IMPROVED MSEL AND ITS MEDICAL APPLICATION HE Huiguang, TIAN Jie, WANG Jing, CHEN Hong, ZHANG X.P. AILAB, Institute of Automation, The Chinese Academy of Sciences, Beijing,100080 Email:
[email protected] [email protected]
Abstract Edge detection is the basic operation in the image processing and analysis. Multiresolution Sequential Edge Linking (MSEL), which is proposed by Edward J.Delp of Purdue University, has a number of advantages over other edge detection schemes, such as lower false alarm rates while maintaining full connectivity of the edge. However, it is not reasonable in the initial value choosing and time consuming. To this problem, we first use anisotropic diffusion to smooth the image while keeping the edge, and then use the feedback method to optimize the initial value. We apply our method to the medical image, and the experiments show that our method is more efficient and accuracy than the old MSEL.
1. Introduction Edge detection is an important operation in pattern recognition and image processing. Generally, edge detection comprises two steps: First, the edges are enhanced, usually based on the spatial derivatives of the image; second, the decisions are made on whether a particular pixel is an edge or not. SEL and MSEL [1-3] are good approaches to edge detection, but they are very sensitive to the initial value. To overcome this drawback, our method includes three steps: First we use anisotropic diffusion to degrade the noise, and then we use feed back method to optimize the initial value, finally we use heuristic search to get the edge of the image. This paper is organized as following: In section 2, we introduce the background knowledge, In section 3, we introduce the MSEL method, In section 4, we introduce our method, at last we will give some experiment results.
2. Background
MSEL [2] was developed from the SEL [1]. The SEL algorithm can be decomposed into two parts: enhancement followed by detection and linking. An enhancement operator such as a Gaussian weighted gradient operator using a relatively large window can be used [4]. The detection and linking phase is based on a sequential search that ranks potential edges and edge paths according to a log-likelihood statistic. A crucial concept in any sequential searching algorithm is that of a path measure of goodness, known as the path metric. In the SEL path metric, both the strength of an edge and the past path of the edge are used to determine the search direction [1-2]. The strength of an edge is measured by the likelihood ratio of the conditional probability that an edge pixel exists and the past path of an edge is modeled by a Markov random chain. In the SEL, path metric Г is n p1 ( f rri ) Γ(m) = ∑ ln + ln P( si si −1 ) i =1 p 0 ( f rri )
(1)
Where m is the current path, f is the collection of pixel r magnitudes for the current path, ri is the ith position vector in the path m, p1(·) is the edge conditional density function, p0(·) is the non-edge conditional density function, and P(sn+1|sn) are the state transition probabilities for each turn in the path m. The sequential searching algorithm begins at a known edge pixel and sequentially examines paths, or sequences of possible edge pixels, in the image. At the each iteration of the algorithm, one of the paths explored so far is extended by one node and the metric for this new path calculated. Decisions are made based on these metrics as to which path should be extended in the next iteration. In order to compute the path metric that is defined in (1), we must know the Markov transition probabilities, and through a priori knowledge or estimation the conditional density functions of both the edge and non-edge pixels, which usually are Gaussian functions:
Supported by the National Natural Science Foundation of China under Grant Nos. 60071002,60072007,69931010,60172057
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p1 ( y ) = p0 ( y) =
1 2πσ
2 1
1 2πσ
2 0
exp( −( y − µ1 ) 2 / 2σ 12 ) exp( −( y − µ 0 ) 2 / 2σ 02 )
(edge)
（2）
(non-edge)
（3）
4. Improved MSEL
So, we must know σ 1 , σ 0 , µ 0 , µ1 ，the Gaussian parameters, and Markov transition probabilities. They depend on the prior knowledge. So, how to reduce the need of the prior knowledge is the motivation of the MSEL.
3. MSEL Method In order to obtain the parameters necessary to execute the SEL algorithm, MSEL uses the multi-resolution analysis, which acquires the relevant parameters in the high layer to guide the SEL in the low layer. That is shown in figure 1. High Layer 2.Markov Par. +
1.Edge Exp.
3.SEL 2.Gauss Par.
Low Layer
Figure 1. MSEL Algorithm 1. Expand the edge in the high layer to the low layer taking into account the increase of the resolution; 2. Use the Hidden Markov Model (HMM) to describe the edge path in the low layer which is got by step 1, and use the expectation-maximization (EM) to estimate the Gaussian parameters; And Markov parameters are estimated by the relative frequency of the state transitions in the edge path of the high layer; 3. Use the parameters obtained by step 2 to execute the SEL in the low layer. Here the Markov transition probabilities are estimated by the statistical method, and the Gaussian parameters are obtained by the HMM, where the hidden random variables indicate whether the pixel is on the edge or not, and explicit model is the conditional probability of (2) and (3). MSEL provide a new solution to the edge detection, however, there is some deficiency in the initial value chosen. Because of the lack of the prior knowledge, in the highest pyramid image, MSEL assume the equality of the Markov transition probabilities, and the root nodes are those with high gradation, then, the initial Gaussian parameters are: µ1 = 0.9 g ； σ 1 = µ1 2 / ratio ；
µ 0 = µ1 / ratio ；
Where g is the gradation and ratio is decided by the prior knowledge. Now, we can get the initial edges, and put it down to the next layer.
σ 0 = σ1 ；
4.1. Anisotropic Diffusion Due to the very complex background and diversity of medical image, most medical images have poorly defined object boundary, and nearby the desired object boundary it may exist noise of strong feature. So we must do some pre-process first. Embedding the original image in a set of images derived from it, we can describe the series of images being processed as I(x,y,t). When t=0, I(x,y,0) represents the original image. Then the image filtering process may be achieved by convolving the original image with a function F(x,y,t) (see equation 4). I(x,y,t) = I(x,y,0) * F(x,y,t) (4) Variable t is the scale-space parameter. Larger value of t corresponds to a coarser resolution. In the classical filtering, Gaussian kernel G(x,y;t) is used as F(x,y,t). Gaussian filter can smooth the images, but it can also distort the edge. So we need a good filter which can smooth the image while keeping the edge. Anisotropic diffusion proposed by Perona and Malik [5] can work well. The diffusion equation is (5) 1 1 It =
1 + ∇I
2
I + I ξξ 1 + ∇I 2 ηη
whereξdenotes the contour direction andηdenotes the gradient direction. From the equation 5, we can see that when |▽I| is large it allows almost no smoothing in the gradient direction, while in the contour direction, it always executes maximal smoothing. In this manner, the image is smoothed without destroying the edges. In the implementation of algorithm, we use the discrete form of equation 5, and make a minor modification. Limited by the length of the paper, it will not be labored here.
4.2. Optimization of Initial Edge Path After using anisotropic diffusion to process the image, we focus on the accuracy of the initial edge path. Of course, we also make use of the prior knowledge as little as possible. Here we take the solution like feedback to improve initial edge path accuracy. First, we also assume the equality of the Markov transition probabilities. According to the root nodes, which are selected by gradient, the conditional probability parameters are approximately computed, and thus we can get initial edge path. But, we do not directly put it down to the next layer like MSEL, instead, we estimated new parameters from the initial edge path, and we get new edge path
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from the new parameters. We repeat this procedure several times until we get the final initial edge path. This is shown in fig.2. Initial Markov Par. &Gauss Par.
SEL New Markov Par. &Gauss Par.
Highest Level
Figure 2. Improved MSEL Algorithm We will give some explanation about the rationality of our modification. When we got the first edge path, we think it is the approximate estimate of the real edge path to some extents, thus, the parameters which are updated with the new edge are more likely to be the real parameters than the initial parameters. It is can be shown on the increase probability of the P01 and P11 . Then, we use the new parameters to start the new round of SEL algorithm, the edge path will be more reflective of the real path, and it is also can be shown in its increase probability of the P01 and P11 . So, we got the better edge path every repetition. The second problem is how many repetitions we need. From the experiments, we find that after about eight repetitions, P01 =0.999， P11 =0.999, so, we think it is enough to set numbers of the repetitions eight when regarding with the numerical precision.
5. Experiment Results In the following, we present some examples to show the improved MSEL algorithm’s superior over the MSEL. First the standard datasets square and circles are shown, and then some examples of applications in the medical image will be given. From the figures 3-8, we can see that Improved MSEL has advantages in connecting the little gaps, which is the deficiency in the MSEL. There is no disconnection in the square and circles through Improved MSEL. Here the image size is 512*512, and pyramid level is 4. Figure 9-18 is some examples of the applications of the medical image. From these figures, we can see that edge detecting is very difficult for the medical image due to its highly complexity. However, because we have efficiently intervened the initial value selection, improved MESL verse MSEL has greatly reduces the false edge, and so the false alarm rate. We have got the fairly satisfactory result especially the result of the figure 12. But, for figure 13, because of the too blurredness of the edge, it loses some edge. So, these still are some improvement needed to this algorithm. If using the SOBEL operator, the result is very poor. It is worth pointing out that due to the new methods of the initial value chosen, improved MSEL has reduced the
needs of the prior knowledge. We explain this point as follows. In the procedure of the implementing of the MSEL, we must consider some practical limits, such as the minimum edge length, and the pixels with how much gradient that can be used as the root nodes. From our experiments, we find out that improved MSEL has been more robust to the change of these parameters. Taking the figure 13 as example, if we change the minimum edge length from 15 to 10, the results are show as figure 17 and 18. From the figure 17 and 18, we can see that MSEL has decayed greatly, but the improved has changed little. In fact, its performance has improved some, referring to the arrow pointing edge that is missed in the figure 16. However, we must pay attention to the compare of the figure 11 and figure 12. We can see that improved MSEL verse MSEL has missed the middle edge, and it can be explained as this. Because of the several optimization of the initial value, it is possible in some optimization that the edges with low competition have been discarded, and the edges with high competition have been remained, just as the edges in the middle of the figure 9. From this, we can see that improved MSEL has some percipience of the selection, and at the same time, its limit is also obvious, because it may lose some edges.
6. Conclusion This thesis applies the anisotropic diffusion to smooth the image while keeping the edge, and then improved the initial value chosen of MSEL. By doing so, we get the better results. Edge detecting is very difficult problem, and there are also great margins of the improvement of the methods proposed by this thesis, And some prior knowledge such as the levels of the pyramid and parameters of the filter are still needed. This is our future work.
Reference [1] Paul Eichel, Edward Delp: “Sequential edge detection in correlated Field”, Proceedings of the IEEE Computer Vision and Pattern Recognition Conference, Jun.1985, San Francisco, pp.14-21 [2] Gregory W. Cook and Edward J. Delp: “Multiresolution Sequential Edge Linking”, International Conference on Image Processing, Oct. 1995, Washington, DC, pp. 41-44 [3] W. Cook and E. J. Delp, "A gaussian mixture model for edge-enhanced images with applications to sequential edge detection and linking," Proceedings of the IEEE International Conference on Image Processing, Oct. 1998, Chicago, Illinois, pp. 540--544 [4] J. Canny, “A computational approach to edge detection”, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. PAMI-8, no. 6, pp. 679-698, November 1986 [5] Pietro Perona and Jitendra Malik, Scale Space and Edge Detection Using Anisotropic diffussion, IEEE Trans On Pattern Analysis and Machine Intelligence, 1990,Vol.12, No.7, pp.629-639
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Figure 3. Square (SNR=0.5)
Figure 4. MSEL Edge of Square
Figure 5. Improved MESL of Square
Figure 6. Circle (SNR=1)
Figure 7. MSEL Edge of Circle
Figure 8. Improved MESL of Circle
Figure 9. CT1
Figure 13. CT2
Figure 14. SOBEL Edge of CT2
Figure 15. MSEL Edge of CT2
Figure 16. Improved MSEL of CT2
Figure 17. MSEL Edge of CT2 (Parameter Changed)
Figure 18. Improved MSEL of CT2 (Parameter Changed)
Figure 10. SOBEL Edge of CT1
Figure 11.
Figure 12.
MSEL Edge of CT1
Improved MSEL of CT1
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