opencv/sec5.ObjectRecognition の編集

quotation@opencv-1.0.0/docs/opencvman_old.pdf
*5 Object Recognition [#y165de99]
**Eigen Objects [#oaf5f32d]
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 [#fc902c60]
           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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