(70g) Study in Binarization Method of Particle Micro-Image

According to the character of the particle micro-image(PMI),a method of binarization of partitioning curved surface has been held up. The method integrates the advantages of the overall binarization and the local binarization. The noise of the particle micro-image and the nonuniformity of the microscopical illumination can be eliminated effectively at the same time. The method has been applied into the analysis system of particle micro-image successfully.

1.        INTRODUCTION

In the study of particle, the analysis system of particle micro-image (PMI) is one of the popular methods in analyzing the particle. In the system of PMI, the particle is magnified by microscope, and then is transmitted to the computer by stylus and image gather card. The transmitted image is named PMI. The size and the shape of the particle are the emphases in the particle study. It must be used while measuring the size and the shape of the particle in PMI.

The binarization method is divided into overall threshold method and local comparison method according to its operating range. In the overall threshold method, a threshold is determined based on the histogram or the spatial distribution of gray-scale image, and change gray-scale PMI into binarizetion PMI according to this threshold. It¡¯s more overall to judge the whole image by overall threshold method, but the resistibility to asymmetric illumination is comparatively weak. However, using local comparison method, the neighborhood is defined, and the gray-scale comparison between investigated points and neighborhood points can be realized by the calculation formwork of the neighborhood.

2.        EXPERIMENTAL PROCESS

During our experimental process, the method of auto threshold value based on the maximum variance (MTMV) is used as the overall threshold method, and Kamel-Zhao and Bernsen is used as local comparison method. The experimental result indicates that MTMV can evidently eliminate the background of PMI and can eliminate the noise effectively, but the nonuniform illumination influence to the optical microscope is comparatively great. Comparing the original gray PMI and monochrome PMI, it can be found that the particle gets smaller at heartland where the illumination is stronger, while it becomes bigger at edge where the illumination is weaker. The monochrome PMI caused by the method Kamel-Zhao and Bernsen is better in resisting the influence of nonuniform illumination than MTVT,     but the elimination to noise is less than MTMV. Apparently it is mismatched to the original intention that we choice the local comparison method. It is because of the particularity of particle micro-image. According to analyzing the gray level of the original image, we can find that the gray value is from 210 to 255,which is thin ,so the gray value is uneven, as the result, the judgement to background images using local comparison method will be mistaken, and some false particle will be produced. While it can obtain satisfied results whether there is obvious second peak value or not in gray histogram by using MTVT.

3.        BINARIZATION OF PARTITIONING CURVED SURFACE

Based on the experimental result, a binarization method of particle micro-image, BPCS (binarization of partitioning curved surface), is held out. The aim to study the method is not only to keep the advantage that no false particle create when eliminating noise to background images based on MTVT, but alsoto eliminate the bad influence for particle size analysis which is brought by uneven illumination. The realization process of BPCS includes: 1) The particle micro-image is dispersed into M*N piece of picture segments (Kij(I=1-M,j=1-N) )firstly; 2) The threshold (fij) of every picture segment is figured out; 3) Curved surface is established according the mode of conicoid; 4) Every image point in particle micro-image is treated using binarization.

3.1 Determine the threshold (fij) of picture segments                                                                             

The algorithm determined the threshold (fij) is based on MTVT. If q(i) is the probability of gradation in i  level, n_i is the times that gray scale l appearing in the image, and n is the total number of image element, then q(i)= ,  0i255. If

g(l)=  0l255, then g= g(255) is the average of the whole image gray scale. If l divided gray scale into two groups, I₁ and I₂,then the probability of I₁ and I₂ separately is    P₁(l)=        P₂(l)==1-P₁(l)

The average of I₁ and I₂ separately is    ₁(l)= =       ₂(l)= =                           

So the variance between I₁and I₂ is    (l)= P₁(l)(₁(l)-g)²+ P₂(l)(₂(l)-g)²   = P₁(l)P₂(l)(₁(l)-₂(l))²

Determine the l value when (l) is the maximum which is the exact threshold we required.

3.2 Build partitioning curved surface        For PMI, a reasonable threshold corresponding every image element is expected, there by the ideal binarization image can be obtained, but it is impossible to get this function. We take the center spot(x_i,y_i)and threshold of every picture segment gained after partitioning as the result of idea function after discretization. This is the origin of partitioning curved surface. The curved surface is formulated as Table 1.

                                             Table 1. Curved surface formulated by form

	...	yj-1	yk	yj	yj+1	...
...	...	...		...	...	...
xi-1	...	f(xi-1,yj-1)		f(xi-1,yj)	f(xi-1,yj+1)	...
xk			g(xk,yk)
xi	...	f(x,yj-1)		f(xi-1,yj)	f(xi,yj+1)	...
xi+1	...	f(xi+1,yj-1)		f(xi+1,yj)	f(xi+1,yj+1)	...
...	...	...		...	...	...

3.3 Determine thresholdcorresponding every image element by interpolation      The curved surface is divided into a lot of small pieces, the four corner¡¯s value of each piece can be found from the form. In order to get the function value of each piece of curved surface, we can construct a binary function, g(x,y).It can approximativelyreplace the f(x,y) of the primary curved surface. Therefore the essential of binary function interpolation is how to construct g(x,y).  G(x,y) takes the parabola form.

Its interpolation step is as follows (seeing as Fig.1).   (1) Find out four peripheral points (a,b,c,d) according to the coordinate of k (x_k,y_k),and then add 5 other points (e,f,r,s,t) according to the taking point method in parabola interpolation , so there is 9 points in all. The taking point method is that if x_i<x<x_i+1,compares the value of (x-x_i)and(x_i+1-x),takes the points which value is smaller as extending direction. While (x-x_i)  (x_i+1-x),takes the three points (x_i-1,x_i,x_i+1),otherwise, takes another three points(x_i,x_i+1,x_i+2).

(2) Find out the above 9 points (a,b,c,d,e,f,r,s,t), then determine the guide line of the three parabolas and their interpolation points, determine point u (corresponding u) by parabolas interpolation through abe, and then determine point v (corresponding v) by parabolas interpolation through cdf, determine point w (corresponding w) by parabolas interpolation through rst. The parabolas interpolation formula is       y=++

(3)Determine point k (corresponding k) by parabolas interpolation through uvw, that is what we need.

Fig.1 Schematic of quadratic interpolation

4. CONCLUSION

Binarization method of partitioning curved surface has been used in the analysis system of particle micro-image successfully.The particle analysis results disposed by the subsequent program coincide with the normal data extremely.