Comparative analysis and implementation of structured edge active contour

ABSTRACT


INTRODUCTION
Image segmentation is very essential part of image processing. Basically in segmentation, we partition original image into several regions, which are useful from our application point of view. Since many decades several techniques of segmentation were projected. The Active contour Model (ACM) [1,2] which was shown by Kass [3], has been demonstrated as good method for image segmentation. The general method for ACM is to start with initial contour then we can make some rule to find steady state condition. it means we can reach correct object boundary. In various publish papers ACM differ in how to select initial contour, various evolution mechanisms and at which time contour should be stopped from other evolution. The existing ACM [4,5] can be divided into two main categories i.e. region based and edge based. Edge based methods used to capture object boundaries in curve evolution. The main problem with these methods is they work poorly in presence of noise. They cannot segment object when there is hazy boundary.
Another problem with these type of method is that in the beginning the contour must be fixed nearby the object, else it is very problematic to get proper segmentation result. Region based model mark complete usage of image geometric analysis as compared to edge based model. There are many benefits of region based segmentation over edge based segmentation like they are less responsive to noise. Also, they are not more profound to contour initialization process. In addition to these, they can easily segment images with weak boundaries. The famous region based method was proposed by Chan-Vese [6] which is based on Mumford shah function. The main assumption in C-V model [7,8]  in each region. So, it would not be useful on images which have intensity inhomogeneity [9,10]. For dense demonstration of texture Linear Structure Tensor can be used. Structure tensor can be calculated from spatial derivatives of the image. LST Structure tensor [11] are matrix representation of partial derivative information It has more powerful descriptions of local patterns as opposed to the directional derivative through its coherence measure.it is useful in many applications like corner detection. For a gray scale image the matrix field of structure tensor is given by where , , For avoiding cancellation of opposite signed gradient, when direct integration is performed, gradient is considered as form of its outer product. In order to make matrix field more immune to noise, smoothing operation is performed by convolving matrix component with a Gaussian kernel K σ with standard deviation σ.
Where, * indicate convolution operator. An LST model can be used for segmentation of texture images. The texture [12,13] type of images which have intensity inhomogeneity cannot be segmented by this model. Therefore this paper suggest the solution of this problem with a combination of filter based tensor values to LST.
The chan-vese model The Chan-Vese model for active contour is a method through which we are able to segment different types of images. The images which are not segmented by thresholding can also be segmented by this model. This model is based on Mumford Shah functional for segmentation which is widely used in image segmentation. This algorithm is also useful to segment the object which does not have clearly defined boundaries. This algorithm is based on level sets [14][15][16].
The chan-vese model can give solution by minimizing following energy function Here, 12 , and    are constant, generally 12 1   . 1 c and 2 c are the intensity means of 0  inside C and outside C . In order to solve energy minimization problem, level set [17][18][19] methods is used, in which level set function ϕ(x,y) is used in place of unknown curve. The problem of minimization can be solved by taking Euler-Lagrange equation and also by updating level set function ϕ(x,y) by gradient descent method Here, 1 c and 2 c updates at each iteration by We have observed that chanvese model and Bhattacharya model are not useful for texture images,where as Gabor based chanvese model works well for texture images but it is not useful for images which have intensity inhomogeneity. Novel structure method only uses LST for edge enhancement.So that these algorithm are not giving better accuracy of texture as well as images which have intensity inhomogeneity. We need to develop some novel technique which give better accuracy of various type of images. Therefore, the objective of the paper to segment the images having following challenges.
 To segment objects from images with constraints of availability of texture region and intensity inhomogeneity simultaneously.
 To improve overall accuracy of active contour based segmentation algorithm by incorporating DOG and LST information inactive contour formulation. In proposed work ,we have developd hybrid model to improve accuracy of various type of images which is explained in next section.

PROPOSED ALGORITHM
In the proposed method we are using Difference of Gaussians (DOG). The DOG can be explained as below. DOG is basically featuring enhancement in which we can get less obscured (blurred) image from the real image. Blurring using Gaussian kernel repress only high frequency spatial data. DOG is a BPF (band pass filter) that repress all spatial frequency except handful of spatial frequencies that are falls in real gray scale image. The principle advantage DOG offers is that it can provide better edge visibility. One more advantage that DOG provides is the removal of noise compare to other algorithms. Also, it is very fast as far as computational complexity is concerned.
The overall algorithm as follows: Determine DOG Kernal: To determine the kernel, the variance plays the important role. If ratio between two of kernel is large, image blurring would be more. Therefore in proposed model, the size of image is used to calculate the kernel variance. 11 Calculate Edges using DOG: DOG Kernels are used to calculate the edges of the image by convolving image with DOG kernels as shown in (8): Calculate local structure tensor: Medical images can be considered as region of similar texture [20]. Therefore to present its orientation, Structure tensor plays an important role. The structure tensor can be obtained by calculating image edges. In the proposed model, the edge obtained using DOG are used in the calculation of Linear Structure Tensor.
Apply Active Contour model [21][22][23] over LST image: Later the LST based orientation Information is used as an external force in ACM model. The equation (10) can be rewritten using LST as shown in (11).

EXPERIMENT RESULTS AND ANALYSIS
For accuracy representation of proposed model, we can use Dice Similarity Coefficient (DSC), which can be defined as follow: Where, True Positive=Number of pixels that detected correctly.
False positive=Number of pixels detected as a member of segmented image but not in ground truth image.
False negative-Number of pixels that are not detected but part of ground truth image. We have immplemented this proposed algorithm for texture images, noisy images blur images and images which have intensity inhomogeneity. These images were taken from berkely database [24]. Figures 1 to 6 shows that proposed algorithm gives better edge visibility compared to novel structure tensor based Chanvese model [8].
We have compared the proposed model with chanvese model, Bhattacharya model, gabor based chanvese model and Linear structure tensor based chanvese model for various types of images. It is proven that we got the best accuracy compared to other existing models which is shown in Table 1.  Table 1 represents the accuracy of proposed Algorithm. We achieve average 99% accuracy of segmentation. CV Model [25] fails to segment texture as well as images having intensity inhomogeneity. Bhattacharya model [26] also not able to segment some images due to texture regions as well as noise within the image. Gabor and LST based ACM are capable to segment images. However, proposed algorithm outperforms these models and obtained 99% accuracy amongst all images by using DOG based edge information in LST.   1847 also mathematically easy to implement. But specifically for texture image Gaussian filter will create some problems. In this paper LST has been modified for removing edge dislocationTexture smotthing can also been done with this method. But the biggest advantage of proposed method is it uses DOG alongwith LST. We can also see the accuracy of the proposed model is better than almost any other model in almost all the cases. The advantage of DOG is that it is less prone to noise. This paper proposed structure tensor using DOG kernel .The orientation information obtained from Linear Structure Tensor is used in active contour model to obtain segmentation. We have shown that the proposed model works effectively for various types of images. We also obtained better Edge enhancement using this method.