quotation@opencv-1.0.0/docs/opencvman_old.pdf

5 Object Recognition

Eigen Objects

This section describes functions that operate on eigen objects.

     Let us define an object u = { u 1, u 2 …, u n } as a vector in the n-dimensional space. For
     example, u can be an image and its components ul are the image pixel values. In this
     case n is equal to the number of pixels in the image. Then, consider a group of input
     objects u i = { ui, u i, …, u i } , where i = 1, …, m and usually m << n. The averaged, or
                              1    2        n
     mean, object u = { u 1, u 2, …, u n } of this group is defined as follows:
                   m
            1
                  ul .
                         k
     u l = ---
           m
               k=1
                                                                                 m×m
     Covariance matrix C = |cij| is a square symmetric matrix                         :
                  n
                
                          i             j
                      ( ul  ? ul ) ? ( ul ? ul ) .
     c ij =
              l=1
     Eigen objects basis e i = { e i, ei, …, e i } , i = 1, … ,           m1 ? m of the input objects group
                                                1   2      n
     may be calculated using the following relation:
                      m
               1
                      vk ? ( ul ? ul ) ,
       i                    i      k
         = ---------
                   -
     el
               λi
                     k=1
                                        i    i       i
                               i
     where λi and                = { v 1 , v2 , …, v m } are eigenvalues and the corresponding eigenvectors
                             v
     of matrix C.
                                                            5-1
                                                                                          Any input object ui as well as any other object u may be decomposed in the eigen
          objectsnm1-D sub-space. Decomposition coefficients of the object u are:
                  el ? ( u l ? u l ) .
                     i
          wi =
                l=1
          Using these coefficients, we may calculate projection u = { u 1, u 2 …, u n } of the object u
                                                                   ?     ??       ?
          to the eigen objects sub-space, or, in other words, restore the object u in that sub-space:
                 m1
                  wk e l + u l .
                        k
          ul =
           ?
                k=1
          For examples of use of the functions and relevant data types see Image Recognition
          Reference Chapter.

Embedded Hidden Markov Models

          This section describes functions for using Embedded Hidden Markov Models (HMM)
          in face recognition task. See Reference for HMM Structures.
                                                 5-2

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Last-modified: 2007-05-08 (火) 17:02:00 (4402d)