Selection Of A Stopping Criterion For Anisotropic Diffusion Filtering In Ultrasound Images

Selection of a Stopping Criterion for AD Filtering in Ultrasound Images Javier Guillen Ibarra1; Sonia Contreras Ortiz PhD1 1Universidad Tecnológica de Bolívar

Abstract Ultrasound imaging is a safe and cost-effective diagnostic tool, but the quality of the images is affected by speckle noise and artifacts. Anisotropic diffusion filters can be used to reduce noise and preserve the edges in the image. However, this technique is very sensitive to the number of iterations selected.

This work proposes a stopping criterion for effective noise removal without blurring the edges, based on the relative variance between the estimated denoised image and the original one. Different quality metrics were evaluated in 25 test images. The results suggest that the proposed stopping criterion can be implemented efficiently and aids in the process of automation of the filter.

1. Introduction Echocardiography is one of the most used medical diagnostic techniques. It provides information on the shape, size, function, and strength of the heart; movement and thickness of its walls; and activity of heart valves in real time. However, the value of echocardiograms depends on the examiner’s skill. Ultrasound images have speckle noise, which hinder areas of interest, and difficult accurate measurements.

Anisotropic diffusion filters are commonly used in medical image enhancement. They are effective to reduce noise in homogeneous regions without blurring the edges by preventing intra-region smoothing. As anisotropic diffusion is an iterative method, it is important to determine the best time to stop the process. In this paper we propose a stopping criterion for anisotropic diffusion that uses the relation between the variance of the filtered image and the original one.

3. Image quality metrics Three metrics were used to quantify the filter’s performance and the image quality in each iteration. They all calculated in a homogeneous region, this one was chosen manually, before the start of the filtering algorithm, from an input pixel inside a region of interest of the image. In this work, the size of the homogeneous region for all images was chosen as 21x21 pixels.

2. Filter design Fig. (A) shows the template of 12 neighboring pixels.

• Signal-to-noise ratio (SNR) • Peak signal-to-noise ratio (PSNR) • Universal quality index (Q)

4. Stopping criterion We defined a minimum improvement in SNR of 2. It means that the relative variance should be less than or equal to 0.25. Therefore, we selected a value of 0.2 for the relative variance as stopping criterion:

𝑟 𝐼𝑇

var 𝐼 𝑡 = = 0.2 var 𝐼 0

𝑡 𝑡 𝐼𝑖,𝑗 = 𝐼𝑖,𝑗 +𝜆

𝑡 𝑐𝑛 ⋅ ∇𝑛 𝐼𝑖,𝑗

Where 𝑐𝑛 and ∇𝑛 are the directional derivatives and the diffusion coefficients for each direction respectively.

5. Experiments and results

Fig. (B) shows the convergence curve of the proposed stopping criterion for three different images.

Conclusions The performance of the AD filter depends on the structure and the selected stopping time. We proposed a simple, effective and computationally efficient stopping criterion based on the desired improvement in SNR. We evaluated the method with 25 ultrasound images and the results are similar to other criteria in the literature. Future work includes the validation of the proposed method with a larger database of images, the use of other metrics to evaluate the quality of edges during the process.

Simulated and real ultrasound images before and after the diffusion filtering. Fig. (C) is the original images. Fig. (D) is the processed images considering the stopping criterion, the filter stops when t = T. Fig. (E) is the overestimated filtered images with t >> T.

Contact

References

Javier Enrique Guillen Ibarra Email: [email protected] Twitter: @JVGuillen0528 Phone: +57 318 8428206

1. Loizou, Christos P y Constantinos S Pattichis. Despeckle filtering algorithms and software for ultrasound imaging. Synthesis Lectures on Algorithms and Software in Engineering. Morgan y Claypool Publishers, 2008. 2. Deepti Mittal, Vinod Kumar, Suresh Chandra Saxena, Niranjan Khandelwal, and Naveen Kalra. Enhancement of the ultrasound images by modified anisotropic diffusion method. Medical & biological engineering & computing, 48(12):1281–1291, 2010. 3. Joachim Weickert. Coherence-enhancing diffusion of colour images. Image and Vision Computing, 17(3- 4):201–212, 1999.