Abstract
Motion estimation on ultrasound data is often referred to as ‘Speckle Tracking’ in clinical environments and plays an important role in diagnosis and monitoring of cardiovascular diseases and the identification of abnormal cardiac motion. The impact of physical effects in the process of data acquisition raises many problems for conventional image processing techniques. The most significant difference to other medical data is its high level of speckle noise, which has completely different characteristics from other noise models, e.g., additive Gaussian noise. In this paper we address the problem of multiplicative speckle noise for motion estimation techniques that are based on optical flow methods and prove that the influence of this noise leads to wrong correspondences between image regions if not taken into account. To overcome these problems we propose the use of local statistics and introduce an optical flow method which uses histograms as discrete representations of local statistics for motion analysis. We show that this approach is more robust under the presence of speckle noise than classical optical flow methods.
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10851-012-0398-z/MediaObjects/10851_2012_398_Fig1_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10851-012-0398-z/MediaObjects/10851_2012_398_Fig2_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10851-012-0398-z/MediaObjects/10851_2012_398_Fig3_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10851-012-0398-z/MediaObjects/10851_2012_398_Fig4_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10851-012-0398-z/MediaObjects/10851_2012_398_Fig5_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10851-012-0398-z/MediaObjects/10851_2012_398_Fig6_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10851-012-0398-z/MediaObjects/10851_2012_398_Fig7_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10851-012-0398-z/MediaObjects/10851_2012_398_Fig8_HTML.gif)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs10851-012-0398-z/MediaObjects/10851_2012_398_Fig9_HTML.gif)
Similar content being viewed by others
References
Achmad, B., Mustafa, M., Hussain, A.: Inter-frame enhancement of ultrasound images using optical flow. In: Proc. 1st Int. Visual Informatics Conf.: Bridging Research and Practice, pp. 191–201 (2009)
Baker, S., Scharstein, D., Lewis, J., Roth, S., Black, M., Szeliski, R.: A database and evaluation methodology for optical flow. Int. J. Comput. Vis. 92, 1–31 (2011)
Becciu, A., Assem, H., Florack, L., Kozerke, S., Roode, V., Haar Romeny, B.: A multi-scale feature based optical flow method for 3D cardiac motion estimation. In: Proc. 2nd Int. Conf. on Scale Space and Variational Methods in Comp. Vis., pp. 588–599 (2009)
Brox, T., Malik, J.: Large displacement optical flow: descriptor matching in variational motion estimation. IEEE Trans. Pattern Anal. Mach. Intell. 33, 500–513 (2011)
D’Ascenzi, F., Cameli, M., Zaca, V., Lisi, M., Santoro, A., Causarano, A., Mondillo, S.: Supernormal diastolic function and role of left atrial myocardial deformation analysis by 2D speckle tracking echocardiography in elite soccer players. Echocardiography 28, 320–326 (2011)
Dawood, M., Büther, F., Jiang, X., Schäfers, K.: Respiratory motion correction in 3D PET data with advanced optical flow algorithms. IEEE Trans. Med. Imaging 9, 1164–1175 (2008)
Dawood, M., Lang, N., Jiang, X., Schäfers, K.: Lung motion correction on respiratory gated 3-d pet/ct images. IEEE Trans. Med. Imaging 25, 476–485 (2006)
Duan, Q., Angelini, E., Lorsakul, A.: Coronary occlusion detection with 4D optical flow based strain estimation on 4D ultrasound. In: Proc. of 5th Int. Conf. on Functional Imaging and Modeling of the Heart, pp. 211–219 (2009)
Fahad, A., Morris, T.: Multiple combined constraints for optical flow estimation. In: Proc. of 3rd Int. Conf. on Advances in Vis. Comp., vol. 2, pp. 11–20 (2007)
Fleet, D., Weiss, Y.: Optical flow estimation. In: Paragios, N., Chen, Y., Fauregas, O. (eds.) The Handbook of Math. Models in Comp. Vis., pp. 241–260. Springer, Berlin (2005)
Horn, B., Schunck, B.: Determining optical flow. Artif. Intell. 17, 185–203 (1981)
Jin, Z., Yang, X.: A variational model to remove the multiplicative noise in ultrasound images. J. Math. Imaging Vis. 39, 62–74 (2011)
Krissian, K., Kikinis, R., Westin, C.-F., Vosburgh, K.: Speckle-constrained filtering of ultrasound images. In: Proc. of IEEE Computer Society Conf. CVPR, vol. 2, pp. 547–552 (2005)
Liu, C., Yuen, J., Torralba, A.: SIFT flow: Dense correspondence across scenes and its applications. IEEE Trans. Pattern Anal. Mach. Intell. 33, 978–994 (2011)
Loupas, T., McDicken, W., Allan, P.: An adaptive weighted median filter for speckle suppression in medical ultrasonic images. IEEE Trans. Circuits Syst. 36, 129–135 (1989)
Papenberg, N., Bruhn, A., Brox, T.: Highly accurate optic flow computation with theoretically justified warping. Int. J. Comput. Vis. 67, 141–158 (2006)
Perreault, C., Auclier-Fortier, M.-F.: Speckle simulation based on B-mode echographic image acquisition model. In: Proc. of 4th Canad. Conf. Comp. and Robot Vis., pp. 379–386 (2007)
Rudin, L., Lions, P., Osher, S.: Multiplicative denoising and deblurring: theory and algorithms. In: Osher, S., Paragios, N. (eds.) Geometric Level Set Methods in Imaging, Vision, and Graphics, pp. 103–122. Springer, Berlin (2003)
Schmid, S., Tenbrinck, D., Jiang, X., Schäfers, K., Tiemann, K., Stypmann, J.: Histogram-based optical flow for functional imaging in echocardiography. In: Proc. of 14th Int. Conf. on Computer Analysis of Images and Patterns, pp. 477–485 (2011)
Segars, W.P., Sturgeon, G., Mendonca, S., Grimes, J., Tsui, B.: 4D XCAT phantom for multimodality imaging research. Med. Phys. 37, 4902–4915 (2010)
Song, S., Leahy, R.: Computation of 3-D velocity fields from 3-D cine CT images of a human heart. IEEE Trans. Med. Imaging 10, 295–306 (1991)
Stricker, M., Orengo, M.: Similarity of color images. In: Proc. of Conf. on Storage and Retrieval for Image and Video Databases, pp. 381–392 (1995)
Stypmann, J., Engelen, M., Troatz, C., Rothenburger, M., Eckardt, L., Tiemann, K.: Echocardiographic assessment of global left ventricular function in mice. Lab. Anim. 43, 127–137 (2009)
Trottenberg, U., Schuller, A.: Multigrid. Academic Press, San Diego (2001)
Veronesi, E.F., Corsi, C., Caiani, E., Sarti, A., Lamberti, C.: Tracking of left ventricular long axis from real-time three-dimensional echocardiography using optical flow techniques. IEEE Trans. Inf. Technol. Biomed. 10, 174–181 (2006)
Xu, L., Jia, J., Matsushita, Y.: Motion detail preserving optical flow estimation. IEEE Trans. Pattern Anal. Mach. Intell. 34, 1744–1757 (2012)
Acknowledgements
We thank Rico Lehmann for supporting us with his extension of the US speckle phantom and Olga Friesen for her helpful hints on statistics. Additionally, we thank Martin Burger and Alex Sawatzky for fruitful discussions on physical noise models. This study was supported by the Deutsche Forschungsgemeinschaft (DFG), SFB 656 MoBil, Münster, Germany (projects B3, C3) and the IZKF Münster Core Unit “Small animal ultrasound: imaging and therapy” (ECHO).
Author information
Authors and Affiliations
Corresponding author
Additional information
D. Tenbrinck and S. Schmid contributed equally to this work.
Rights and permissions
About this article
Cite this article
Tenbrinck, D., Schmid, S., Jiang, X. et al. Histogram-Based Optical Flow for Motion Estimation in Ultrasound Imaging. J Math Imaging Vis 47, 138–150 (2013). https://doi.org/10.1007/s10851-012-0398-z
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10851-012-0398-z