Content-type: text/html Man page of mlib_SignalDTWScalarPath_F32

mlib_SignalDTWScalarPath_F32

Section: mediaLib Library Functions (3MLIB)
Updated: 23 May 2007
Index Return to Main Contents
 

NAME

mlib_SignalDTWScalarPath_F32 - perform dynamic time warping on scalar data  

SYNOPSIS

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

mlib_status mlib_SignalDTWScalarPath_F32(mlib_d64 *dist, mlib_s32 *path,
    mlib_s32 *lpath, const mlib_f32 *dobs, mlib_s32 lobs, void *state);

 

DESCRIPTION

The mlib_SignalDTWScalarPath_F32() 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.

path

The optimal path.

lpath

The length of the optimal path.

dobs

The observed data array.

lobs

The length of the observed data array.

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 TYPEATTRIBUTE VALUE

Interface StabilityCommitted

MT-Level

 

SEE ALSO

mlib_SignalDTWScalarInit_F32(3MLIB), mlib_SignalDTWScalar_F32(3MLIB), mlib_SignalDTWScalarPath_F32(3MLIB), mlib_SignalDTWScalarFree_F32(3MLIB), attributes(5)


 

Index

NAME
SYNOPSIS
DESCRIPTION
PARAMETERS
RETURN VALUES
ATTRIBUTES
SEE ALSO

This document was created by man2html, using the manual pages.
Time: 02:38:27 GMT, October 02, 2010