In this paper, a phase based motion estimation method is presented. We also introduce a motion trajectory estimation technique. Our method is applied to cardiac motion estimation using MRI tagged image sequences. We show that our method provides roughly 15% less error than a recent motion estimation method proposed in the literature. Moreover, the estimated motion trajectories could be a good indicator of cardiac diseases.
Quantitative assessment of left ventricle myocardium deformation provides important information about several cardiovascular pathologies. This deformation can be obtained using the motion estimated in a temporal image sequence. The motion can be estimated using different medical imaging modalities, such as ultrasound or MRI. In this paper, we address the problem of myocardium motion estimation in tagging MRI (denoted by MRIT in the following) (Zerhouni et al., 1988, Axel et Dougherty, 1989). With this technique, cardiac tissue is marked with a grid of magnetically saturated tags, whose deformation in time will follow the heart deformation during a cardiac cycle.
In MRIT, the motion can be estimated using classical techniques such as optical flow or block matching based on similarity functions like spatial correlation, sum of absolute or squared differences, etc. However, these methods still have serious drawbacks such as the sensibility to noise for the optical flow or the computational complexity for subpixel estimation with block matching.
In order to overcome these problems, methods adapted to MRIT and estimating the motion in the frequency domain have been proposed. The state of the art method is called HARP (Harmonic Phase) and estimates the motion using the first harmonic, exploiting in this way the regularity of the tags (Osman et Prince, 2000). As a consequence, the motion estimation is preceded by a bandpass filtering of the images, around the frequency of the first harmonic. More recently, a method called SinMod has been proposed in (Arts et al., 2010) and uses a local sinus model of the images. It was shown that this method outperforms HARP and classical approaches. For this reason, the results of the proposed method will be compared to those provided by SinMod.
The main purpose of this paper is to propose a 2D+t motion estimation method adapted to MRIT, based on the spatial 2D phase of the images and on a non rigid local motion model, controlled by a bilinear transformation.
2D spatial phases for images can be obtained using different mathematical tools, such as multidimensional analytic signals (Bulow et Sommer, 2001) or the monogenic signal (Felsberg et Sommer, 2001). In both cases, the spatial phase contains a structural information of the images, which makes it a good choice for motion estimation (Felsberg, 2006). The method proposed herein is based on spatial phases obtained using two single-orthant analytic signals, for which the information contained by one quadrant in the Fourier domain is exploited (Hahn, 1992). In this way, for each MRIT image, two different spatial phases are obtained. Combining the information of these two phases, for two consecutive images of a MRIT sequence, we provide an analytical estimator for 2D local translation. The main advantage of the proposed estimator is that it does not require a preliminary filtering and accordingly it is not based on a linear model of the phases. Moreover, the local estimated translations are used to estimate a bilinear deformation model, as previously shown in (Basarab et al., 2008).
We also propose in this paper a way of estimating the motion trajectory of local structures, in a cardiac sequence. For this, a temporal motion initialization is proposed. For an instance n in the sequence, the estimation at instance n-1 is used as initialization. The residual motion is after that estimated using the proposed phase based estimator. In addition to allowing trajectory estimation and temporal motion regularization, the proposed initialization technique allows the phase based estimator to assess local translations larger than half of the period, which is normally not possible with such approaches.
The performance of the proposed 2D+t motion estimation method is evaluated on simulated and in vivo sequences. The results are compared to those obtained with SinMod, using the absolute error in the simulated case (when the true motion is available) and a correlation criterion applied to registered images in the experimental case. A more detailed explanation of this criterion is given in (Basarab et al., 2008). The simulated sequence was obtained by using the analytic motion model proposed in (Clarysse et al., 2000). We show a standard deviation error diminution of 15% using our method compared to SinMod. The gain in precision is roughly the same on experimental data.
Finally, the case of a patient with infarct is presented. In this case, we show that the estimated trajectories could be an interesting indicator of cardiac diseases. By placing four regions of interest in the myocardium (two in the normal region and two in a pathological one) and by following them in time, we show that the motion amplitude is between two and three times larger in the normal region.
Nous proposons dans cet article une méthode d’estimation du mouvement utilisant la phase spatiale 2D des images, ainsi que l’extension de cette méthode à l’estimation de trajectoires. Appliquée à l’estimation du mouvement cardiaque sur des images par RM marquées, notre méthode s’avère plus précise (diminution des écarts types de l’erreur d’approximativement 15 %) qu’une méthode récemment publiée aussi bien en simulation que sur des images expérimentales. De plus, nous montrons sur un cas clinique que les trajectoires de mouvement estimées pourraient être un très bon indicateur d’une pathologie cardiaque.
motion estimation, trajectory, phase, multidimensional analytic signal, tagged MRI, cardiac imaging.
estimation de mouvement, trajectoires, phase, signal analytique multidimensionnel, IRM marquée, imagerie cardiaque.
Arts T., Prinzen F.W., Delhaas T., Milles J., Clarysse P. (2010). Mapping displacement and deformation of the heart with local sine wave modeling. IEEE Trans. on Medical Imaging, vol. 29, n° 5, p. 1114-1123.
Axel L., Dougherty L. (1989). MR imaging of motion with spatial modulation of magnetization. Radiology, vol. 171, p. 841-5.
Basarab A., Liebgott H., Morestin F., Lyshchik A., Higashi T., Asato R., Delachartre P. (2008). A method for vector displacement estimation with ultrasound images and its application for thyroid nodular disease. Medical Image Analysis, vol. 12, n° 3, p. 259-274.
Bulow T., Sommer G. (2001). Hypercomplex signals-a novel extension of the analytic signal to the multidimensional case. IEEE Transactions on Signal Processing, vol. 49, n° 11, p. 2844-2852.
Clarysse P., Tafazzoli J., Delachartre P., Croisille P. (2011). Simulation based evaluation of cardiac motion estimation methods in tagged-MR Image sequences. Journal of Cardiovascular Magnetic Resonance, vol. 13, n° Suppl 1, p. P360.
Clarysse P., Basset C., Khouas L., Croisille P., Friboulet D., Odet C., Magnin I.E. (2000). 2D spatial and temporal displacement field fitting from cardiac MR tagging. Medical Image Analysis, vol. 3, p. 253-268.
Felsberg M. (2006). Optical flow estimation from monogenic phase. International Workshop on Complex Motion, 3417:1.
Felsberg M., Sommer G. (2001). The monogenic Signal. IEEE Trans. Signal Proc., vol. 49, p. 3136.
Hahn S. L. (1992). Multidimensional complex signals with single-orthant spectra, Proceedings of the IEEE, vol. 80, n° 8, p. 1287-1300.
Osman N.F., Prince J.L. (2000). Visualizing myocardial function using HARP MRI. Phys. Med. Biol., vol. 45, p. 1665-1682.
Petitjean C., Rougon N., Cluzel P. (2005). Assessment of myocardial function: A review of quantification methods and results using tagged MRI. J. Cardiovasc. Magn. Reson., vol.7, p. 501-516.
Zerhouni E.A., Parish D.M., Rogers W.J., Yang A., Shapiro E.P. (1988). Human heart: tagging with MR imaging - A method for noninvasive assessment of myocardial motion. Radiology, vol. 169, p. 59-63.