INTRODUCTION
Automatic color microscopic image segmentation is one of the most important
segmentation problems because of both the complex nature of the microscopic
cell tissues and problems inherent to microscopy image (Mao
et al., 2006; NavarroJover, et al.,
2009). For instance, object multiplicity, clutter, nonrandom noise and
the intensity inhomogeneity caused by uneven illumination are some main difficulties.
Many microscopic image segmentation methods were presented. Image thresholding
segmentation is the simplest scheme (Haralick and Shapiro,
1985; Sahoo et al., 1988), but it is only
suitable for those image which has obvious two peak in histogram; other methods
such as watershed (Bleau and Leon, 2000) and deformable
model can obtain better segmentation results but they often deal with gray image,
meanwhile, they often conquer for the influence of noises but omit the intensity
inhomogeneity caused by uneven illumination. However, for the color microscopic
image, it is important step to choose the feasible color space and better segmentation
method. In general, the color image was divided three color components and segmentation
it respectively such as RGB space (Cheng et al.,
2001), However, the color components have high interdependency in RGB space
models and their data size is very large, therefore, it is not suitable for
segmentation in RGB space. To reduce data volumes, some methods have presented.
In YuanYuan and XianGang (2009), first cluster the
data in RGB space then segment it by threshold method, but the efficiency rely
on the performance of clustering badly. In ZhiQiang et
al. (2009), segment every component in HSV space and choose the best
result which has maximum entropy, but it is inefficiencies when their entropies
are equal in three components. At the same time, they do not take into account
the influence of intensity inhomogeneity caused by uneven illumination.
In this study, we propose a novel color microscopic image segmentation approach
with simultaneous uneven illumination estimation. First transform RGB space
into 3components by PCA (principal component analysis) and choose the first
component, then model the intensity inhomogeneity field as a linear combination
of smooth basis functions (Powell, 1981) and build an
energy function, finally, obtain the segmentation results by means of minimum
the energy function (Li et al., 2009). A salient
advantage of this method is that it retains the most information in single component
and eliminates the influence of intensity inhomogeneity field.
SEGMENTATION METHOD WITH SIMULTANEOUS UNEVEN ILLUMINATION ESTIMATION BASED ON PCA
Principal component analysis: PCA is one of the most common approaches
to reduce the dimensionality of data set while retaining those characteristics
of the dataset (Yeung and Ruzzo, 2001). It is a linear
transformation that maps the data to a new coordinate system so that the greatest
variance across the dataset comes to lie on the first coordinate or principal
component, the second greatest variance on the second coordinate and so on.
Assume M_{mxn} is m collection of Ndimension data samples, denotes by X = (x_{1}, x_{2}, ..., x_{m})^{T}, its covariance is C = cov(X). To calculate its principal components, find a orthogonal matrix E = (E_{1}, E_{2}, L, E_{p})^{T}, its column vector E_{i} = (I = 1, 2, ..., p) is the unit eigenvector corresponding to the eigenvalue λ_{i} of C and satisfied λ_{1}≥λ≥...λ_{p}, then Z = EX = (z_{1}, z_{2},...,z_{p}) are new components of data set X that their importance is descend. For the matrix E is orthogonal, the correlation of X was eliminated. So, the main component z_{i} corresponding to the maximum eigenvalue and includes more information. The results of 3 components by PCA with cell image are shown in Fig. 1. It can be found that the first component include the most image information.
The model of uneven illumination field: Spatial intensity variations
caused by uneven illumination have been a challenge for image segmentation and
many other computer vision tasks. Suppose the real image is I_{r}, acquired
image data from I_{r} is I, the Spatial intensity variations field is
B, noise is N, then the I was denoted by:
Image is the projection of 3dimensional objects in 2dimension space. The image data acquired was quantized by 2 value corresponding to objects and background in image segmentation. For this reason the real image is 2 value scenes only include objects and background, the image data acquired is gray or color because of uneven illumination field.
So, the image is denotes by I(x) = B(x) . I_{r}(x) without noise. Meanwhile, I_{r} is real image just include objects and background, which can be modeled as piecewise approximately constant, therefore, the real image is divided as:
denote objects and background respectively. So, the real image I_{r}
is denoted as:

Fig. 1: 
Original image and PCA components 
u_{i}(x) is the member function of Ω_{i}, it satisfied as:
Suppose the influence of uneven illumination field is B, it can estimated by a linear combination of a set of basis function because the field effect is smooth. Let, g_{1}, g_{2}, ... , g_{M} be a set of basis functions defined on Ω. We estimate the field effect by a linear combination of the basis functions:
where, w_{k} ε R, k = 1,..., M, are the combination coefficients, g_{k}(x) is orthogonal polynomial.
So, the image data acquired is model as:
Energy minimize method: It is difficult to estimate the w_{k}, c_{i}, u_{i} in the condition that only the image data is known. So we formulate the problem of segmentation and intensity inhomogeneity field estimation as a task of seeking the better coefficient of w_{k}, c_{i}, u_{i}. The fitting error is defined as follows:
The formula is convex in each of its variables; therefore it can be minimized
by an iterative process of interleaved minimization with respect to each variable.
Solve the partial derivative of F and let them equal to 0, so these coefficient
are solved respect as follows Eq. 10:
Let ∂F/∂w = 0, solve the w is:
G(x) = (g_{1}(x), ..., g_{M}(x))^{T}, I_{r}(x) has the form of Eq. 2.
Microscopic image segmentation scheme:
• 
Transform the image data by PCA method, choose the first component 
• 
Iterate solve Eq. 710 in main component
data, obtain the c_{1}u_{1}(x), c_{2}u_{2}(x)
which corresponding to objects and background. The number of iteration is
decided by the threshold of fitting error 
• 
Utilize the result c_{1}u_{1}(x) and c_{2}u_{2}(x),
segment the color microscopic image 
EXPERIMENTAL RESULTS
In the experiments, we select some images with the intensity inhomogeneity field such as T shape image I1 (size is 640, 480), the cell image of rat’s urinary tissues I2 (size is 500, 400) and blood cell image.
To verify the validity and efficiency of this segmentation method, we compare
it with traditional Otsu (1979) segmentation method and
PCNN (pulse coupled neural networks) (Bi and Qiu, 2005)
method for image I1, the experimental results as show in Fig.
2ad. It is obvious that proposed method has better result
with the influence of intensity inhomogeneity field effect.
Meanwhile, we compare the run time of PCNN method and proposed method for color
microscopic image. In PCNN method, segments every component in RGB with PCNN
then combine 3 segmentation results, as show in left column in Fig.
3ad. The proposed method segments the main component
in RGB space directly and then achieves the color segmentation result, which
is showed in right column in Fig. 3.
From the experiments results, it’s obvious that the proposed method is
better than classical Ostu and PCNN image segmentation method for those color
microscopic image with the influence of uneven illumination field, meanwhile,
the efficiency is developed largely, Table 1 shows the efficiency
between this method and color image segmentation based on PCNN.

Fig. 2: 
Comparisons of segmentation results with different method
(a) Original image; (b) OSTU method; (c) PCNN method and (d) Proposed method 

Fig. 3: 
Comparisons of segmentation results in different space (a)
PCNN segmentation result in RGB for I2; (b) Segmentation result with proposed
method for I2 main component; (c) PCNN segmentation result in RGB for I3
and (d) segmentation result with proposed method for I3 main component 
Table 1: 
The comparison of running time with different methods 

CONCLUSION
We have presented a new scheme for microscopic image segmentation under the circumstances of uneven illumination. The proposed scheme is based on PCA, moreover, it can estimate the uneven illumination field simultaneously. Our method is able to obtain more details in segmentation results and free from the influence of uneven illumination. Comparisons with two wellknow color image segmentation methods demonstrate the advantages of the proposed method.
ACKNOWLEDGMENT
The authors would like to thank the reviewers for their valuable comments and suggestions.