ) is expressed as B ⁿ _q (i, j) = B ⁿ _{q (} i-
2, j-1) When D ⁿ _q (i, j) = B ⁿ _q (i, j) = B ⁿ _q (i-
1, j-1) When D ⁿ _q (i, j) = B ⁿ _q (i, j) = B ⁿ _q (i-
1,j-2). Further, the initial value of B ⁿ _q (i, j) is B ⁿ _q (i, 1)=i−1. FIG. 6 explains the meaning of D ⁿ _q (i, j) on i=i. 8,
The straight line 10, 12 has a slope of 1/2, 9, 11, 13
The straight line has a slope of 2, and (i, j) = (i, j ⁿ )
The path leading to (point 26) is included in the area between straight lines 8 and 9, the matching path passing through point 16 is included in the area between straight lines 10 and 11, and the matching path passing through point 17 is included in the area between straight lines 8 and 9. It is included in the area between 12 and 13. In other words, a path through point 16 has a starting point between 18 and 19 and an ending point between 20 and 21 for word n, and a path through point 17 has a starting point between 22 and 23. , the terminal is 24
This means that it is between 25 and 25. After all, i=
D ⁿ _q (i, j) on i is the cumulative distance D ⁿ _q (i″)=D ⁿ _q (i″ , J ⁿ ) (hereinafter D ⁿ _q (i, j)).
is called the intermediate cumulative distance) Also, the recurrence formula
As is clear from (9), in order to obtain D ⁿ _q (i, j), if only the intermediate cumulative distance between frames i-2 and i-1 and the inter-frame distance between frames i-1 and i are known, then Often, you can forget about previous values. To summarize the above, to find D _q (i), j = 1, 2, ..., J ⁿ , n for each frame i
Find D ⁿ _q (i, j) for = 1, 2,..., N, q = q ₁ , q ₂ ,..., q| _s | _-1 , m^, q^ _k = argmin [D ⁿ When _q (i, j ⁿ ), q=Δ(q _k , n), D _q (i)=D ⁿ ^ _q (i, j ⁿ ^) B _q (i)=B ⁿ _q (i, j ⁿ ^) Q _q (i) = q^ _k N _q (i) = n^. In this way, the calculation of d ⁿ (i, j) at each grid point (i, j) only needs to be done once for each word n, and the calculation of D ⁿ _q (i, j) only needs to be performed once for each word n.
It only needs to be done once for q _k where n, Δ(q _k , n) = q,
The amount of calculation is significantly greater than the method of directly solving equation (3), which requires calculating d ⁿ (i', j) and D ⁿ (m+1:i) for the grid points inside the diagonal lines shown in Figure 5 for each frame. decreases. Furthermore, although this method proceeds with the processing for each frame i of the input pattern, it is also possible to perform the processing for each frame j of the standard pattern. That is, as is clear from recurrence formula (6), in order to obtain D ⁿ _q (i, j) also in the j direction, frame j−
Since it is sufficient to know the interframe distance D ⁿ (i, j) between frame 1 and frame j and the intermediate cumulative distance between frame j-2 and frame j-1, j=
It is also possible to find D ⁿ _q (i, j) on j. The above method is called the automaton-controlled clock synchronized propagation type DP method (FSACWDP). At this time, in order to introduce the idea of equation (8), the initial value of D ⁿ _q (i, j) may be set as follows in the calculation of recurrence equation (9). That is, for q _k that satisfies q = Δ(q _k , n), q^ _k = argmin [D _qk (i-1)]
In this case, D ⁿ _q (i, 0)=D _q ^ _k (i-1) (10). FIG. 8 is a block diagram showing one embodiment of the present invention. 100 is an input terminal for audio signals. 10
Reference numeral 1 denotes a feature extraction unit which converts an input audio signal into a series of feature vectors. 102 is a standard pattern storage unit in which each word (syllable) to be recognized is stored as a series of similar feature vectors. Reference numeral 103 denotes an interframe distance calculation unit that calculates the difference between the feature vector output from the feature extraction unit 101 and the feature vector stored in the standard pattern storage unit 102. 104 is an interframe distance storage unit that temporarily stores the calculated interframe distance. 105
is the automaton control rule storage section. Reference numeral 106 is a cumulative distance storage unit in which cumulative distance D _q (i) is stored for each frame. Reference numeral 107 is an initial value calculation unit which calculates the initial value in the calculation of recurrence formula (9) according to formula (10). Reference numeral 108 is a recurrence formula calculation unit, which calculates the recurrence formula (10) based on the initial value calculated in 107. 109
is a final value determining unit, which determines n^=argmin [D ⁿ _q (i, J ⁿ ) N _q (i)=n^ D _q (i ) = D ⁿ ^ _q (i, J ⁿ ^) B _q (i) = B ⁿ ^ _q (i, j ⁿ ^) Q _q (i) = argmin [D _qk (B _q (i))] Calculate This is the part to do. 113, 114, 115
are the last word memory section, the previous state memory section, and the last word memory section, respectively.
The last word N _q , which is a back pointer storage unit, and which is determined by the final value determining unit 109.
(i), state immediately before q _q (i), back pointer
B _q (i) is stored for each frame. 11
2 is a part that determines the state of the input audio in the final frame. That is, when q _f F, the state q of the final frame I is determined as q=argmin(D _qf (I)). 110 is a voice section detection unit; 111
is the frame number coefficient part. Reference numeral 116 is a backtrace control unit, which stores the last word storage unit 113.
Then, from the contents of the previous state storage section 114 and the back pointer storage section 115, the last word storage section 11 is stored in the reverse order according to the flowchart shown in FIG.
The recognition results are output from step 3. FIG. 9 is a chart showing an example of the case where the operation of the above embodiment is realized by software. Steps 200 to 204 are the parts that initialize the entire frame, steps 205 to 214 are the parts that perform processing in frame i, and steps 206 to 212 are the parts that perform the processing for each standard pattern n (n
= 1, 2, ..., N), the part where D ⁿ _q (i), B ⁿ _q (i) are calculated, steps 213 to 214, are the last part when it is assumed that the input audio ends at frame i. Word (syllable) name, corresponding cumulative distance,
The back pointer is the part that determines the previous state for each state. Step 208 corresponds to the operations of the interframe distance calculation section 103 and the interframe distance storage section 104. Step 210 is the initial value calculation section 10
Corresponds to operation 7. Step 211~Step 212
corresponds to the operation of the recurrence formula calculation unit 108. Steps 213 and 214 correspond to the operations of the final value determining section 109. Steps 215 to 217 are processes for determining recognition results in reverse order starting from the last frame of the input audio, and include the final frame state determining section 118, last word storage section 113, and previous state storage section 114 back pointer storage. This corresponds to the operation performed between the back trace control section 115 and the back trace control section 116. Another known method for directly determining and solving D ⁿ _q (i, j) is the automaton control level building method (FSALB). The idea of the present invention can also be introduced to this, and the amount of calculation can be significantly reduced. Figure 10 shows the sound of a 5-digit number, for example,
Seventy-three thousand two hundred and eighty-six, and so on.
This is an automaton expression for reading 10. In contrast, devices using conventional FSACWDP and FSALB, and degenerate FSACWDP and degenerate device according to the present invention.
Table 1 compares the calculation amount and work memory storage amount for devices using FSALB. According to this table, for the task shown in Figure 10,
The amount of calculation is greatly reduced, and the amount of memory is also less than the same amount, so it has a great practical effect.

[Table] Effects of the Invention As described above, when the control regulation of the automaton is q = Δ(q _k , n), and there are multiple states q _k for pattern n, conventionally the last pattern The cumulative distance for n is calculated for the previous state q _k , and if any of the states immediately before becoming state q have the same pattern n, then the process returns to those immediately previous states. By taking advantage of the fact that the process continues from the state with the minimum cumulative distance, it has become possible to significantly reduce the amount of calculation depending on the task.

[Brief explanation of the drawing]

Figures 1 to 3 are diagrams explaining the basic principle of DP matching, Figure 4 is a flowchart showing the procedure for segmentation and recognition word determination in continuous word speech recognition by automaton control, and Figure 5 is a flowchart of the present invention. 6 and 7 are diagrams illustrating the principle of an embodiment of the present invention, and FIG. 8 is a block diagram illustrating an embodiment of the present invention. Figure 9 is a chart when the functions of the same embodiment device are realized by software.
FIG. 10 is a diagram showing the effect of the same embodiment. 101...Feature extraction unit, 102...Standard pattern storage unit, 103...Interframe distance calculation unit, 1
04...Interframe distance storage section, 105...Automaton control rule storage section, 106...cumulative distance storage section, 107...Initial value calculation section, 108...Recurrence equation calculation section, 109...Final value determination section , 110...
Voice section detection section, 111... frame number coefficient section,
112...Final frame state determination unit, 113...
Last word storage unit, 114... Immediate state storage unit,
115... Back pointer storage unit, 116... Back trace control unit.

Claims (1)

[Claims] 1 Input signal as feature vector a ₁ , a ₂ ,...a _i ,...a _I
and a standard pattern R ⁿ (where n=1, 2,..., N) consisting of a series of feature vectors b ⁿ ₁ , b ⁿ ₂ , ... b ⁿ _J , ... b ⁿ _Jo The distance between the standard pattern storage means to be stored and the feature vectors a _i and b _j in the i-th frame of the input pattern.
d ⁿ (i, j) as j=1,2,...,j ⁿ ;n=1,2,
..., N, and in the i-th frame of the input pattern, j=
1, 2,..., j ⁿ ; For n=1, 2,..., N,
Intermediate cumulative distance D ⁿ _q when state is q
Let (i, j) be the minimum value of the cumulative distance D _qk (i-1) along the path leading to state q _k in the i-1st frame among the immediately preceding states q _k that continue to q in pattern n. A cumulative distance calculation means for calculating the intermediate back pointer B ⁿ _q (i, j) along the path that led to the calculation, and the last pattern n when it is assumed that the i-th frame ends in state q. n that minimizes the intermediate cumulative distance D ⁿ _q (i, j ⁿ )
, and the pattern name at that time is N _q (i)
= n^, the cumulative distance is D _q (i) = D ⁿ ^ _q (i, j ⁿ ^), the back pointer is B _q (i) = B ⁿ ^ _q (i, j ⁿ ^), the previous in state
When q _k that minimizes D _qk (B _q (i)) is q^ _k , Q _q
(i) A final determination means for setting = q^ _k , a last pattern storage means for storing these values for each frame, a back pointer storage means, a previous state storage means, and input is completed at the last frame I of the input pattern. Then, the cumulative distance D _qf (I) for the state q _f allowed as the final state is read from the cumulative distance storage means, and q^ _f that gives the minimum value of D _qf (I) is set as the state q in the final frame. , from the contents of the pack pointer storage means, the previous state storage means, and the last word storage means, n=N _q (i), i=B _q (i) until B _q (i)=0. , q=Q _q (i) and outputs the recognition results in reverse order.