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.
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