Graphics Reference
In-Depth Information
p
q
1
s

===
μ
=
I
(2)
ijk
pqs
i
111
j
k
Use the average to centralize every image matrix, and compute the covariance
matrix of sample space:
1
p
q
s

===
T
C
=
(
I
μ
)
(
I
μ
)
(3)
ijk
ijk
pqs
i
111
j
k
Compute all the orthonormalized eigenvectors of covariance matrix C and
corresponding eigenvalues, then, the eigenvectors corresponding to largest ʵ
eigenvalues are elected to form a matrix E , the size of E is m / b × ʵ , and E × E T is an
identity matrix. The projection of a matrix form sample space to eigen space is:
)
T
δ
=
E
(
I
μ
(4)
Where I ijk is the ( ijk )th image matrix in sample space, that is also the k th sub-block
of j th sample in i th class, and δ ijk is the corresponding projection matrix in eigen space.
The mean projection of a sub-block in same class is computed as:
ijk
ijk
q
1
=
η
=
δ
(5)
ik
ijk
q
j
1
Every m / b × n / b dimensional matrix in sample space represent as a ʵ × n / b dimensional
matrix in eigen space, ʵ m / b (generally ʵ is much less than m / b ).
2.2 Classification Phase
A character image needs to be recognized is a considered as a test sample, the kth
sub-block of test sample is a matrix I test,k , the low dimensional projection of which in
eigen space is:
η
=
E
T
(
I
μ
)
(6)
test,
k
test,
k
Euclidean distance from I test to i th class in training database is computed as:
=
1
s
d
=
η
η
(7)
i
test,
k
ik
s
k
1
At last, the test sample could be classified to Γ th class when:
)
Γ (8)
Where D is a set composed by the distances between test sample and all classes,
D ={ d 1, d 2, … d p }.
=
argmin( D
3
Hardware Architecture Design
3.1
Modified Distance Equation
A modified distance equation is introduced to simplify the operations of M2DPCA
eigen space projection for hardware implementation. Based on Equation (4)~(6), the
distance between input character and i th class on k th sub-block can be computed as:
 
Search WWH ::




Custom Search