Image Processing and Bioimaging Research Laboratory, System Research Institute & Department of Advanced Technologies, Alcorn State University, Alcorn State, MS, USA

School of Computing, University of Southern Mississippi, 118 College Drive, Hattiesburg, MS 39406-0001, USA

SpecPro Inc, 3909 Halls Ferry Road, Vicksburg, MS 39180, USA

The Fifth Hospital of Harbin, Harbin, Heilongjiang, China

Abstract

Background

Ultrasound imaging technology has wide applications in cattle reproduction and has been used to monitor individual follicles and determine the patterns of follicular development. However, the speckles in ultrasound images affect the post-processing, such as follicle segmentation and finally affect the measurement of the follicles. In order to reduce the effect of speckles, a bilateral filter is developed in this paper.

Results

We develop a new bilateral filter for speckle reduction in ultrasound images for follicle segmentation and measurement. Different from the previous bilateral filters, the proposed bilateral filter uses normalized difference in the computation of the Gaussian intensity difference. We also present the results of follicle segmentation after speckle reduction. Experimental results on both synthetic images and real ultrasound images demonstrate the effectiveness of the proposed filter.

Conclusions

Compared with the previous bilateral filters, the proposed bilateral filter can reduce speckles in both high-intensity regions and low intensity regions in ultrasound images. The segmentation of the follicles in the speckle reduced images by the proposed method has higher performance than the segmentation in the original ultrasound image, and the images filtered by Gaussian filter, the conventional bilateral filter respectively.

Background

Ultrasound imaging technology has wide applications in cattle reproduction and has been used to monitor individual follicles and determine the patterns of follicular development

In the applications of ultrasound imaging to monitoring individual follicles and determining the patterns of follicular development, the acquisition of the measurements of the individual follicles such as diameters, areas and perimeters is very important. In order to acquire the measurements of an individual follicle, image segmentation techniques are often used to extract the individual follicles. However, speckles in ultrasound images affect the segmentation and finally affect the measurement of the follicles. Speckle noise, seen as a granular structure, is caused by the interaction between the ultrasound waves and the scatters within the tissue

In this paper, we will investigate using bilateral filter to reduce the speckles in ultrasound images for cattle follicle segmentation. It is well known that bilateral filter has good performance in noise reduction and edge preservation. However, current existing bilateral filters are mainly used for additive noise reduction. It is not effective when it is applied to speckles, which are generally modelled as multiplicative noise. In order to solve this issue, we propose an adaptive bilateral filter, which can reduce the speckles effectively.

Methods

Bilateral filter

Bilateral filter was developed by Tomasi and Manduchi

where _{d}^{2} and _{r}^{2} are the parameters controlling the fall-off of weights in spatial and intensity domains, respectively,

In the above equation, when

Bilateral filter is a good choice for image de-noising because it is stable and simple. The effectiveness of bilateral filter lies in the combined use of the domain filter, which is used to enforce spatial closeness by weighting pixel values with coefficients that fall off with distance _{d}^{2} and _{r}^{2} is very important. If their values are set too high, the filter will act as a smoothing filter and will blur the edges. If their values are set too low, the noise cannot be removed. Generally speaking, the choice of _{d}^{2} and _{r}^{2} depends on the variance of the noise. Based on the research in _{d}^{2} is relatively insensitive to noise variance while the optimal _{r}^{2} changes significantly as the noise standard deviation changes _{r}^{2} and noise variance are linearly related to a large degree. The research in _{r}^{2} and noise variance will not be established because speckle noise is multiplicative noise. In order to reduce the speckles in ultrasound images effectively, we develop speckle reducing bilateral filter.

Speckle reducing bilateral filter

Generally speaking, noise can be modelled by an additive model or a multiplicative model. Additive noise model is the simpler case of the two and can be described by a linear model

where

It is well known that multiplicative noise appears much worse in bright image regions than dark regions since it multiplies the gray intensities.

Speckle noise is generally treated as multiplicative noise and can be modelled using equation (4). Thus, compared with other types of noise, speckle noise is generally difficult to be removed. Our research below shows that the conventional bilateral filter described in equation (1) and (2) generally gets bad results when it is applied to speckle reduction directly. Thus, the bilateral filter described in (1) and (2) needs improvement or enhancement so that it can be applied to reduce the speckles in images effectively. In order to do this, we will first analyze the behavior of

Let

||

If both

||

Equation (6) means that the difference between any two pixels from the same homogenous region is only related to the difference of the noise. If

||

Similarly, if both

||

From equation (8), we can understand that the difference between two pixels in the same homogenous region(in the image corrupted by multiplicative noise) is not only related to the difference of the noise. It also depends on the intensity of the region. As is seen in equation (8), the difference is big when the intensity of the region is big while the difference is small when the intensity of the image is small.

The above analysis shows the bilateral filter described in (1) and (2) is not suitable for removing speckle noise, which is multiplicative noise. The reason lies in the difference of the corrupted image has different distributions in different homogenous regions. For example, if _{r}^{2} is fixed in the processing, when _{r}^{2} is set to be big, the edge in lower intensity regions will be removed, while the noise can’t be removed in the higher-intensity regions when _{r}^{2} is set to be small. Thus, in order to develop an effective bilateral filter to remove the speckle, we need to develop a new representation of the difference. Dividing each side of equation (8) by ||

Equation (9) shows that the normalized difference is only related to the noise and doesn’t depend on the intensities of the region. Thus, the proposed adaptive bilateral filter can be expressed as follows

where

Bilateral filter is famous because it is non-iterative, however, the non-iterative bilateral filter doesn’t yield good results. In order to improve its effectiveness, we use iterative bilateral filter. The basic idea of iterative bilateral filter is to use the filtered image obtained by equation (10) as the input of equation (1) and implement it many times, the mathematical expression is as follows:

where

Where

Cattle follicle segmentation

In order to analyze and monitor the reproduction of cattle, the acquisition of some quantitative parameters is very important. These parameters include diameters, areas and perimeters of the follicles. These parameters can be used to monitor the development and maturity of follicles. In order to get these parameters, we need to segment the follicles.

Many image segmentation methods have been proposed, which includes histogram based methods, edge detection based methods, region based methods, active contour model based methods, etc. Active contour model based methods have drawn a lot of attention in the past decade because of their significant advantages. In this paper, we adopt active contour model based method for the segmentation of the follicles. An active contour or a snake

where

Here

GVF provides external forces for a snake model, we also need internal forces to smooth the contour. In this paper, we use B-spline to represent the contour instead of the real internal forces. B-spline has been used in snake model in several applications and get pretty good results _{0} through _{m}_{0} through _{m}_{+4}, and _{i}_{i-}_{3}, _{i-}_{2}, _{i-}_{1}, _{i}_{i-}_{3,4}, _{i}_{-2,4}, _{i}_{-1, 4}, _{i}_{, 4} (

_{i}_{i-}_{3} · _{i-3, 4} + _{i-2} · _{i}_{-2,4} + _{i}_{-1} · _{i}_{-1,4} + _{i}_{i}_{,4} (

where 3 _{i} ≤ t ≤ t_{i+}_{1}. The blending functions can be obtained using recursion as follows

When

For the segmentation of the follicles, we initialize the B-spline GVF snake using a circle inside each follicle. The circle is represented by B-spline and the number of control points is set to 48 in this paper. Then, starting from the initial contour, the GVF is used to drive the contour to the boundary of the follicle. The evolution of the contours is the same as that in the B-spline GVF snake in single scale proposed by

Results

Results from Synthetic Images

To test the effectiveness of the proposed bilateral filter, we used both conventional bilateral filter and the proposed bilateral filter to process the synthetic image with speckles and compare the results. Fig.

Synthetic image and despeckling results. (a) original synthetic image; (b) multiplicative noise image; (c) the best result by the conventional bilateral filter(σr = 3 σd =0.3); (d) the result by the proposed bilateral filter(σr = 3 σd =0.3); (e)the result by the conventional bilateral filter(σr = 3 σd =0.7); (f) the best result by the proposed bilateral filter(σr = 3 σd =0.7).

**Synthetic image and despeckling results.** (a) original synthetic image; (b) multiplicative noise image; (c) the best result by the conventional bilateral filter(_{r}_{d}_{r}_{d}_{r}_{d}_{r}_{d}

where I_{0} and I are the original image and the corrupted image, respectively, N is the pixel number of the image I_{0} (or) I, _{0}, respectively. The NMSE generally represents the difference between the original image and the processed image. The noise reduction measure is defined as

where

The edge preservation parameter is given by

where Δ is the Laplacian operator. Higher

The conventional bilateral filter and the proposed bilateral filter were applied to process the speckled images. In both filters, _{d}_{r}_{r}_{r}_{r}_{r}_{r}_{r}^{T}_{r}_{r}^{T}_{r}_{r}

NMSE value comparison. The blue line shows the NMSE values obtained by the conventional bilateral filter and the red line shows the NMSE values obtained by the proposed bilateral filter. Both filters have big NMSE values when σr is small. The proposed filter has smaller NMSE values than the conventional bilateral filter after σr reaches the optimal point.

**NMSE value comparison.** The blue line shows the NMSE values obtained by the conventional bilateral filter and the red line shows the NMSE values obtained by the proposed bilateral filter. Both filters have big NMSE values when _{r}_{r}

Noise reduction measurement comparison. The blue line shows the a values obtained by the conventional bilateral filter and the red line shows the a values obtained by the proposed bilateral filter. The proposed filter has much better performance in noise reduction than the conventional bilateral filter after σr reaches the optimal point.

**Noise reduction measurement comparison.** The blue line shows the _{r}

Edge preservation measurement comparison. The blue line shows the β values obtained by the conventional bilateral filter and the red line shows the β values obtained by the proposed bilateral filter. The proposed filter has much better performance in edge preservation than the conventional bilateral filter after σr reaches the optimal point.

**Edge preservation measurement comparison.** The blue line shows the _{r}

Fig._{r}_{r}_{r}_{r}

All of the above experiments show that the proposed bilateral filter can achieve better performance in noise removal and edge preservation than the conventional bilateral filter.

Results from real ultrasound Images

In this subsection, we will compare the proposed bilateral filter with Gaussian filter and the conventional bilateral filter in speckle reduction using real ultrasound images. Fig.

Denoised ultrasound images of cattle follicles. (a) shows the origianl image and (b),(c),(d) show the results obtained by Gaussian filter(standard deviation of the Gaussian kernel is 3.0 and window size is 9), the conventional bilateral filter and the proposed filter respectively(σr = 3 σd =0.5,iteration=40).

**Denoised ultrasound images of cattle follicles.** (a) shows the origianl image and (b),(c),(d) show the results obtained by Gaussian filter(standard deviation of the Gaussian kernel is 3.0 and window size is 9), the conventional bilateral filter and the proposed filter respectively(_{r}_{d}

To compare and evaluate the three filters quantitatively, we used them to reduce the speckles in real ultrasound image and then calculated the contrast of the homogenous region and edges in the image. A good filter should preserve the edges and reduce speckles in the image, which means the contrast in homogenous region should be low while the contrast in edges should be high. The contrast measure used in this paper is the measure adopted in

where

where

Fig.

Contrast comparison. (a) Contrast of homogenous region; (b) Contrast of edge points set.

**Contrast comparison.** (a) Contrast of homogenous region; (b) Contrast of edge points set.

After the images were processed, we applied B-spline snake

Final boundaries of follicles. (a) shows the final contours of the follicle obtained from the origianl image and (b),(c),(d) show the contours of the follicle obtained from the images filtered by Gaussian filter,the contional bilateral filter and the proposed filter respectively.

**Final boundaries of follicles.** (a) shows the final contours of the follicle obtained from the origianl image and (b),(c),(d) show the contours of the follicle obtained from the images filtered by Gaussian filter,the contional bilateral filter and the proposed filter respectively.

In order to evaluate the segmentation results, we adopted the segmentation metric, Pratt's quality measurement metric (FOM), which is defined as

where I_{A} is the number of boundary pixels delineated by an automatic segmentation method, I_{I} is the number of boundary pixels delineated by the technicians.

Fig.

Comparison of FOM values. The blue, red, and purple lines show the FOM values for the follicle segmentation using the original image, the filtered image by Gaussian filter, the filtered image by conventional bilateral filter, and the filtered image by the proposed filter(with the best FOM value).

**Comparison of FOM values.** The blue, red, and purple lines show the FOM values for the follicle segmentation using the original image, the filtered image by Gaussian filter, the filtered image by conventional bilateral filter, and the filtered image by the proposed filter(with the best FOM value).

Discussion

Bilateral filter is a powerful technique in image de-noising due to its stability, and simplicity. The basic idea of bilateral filter is to replace a pixel value by a weighted average of its neighbours in both space and range (pixel values). However, the conventional bilateral filter performs poorly on ultrasound images due to the speckles. From the multiplicative noise model, we investigated a normalized scheme based on the conventional bilateral filter so as to remove the speckles effectively while preserving useful details. For bilateral filter, the parameters including _{d}^{2} and _{r}^{2}_{}_{d}^{2} is relatively insensitive to noise variance while the optimal _{r}^{2} value changes significantly as the noise standard deviation changes. To investigate the performance of bilateral filter with different values of _{r}^{2}, we applied the bilateral filters on synthetic images and used three quantitative measures including NMSE, noise reduction measure and edge preservation measure for analysis and comparison. We can see that the proposed method is more robust and effective than the conventional bilateral filter. The above three measures can be used for parameter selection of bilateral filters. However, since the ideal signals or non-noised images are usually unknown for real biomedical images, we should define other measures such as local contrast of homogenous regions and edge points set. Our local contrast is more robust and effective for algorithm evaluation in noise reduction and details preservation. This kind of measure can be adopted for parameter selection in bilateral filters when the filters are applied to real images. We compared the proposed filter with the conventional bilateral filter and Gaussian filter. Although Gaussian filter can reduce noises more or less, most of the edges and details have been smeared out. The conventional bilateral filter behaved poorly in speckle reduction. Experimental results of real ultrasound images of follicles illustrate that our proposed algorithm could obtain the best performance.

Conclusions

We presented a normalized bilateral filter for speckle reduction in ultrasound images for follicles segmentation. We compared the conventional bilateral filter with the proposed filter using synthetic speckled images and demonstrated its good performance in speckle reduction and edge preservation. Besides, we also tested the proposed filter, the conventional bilateral filter and Gaussian filter using real ultrasound images of cattle follicles. The contrast values of homogenous regions and edge points set demonstrated the proposed algorithm could achieve the best performance. The segmentation experiments also proved that B-spline snake can accurately find the boundary of the follicles from the filtered images by the proposed method. Experimental results validated the effectiveness and the accuracy of the proposed filter in noise reduction and edge preservation for follicle segmentation.

Competing interests

The authors declare that they have no competing interests.

Authors' contributions

JT developed the algorithm and wrote non-results part of the paper. SG implemented the algorithm and wrote the result part. QS attended to develop the algorithm. YD and DZ helped data analysis. All authors read and approved the final manuscript.

Acknowledgements

This work has been supported by the United States Department of Agriculture (award No. 2007-38814-18488). The authors appreciate Dr. Evelin Cuadra and Ms. Melissa C. Mason's work in the acquisition of the cattle follicle images. Publication of this supplement was made possible with support from the International Society of Intelligent Biological Medicine (ISIBM).

This article has been published as part of BMC Genomics Volume 11 Supplement 2, 2010: Proceedings of the 2009 International Conference on Bioinformatics & Computational Biology (BioComp 2009). The full contents of the supplement are available online at