A Method of the Adaptively Selected Auto-focusing Evaluation Function According to the Image Noise

Strength

Jintao JIANG Faculty of Information Science and Engineering

Ningbo University Ningbo, China

jiangjintao@nbu.edu.cn

Feilong ZHU Faculty of Information Science and Engineering

Ningbo University Ningbo, China

zhfl1314@163.com

Abstract—This paper has done the detailed analysis on the focusing curve characteristics for several auto-focusing functions including the Brenner function, energy gradient function, average variance function and entropy function and further discussed different characteristics of the interference immunity of those functions. According to the image noise strength, different definition evaluation functions is selected to obtain the purpose of the best focusing effect. The method proposed in this paper has achieved the effective verification on the auto-focusing platform of the microscope developed independently.

Keywords-Auto-focusing; Noise; Evaluation Function

I. INTRODUCTION

With the combination of the information technology and traditional industries, new vitality and activity are shown in various products in the traditional industries. After the traditional microscope products combining the information technology, the traditional visual observation by a single person has transferred to the current digital microscope which can observe and process by the computer screen. Meanwhile, the microscope equipped with the auto-focusing function has been developed[1][2][3], greatly decreasing the labor intensity of the staff.

In the process of auto-focusing, it is the most key link to select the evaluation function for the effective image definition. This paper deeply discusses the performance characteristics of several definition evaluation functions and analyses the interference immunity strength of each function, finally selecting different definition evaluation functions according to the image noise strength so as to obtain the purpose of the best focusing effect.

II. CHARACTERISTICS FOR THE FOCUSINGCURVES OF SEVERAL EVALUATION FUNCTIONS FOR

THE IMAGE DEFINITION While the auto-focusing adjustment is realized by using the

image process method, one key question is to select the evaluation function for the image definition. The ideal evaluation should have the un-bias, uni-modality and the defocus level which can be reflected, and have the adequate signal-to-noise ratio at the same time. Currently, the evaluation

functions for definition with the relatively-strong practicability mainly include the Brenner function based on the gradient, energy gradient function, average variance function and entropy function[4][5][6].

The Brenner function which can be expressed as (1) is the evaluation function which is very practical and based on the gradient. It is used for calculating the grey level difference of two pixels of two units. The value of f(I) is getting larger, which explains that the edge information contained in the image is more rich, namely the image is more clear.

−+=x y

yxIyxIIf 2)],(),2([)( (1)

The energy gradient function which can be expressed as (2) uses the Sobel operator to extract the gradient value on the horizontal and vertical directions, calculating the edge from two directions so as to make the judgment on the image definition more complete.

−++−+=x y

yxIyxIyxIyxIIf })],()1,([)],(),1({[)( 22

(2)

Although the auto-focusing evaluation function based on (3) is applied to a certain degree, it is eliminated because of the large calculating quantity, to which has not been attached adequate importance. The variance function is defined as (3):

−=x y

yxIIf ]),([)( μ (3)

−=x y

yxINIf ),()( 2 (4)

Where μ is the average grey level which can be expressed as (4).

The image entropy H(I) of one image is expressed as:

978-1-4244-7874-3/10/$26.00 ©2010 IEEE

−=i

PiPiIH )ln()( (5)

In the image sequences, the H value is becoming larger, while the lens defocusing quantity is getting larger, the achieved image is turning fuzzy and the pixel distribution is approaching average; the H value is in the minimum, while the lens is correctly focusing on the plane, the achieved image is clear and the pixel grey gradient distribution has the longest distance with the average distribution state. In the practical application, the inverse number of H is used as the evaluation function for convenience of calculating.

In order to compare and analyze different characteristics for the above-mentioned four focusing methods, they are used in the focusing process of the same section team, achieving the evaluation function curve for each one. By normalizing, the four curves are put into the same coordinate, showing in Figure1(According to experiments by several section teams with different types for the focusing process, curves similar to those in Figure1 are achieved in all experiments).

Figure1. Focusing Evaluation Function Curves

According to the focusing function curves in Figure1, we can find out:

• The focusing curve for the entropy function is most flat, comparing to other three steep curves;

• Comprehensively analyzing, the Brenner evaluation function performance is relatively good with the calculation quantity smaller than the energy gradient function and the curve shape steeper than the average variance, which is similar to the curve shape of the energy gradient function.

III. THE INTERFERENCE IMMUNITY COMPARISONAMONG SEVERAL EVALUTION FUNCTIONS FOR THE

IMAGE DEFINITION

A. The Noise Interference In the Image Essentially, many focusing evaluation functions use the

high frequency component of the image to judge. However, the high frequency component of the image is pretty sensitive to noise. The signal to noise ratio of the high frequency part of the

polluted image rapidly decreases and the noise will heavily affect the effect of the evaluation function based on the high frequency component. The image noise collected by CCD camera mainly includes the dark current noise, transfer noise and shot noise; the dark current noise and transfer noise are the fixed noise of CCD devise. Currently, the high-end CCD camera could decrease the dark current noise and transfer noise into the shot noise by using the method of cooling. Therefore, the shot noise is the main noise in the image noise.

B. The Interference Immunity Comparison Among Several Evaluation Functions Due to the shot noise normally obeying the Gaussian

distribution, the Gaussian noise with the average value 0 and variance 0.02 is added in the same above-mentioned sequence to implement the focusing evaluation over the noise image sequence. Figure2 uses the several above-mentioned focusing methods to focus the image sequence polluted by the noise, achieving the focusing evaluation function curve picture.

Figure2. Noise Image for Focusing Evaluation Function Curves

It could be seen from the Figure2 that when the image is polluted by noise, the tenengrad evaluation function is maximally affected, changing from the original steep curve to pretty flat curve and producing lots of local extreme values, which explains its poor interference immunity performance and the accurate focusing could not be done under the circumstance of the heavy noise interference; after the interference, the multiple extreme values phenomenon also occur in the Brenner evaluation function and it is hard to focus; whereas the entropy function and average variance are minimally affected, which explains that both two evaluation functions have strong interference immunity performance, and it is, however, not beneficial for accurately searching the extreme value point of the focusing function because of the excessive flat of the focusing curve of the entropy function so that the focusing judgment is not ideal; apart from some fluctuation under the circumstance of the heavy noise interference by using the method of the average variance in the relatively-far place on the right side that could be seen in the figure2, the whole focusing curve still keeps the uni-modality and has a certain abruptness which is the most ideal one among the focusing effects under the heavy noise interference by using different methods.

IV. THE ADAPTIVELY SELECTED FOCUSINGEVALUATION FUNCTION ACCORDING TO THE IMAGE

NOISE STRENGTH

A. The Estimation For the Image Gaussian Noise It can be seen from the above-mentioned analysis that the

interference immunity is different from each other in all focusing evaluation functions. This paper uses the method of adaptively selecting different focusing functions according to the strength of the image noise interference so as to achieve the best focusing effect. Therefore, the estimation for the image noise should be done at first. The image noise strength could be estimated by using the local standard deviation method and the specific thoughts are listed as follows.

1) Firstly, images are divided into small parts by 8×8. 2) The average of the grey level of all small parts is

calculated by (6).

=

=N

iiS

N 1

1μ (6)

3) The local standard deviations of all small parts defined as (7) will be evaluated and then the maximum and minimum ones will be found among those deviations.

=

−−

=N

iiS

N 1

22 )(1

1 μσ (7)

The interval of the maximum and minimum local standard deviation is divided into several equal divisions, and it is classified into the corresponding interval according to the local standard deviation of each sub-part. The average of the local standard deviation of the interval containing the maximum parts is selected as the noise value for the whole image.

B. The Adaptive Selection For The Evaluation Function After the image noise estimation has been achieved by

using the above-mentioned method, the Brenner evaluation function is used for focusing when the image noise is small, and the average variance is used for focusing when the image noise is larger than the noise threshold, namely realizing the adaptive selection of the focusing function by using the below-mentioned equation.

>−=

≤−+=

x y

x y

thifyxIIf

thifyxIyxIIf

2

2

]),([)(

)],(),2([)(

σμ

σ (8)

where th is the threshold of noise.

The noise threshold selection could be determined by experiments, which could avoid the circumstance that the auto-focusing could not be realized when there is the relatively-large interference in the image sequence in the process of focusing.

V. CONCLUSION

According to the above-mentioned analysis for several focusing evaluation functions and their interference immunity,

the Brenner algorithm is used under the circumstance of the relatively-small image noise interference and by judging the image noise, and the average variance algorithm is used under the circumstance of the relatively-large noise interference which makes the abnormal focusing by using the Brenner algorithm, ensuring that the auto-focusing is realized under complicated circumstances. The algorithm in this paper has been effectively verified over the auto-focusing microscope platform developed independently. The successive improvement for the algorithm is performed so as to further increase the focusing velocity and efficiency.

ACKNOWLEDGMENT

This work was supported by the Science and Technology Planning Projector of Zhejiang Province, China(2007C21028) and the Research Fundation of Ningbo University(XY0700011).

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