Basic Dynamic Projection Warping

In the previous sections all the fundamental concepts and techniques, feature vectors, dynamic programming technique, the “path”, fundamental paths, etc., had been introduced, the character recognition method, dynamic projection warping, will be discussed here.

Dynamic projection warping method is a method that can automatically choose the optimal mapping way, the “path”, between PAV_x and the PAV_y of each reference character image. By utilizing the dissimilarity, which is considered as the cost of a path, related to the path between PAV_x and each PAV_y, the input character can be classified to a suitable class by the minimum dissimilarity. The function is denoted as the partial dissimilarity between two feature vectors and represents the partial cost of a path when the path goes through the grid point

(

^{i j}

d ,

)

( )

^i,j . Consequently, each partial dissimilarity ^dr

(

ⁱ, ^j

)

and d_c

( )

i,j have to be respectively calculated as

(3.19) and (3.20). After defining the partial dissimilarity, the cost of each path, ,

and extracted character image and k-threference character image can be computed as (3.21), (3.22), and (3.23), where P_r is the related minimum cost path, from beginning point to ending point, between ϕ_xr and ϕ_yr and Pc is the related minimum cost paths, from beginning point to ending point, between ϕ_xc and ϕ_yc. By utilizing dynamic programming technique, the minimum cost paths could be found feasibly with two constraints, called beginning region and ending region constraint and legal path constraint, which are illustrated in Figure 3-11. The size of ϕ and _r ϕ_c is denoted as T_r=30, and T_c=15, respectively. Figure 3-11, which only shows a concept of the two constraints, uses T to represent the size of ϕ_x and ϕ_y.

Figure 3-11. The legal region of the path.

„ Beginning region and ending region constraint

For an over-extracted character image which contains several rows or columns of disturbances which are not a part of the desired character image. The disturbances may appear in the left, right, top, or bottom. For an under-extracted character image which is pared several rows or columns of desired character image. The pared rows or column may also in the left, right, top, or bottom. Reviewing Figure 3-6 to explain the concepts of beginning region and ending region, the under “Z” in Figure 3-6 is an example of an over-extracted character image which contains two-column disturbance

in the left side and is pared two-column in the right side. Therefore, the beginning

point is on the line j=1 when the character image is over-extracted. How far away

from the beginning point to the point

( )

^1,1 represents the number of columns over-extracted in left side of character image. To make the DPW robust to over-extracted character image, the region of beginning point, called beginning region and denoted as , under the over-extracted condition includes beginning points shows in (3.24).

RBx x_o1

{ ( )

_o1

}

Bx i j j 11 i x

R = , = , ≤ ≤ , i,j∈N (3.24)

where is an experiment value that depends on the reliability of character

extraction step. In other words, if the number of over-extracted columns in the left side of extracted character image is usually smaller than a constant, , then

will be chosen as the maximum tolerance of over-extracted tolerance of over-extracted disturbance. Here, the value two of is selected by experiments.

The same method applying to the right side of extracted image, the parameter is selected two, which equals to . The region of endpoint, called ending region and denoted as , under the over-extracted condition includes T

1

{ ( )

_{c c o3 c}

}

is at . It can be found that “an image over-extracted from the other image” is the same as “an image under-extracted from the other image”. Therefore, by utilizing the symmetry of i=j, and under the pared condition can be chosen as (3.26) Thus, to make the DPW method robust to both over-extracted character image and under-extracted one, the beginning region and the ending region are defined as below.

By Applying the same concepts to ϕ , (3.28) and (3.29) still holds. Table 3-1 shows the _r

important experiment parameters of ϕ_c and ϕ . _r

Table 3-1 The value of important parameters of R_B and R_E

„ Legal path constraint

In Figure 3-11, the legal region R which constraints the legal path of mapping a

ϕc to another or mapping a ϕ to another is limited by six lines. How to define the _r six lines of ϕ_c will be stated in detail, and applying the same concepts to ϕ , e six _r lines corresponding to _r

th ϕ n be selected, too. ca

Considering a worst case of over-extracted character image in this paper, which over extracted xo1 columns in the left side and xo3 columns in the right side, the related path will has an average slope from beginning point to ending point as

11 , are given by (3.30). Considering another worst case of under-extracted character

image in this paper, which under extracted y

L1

m

L2

m

o1 columns in the left side and yo3

columns in the right side, the related path will has an average slope from beginning

point to ending point as , are give by (3.31). The legal path region is still limited by two lines, L

L3

m

L4

m ₅ and L6,

which are parallel to the line i=j. For general extracted character images, the slope of corresponding path should equals to 1, which is adopted as the slope of L₅ and L₆. However, encountering disturbances, the path will move a short distance from i=j.

The appearance is shown as )

Combining the two constraints with basic DPW, the complete character

recognition method, called DPW, is shown as three steps below.

„ Step 1. Calculate the dissimilarity between two columns or two rows.

( )

i,j =

( )

i −

( )

j ,1≤i,j≤30

d_r ϕ_xr ϕ_yr (3.35)

( )

i,j =

( )

i −

( )

j ,1≤i,j≤15 d_c ϕ_xc ϕ_yc

(3.36)

„ Step 2. Calculate the total dissimilarity between extracted character image and

the k-th reference character image.

„ Step 3. Recognize extracted character image by the minimum dissimilarity

( )

在文檔中 以動態投射校準技術建立之穩健車牌辨識系統 (頁 50-57)