mlib_SignalDTWScalar_S16(3MLIB) 			    mediaLib Library Functions				   mlib_SignalDTWScalar_S16(3MLIB)

NAME

       mlib_SignalDTWScalar_S16 - perform dynamic time warping on scalar data

SYNOPSIS

       cc [ flag... ] file... -lmlib [ library... ]
       #include <mlib.h>

       mlib_status mlib_SignalDTWScalar_S16(mlib_d64 *dist,
	    const mlib_s16 *dobs, mlib_s32 lobs, mlib_s32 sobs,
	    void *state);

DESCRIPTION

       The mlib_SignalDTWScalar_S16() function performs dynamic time warping on scalar data.

       Assume the reference data are

	     r(y), y=1,2,...,N

       and the observed data are

	     o(x), x=1,2,...,M

       the dynamic time warping is to find a mapping function (a path)

	     p(i) = {px(i),py(i)}, i=1,2,...,Q

       with the minimum distance.

       In K-best paths case, K paths with the K minimum distances are searched.

       The distance of a path is defined as

		     Q
	     dist = SUM d(r(py(i)),o(px(i))) * m(px(i),py(i))
		    i=1

       where  d(r,o) is the dissimilarity between data point/vector r and data point/vector o; m(x,y) is the path weighting coefficient associated
       with path point (x,y); N is the length of the reference data; M is the length of the observed data; Q is the length of the path.

       Using L1 norm (sum of absolute differences)

		      L-1
	     d(r,o) = SUM |r(i) - o(i)|
		      i=0

       Using L2 norm (Euclidean distance)

			     L-1
	     d(r,o) = SQRT { SUM (r(i) - o(i))**2 }
			     i=0

       where L is the length of each data vector.

       To scalar data where L=1, the two norms are the same.

	     d(r,o) = |r - o| = SQRT {(r - o)**2 }

       The constraints of dynamic time warping are:

	   1.	  Endpoint constraints

			px(1) = 1
			1 <= py(1) <= 1 + delta

		  and

			px(Q) = M
			N-delta <= py(Q) <= N

	   2.	  Monotonicity Conditions

			px(i) <= px(i+1)
			py(i) <= py(i+1)

	   3.	  Local Continuity Constraints

		  See Table 4.5 on page 211 in Rabiner and Juang's book.

		  Itakura Type:

			py
			|
			*----*----*
			|p4  |p1  |p0
			|    |	  |
			*----*----*
			|    |p2  |
			|    |	  |
			*----*----*-- px
			      p3

		  Allowable paths are

			p1->p0	  (1,0)
			p2->p0	  (1,1)
			p3->p0	  (1,2)

		  Consecutive (1,0)(1,0) is disallowed. So path p4->p1->p0 is disallowed.

	   4.	  Global Path Constraints

		  Due to local continuity constraints, certain portions of the (px,py) plane are excluded from the region the optimal warping path
		  can traverse. This forms global path constraints.

	   5.	  Slope Weighting

		  See Equation 4.150-3 on page 216 in Rabiner and Juang's book.

       A path in (px,py) plane can be represented in chain code. The value of the chain code is defined as following.

	     ============================
	     shift ( x , y ) | chain code
	     ----------------------------
		 ( 1 , 0 )   |	   0
		 ( 0 , 1 )   |	   1
		 ( 1 , 1 )   |	   2
		 ( 2 , 1 )   |	   3
		 ( 1 , 2 )   |	   4
		 ( 3 , 1 )   |	   5
		 ( 3 , 2 )   |	   6
		 ( 1 , 3 )   |	   7
		 ( 2 , 3 )   |	   8
	     ============================

		 py
		 |
		 *  8  7  *
		 |
		 *  4  *  6
		 |
		 1  2  3  5
		 |
		 x--0--*--*-- px

       where x marks the start point of a path segment, the numbers are the values of the chain code for the segment that ends at the point.

       In following example, the observed data with 11 data points are mapped into the reference data with 9 data points

		 py
		 |
	      9  | * * * * * * * * * *-*
		 |		    /
		 | * * * * * * * *-* * *
		 |		/
		 | * * * * * * * * * * *
		 |	      /
		 | * * * * *-* * * * * *
		 |	  /
		 | * * * * * * * * * * *
		 |	 |
		 | * * * * * * * * * * *
		 |	/
		 | * * * * * * * * * * *
		 |    /
		 | * * * * * * * * * * *
		 |  /
	      1  | * * * * * * * * * * *
		 |
		 +------------------------ px
		   1		       11

       The chain code that represents the path is

	     (2 2 2 1 2 0 2 2 0 2 0)

       See Fundamentals of Speech Recognition by Lawrence Rabiner and Biing-Hwang Juang, Prentice Hall, 1993.

PARAMETERS

       The function takes the following arguments:

       dist	The distance of the optimal path.

       dobs	The observed data array.

       lobs	The length of the observed data array.

       sobs	The scaling factor of the observed data array, where actual_data = input_data * 2**(-scaling_factor).

       state	Pointer to the internal state structure.

RETURN VALUES

       The function returns MLIB_SUCCESS if successful. Otherwise it returns MLIB_FAILURE.

ATTRIBUTES

       See attributes(5) for descriptions of the following attributes:

       +-----------------------------+-----------------------------+
       |      ATTRIBUTE TYPE	     |	    ATTRIBUTE VALUE	   |
       +-----------------------------+-----------------------------+
       |Interface Stability	     |Committed 		   |
       +-----------------------------+-----------------------------+
       |MT-Level		     |MT-Safe			   |
       +-----------------------------+-----------------------------+

SEE ALSO

       mlib_SignalDTWScalarInit_S16(3MLIB),	mlib_SignalDTWScalar_S16(3MLIB),     mlib_SignalDTWScalarPath_S16(3MLIB),    mlib_SignalDTWScalar-
       Free_S16(3MLIB), attributes(5)

SunOS 5.11							    23 May 2007 				   mlib_SignalDTWScalar_S16(3MLIB)