形变立体跟踪-基于稠密运动估计和力学仿真(1)
參考文獻：Real-time target tracking of soft tissues in 3D ultrasound images based on robust visual information and mechanical simulation
期刊水平：MIA， medical imaging analysis
?圖一：作者方法的計算流程圖。深色的表示數據的輸入和輸出；淺色的表示作者的處理方法。
1. Introduction
Soft-tissue motion tracking is an active research area that consists in providing accurate evaluation about the location of anatomical structures. To do so, ultrasound imaging is often used since it is non-invasive, real-time and portable. Thus, several
ultrasound tracking approaches have been developed in order to estimate soft tissue displacements that are caused by physiological motions and manipulations by medical tools. These methods have gained significant interest for image-guided therapies such as radio-frequency ablation (RFA) ?or high-intensity focused ultrasound (HIFU) (Pernot et al., 2004) that consist in eliminating tumors by delivering a local treatment on a targeted anatomical region. However, these tracking techniques remain sensitive to different ultrasound imaging shortcomings such as large ultrasound shadows, gain change and speckle noise. In this paper, we propose a novel tracking approach to tackle these limitations. Our method combines an intensity-based approach with a mechanical regularization（機械正規化）. We also propose an ultrasound-specific similarity criterion that has the advantage to be computationally efficient and robust to gain changes introduced by ultrasound imaging.
軟組織的運動跟蹤是一個活躍的研究領域，在于可以準確定位解剖結構位置。超聲圖像因為無損傷、實時、便攜，被廣泛使用。因此，一些研究人員設計了基于超聲圖像的跟蹤方法，用于估計軟組織的偏移（這些偏移主要是由生理運動和手術器械的操作造成的）。這些方法使得基于圖像的治療技術，如射頻消融、高強度聚焦超聲，受益良多（通過對靶向區域提供局部治療進而消除腫瘤）。然而，這些方法仍然對超聲圖像的聲影、斑點噪聲、增益變化敏感，這篇文章，作者就是為了解決這些問題。作者的方法主要聯合了基于灰度的方法和機械正則化。作者找到了一種適用于超聲的相似性測度，使得相似度計算過程有效且魯邦。
RFA參考文獻：Higgins H, Berger D L. RFA for Liver Tumors: Does It Really Work?[J]. Oncologist, 2006, 11(7): 801-808.
HIFU參考文獻：Pernot, M., Tanter, M., Fink, M., 2004. 3-D real-time motion correction in high-intensity focused ultrasound therapy. Ultrasound Med. Biol. 30 (9), 1239–1249.
2. Related work
2.1 基于特征的跟蹤
基于表面和生物力學的匹配跟蹤：Papademetris X, Sinusas A J, Dione D, et al. Estimation of 3-D left ventricular deformation from medical images using biomechanical models[J]. IEEE Transactions on Medical Imaging, 2002, 21(7): 786-800.
基于關鍵點的匹配跟蹤（SIFT）：Schneider R J, Perrin D P, Vasilyev N V, et al. Real-time image-based rigid registration of three-dimensional ultrasound[J]. Medical Image Analysis, 2012, 16(2): 402-414.
為了提高對噪聲的魯棒性，這些方法可以基于貝葉斯框架來包含對目標形狀的先驗知識。
Angelova D S, Mihaylova L. Contour segmentation in 2D ultrasound medical images with particle filtering[J]. machine vision applications, 2011, 22(3): 551-561.
Rothlubbers, S., Schwaab, J., Jenne, J., Gunther, M., 2014. MICCAI CLUST 2014-Bayesian real-time liver feature ultrasound tracking. In: Proceedings of MICCAI Workshop on Challenge on Liver Ultrasound Tracking, p. 45
Zhang X, Gunther M, Bongers A, et al. Real-time organ tracking in ultrasound imaging using active contours and conditional density propagation[C]. international conference on medical imaging and augmented reality, 2010: 286-294.
但是，當關鍵特征由于聲影等原因不可見時，這些方法就很容易跟蹤失敗。另一類方法是基于對強度損失函數的最小化；該損失函數使用單模相似度，如誤差平方和（SSD）構建。
2.2 基于強度的損失函數優化
誤差平方和 Sum of Squared Difference, SSD:
Lubke, D., Grozea, C., 2014. High performance online motion tracking in abdominal ultrasound imaging. In: Proceedings of MICCAI Workshop on Challenge on Liver Ultrasound Tracking, p. 29
Royer, L., Marchal, M., Le Bras, A., Dardenne, G., Krupa, A., 2015. Real-time tracking of deformable target in 3d ultrasound images. In: Proceedings of IEEE International Conference on Robotics and Automation
Yeung F, Levinson S F, Fu D, et al. Feature-adaptive motion tracking of ultrasound image sequences using a deformable mesh[J]. IEEE Transactions on Medical Imaging, 1998, 17(6): 945-956.
絕對誤差和 Sum of Absolute Difference, SAD:
Touil B, Basarab A, Delachartre P, et al. Analysis of motion tracking in echocardiographic image sequences: Influence of system geometry and point-spread function[J]. Ultrasonics, 2010, 50(3):373-386.
交叉相關 Cross-Correlation,?CC:
Basarab A, Liebgott H, Morestin F, et al. A method for vector displacement estimation with ultrasound imaging and its application for thyroid nodular disease[J]. Medical Image Analysis, 2008, 12(3):259-274.
De L V, Tschannen M, Székely G, et al. A Learning-Based Approach for Fast and Robust Vessel Tracking in Long Ultrasound Sequences[M]// Medical Image Computing and Computer-Assisted Intervention – MICCAI 2013. Springer Berlin Heidelberg, 2013:518-25.
其實吧，如果目標的灰度不變，那么這些相似性測度都是很有效的，然而不幸的是，超聲成像很特別，增益變化將會引起目標灰度強烈變化。
2.3 特異性的超聲相似性測度
Baumann M, Mozer P, Daanen V, et al. Prostate biopsy tracking with deformation estimation[J]. Medical Image Analysis, 2012, 16(3):562-576. 提出了一種基于相關性的距離測度，這種測度還能夠處理局部強度偏差（當超聲束角度發生偏差就會出現灰度偏差）
Cohen B, Dinstein I. New maximum likelihood motion estimation schemes for noisy ultrasound images ☆[J]. Pattern Recognition, 2002, 35(2):455-463. 設計了新的相似度測度，該設計的靈感來源于超聲的斑點噪聲近似瑞利分布，所以對于超聲斑點噪聲污染嚴重的情況非常有用，但是對聲影沒有用。
Elen A, Choi H F, Loeckx D, et al. Three-dimensional cardiac strain estimation using spatio-temporal elastic registration of ultrasound images: a feasibility study[J]. IEEE Trans Med Imaging, 2008, 27(11):1580-1591. 建議采用互信息作為相似性測度，這樣可以抵抗增益變化的影響，但是互信息計算量太大了。
Masum M A, Pickering M, Lambert A, et al. Accuracy assessment of Tri-plane B-mode ultrasound for non-invasive 3D kinematic analysis of knee joints[J]. Biomedical Engineering Online, 2014, 13(1):122. 建議使用條件方差和，雖然條件方差和可以降低對增益變化的敏感度，但是對于聲影，條件方差和仍然束手無措。
2.4 Warping Model-變形模型
變形模型主要在于變形函數的設計。目前研究比較透得是平移變形函數 和 彷射變形函數； 研究的比較深的還是形變模型。
平移模型-平移形變函數：
Veronesi F, Corsi C, Caiani E G, et al. Nearly automated left ventricular long axis tracking on real time three-dimensional echocardiographic data[C]// Computers in Cardiology. IEEE, 2006:5-8.
彷射模型-彷射變形函數：
Wein, W., Cheng, J.-Z., Khamene, A., 2008. Ultrasound based respiratory motion compensation in the abdomen. In: Proceedings of MICCAI Worshop on Image Guidance and Computer Assistance for Soft tissue Interventions, 32, p. 294.
形變模型-形變變形函數：
A：基于傳統的塊匹配算法-計算兩個連續幀之間小的圖像塊偏移量。
Basarab A, Liebgott H, Morestin F, et al. A method for vector displacement estimation with ultrasound imaging and its application for thyroid nodular disease[J]. Medical Image Analysis, 2008, 12(3):259-274.
De L V, Tschannen M, Székely G, et al. A Learning-Based Approach for Fast and Robust Vessel Tracking in Long Ultrasound Sequences[M]// Medical Image Computing and Computer-Assisted Intervention – MICCAI 2013. Springer Berlin Heidelberg, 2013:518-25.
Touil B, Basarab A, Delachartre P, et al. Analysis of motion tracking in echocardiographic image sequences: Influence of system geometry and point-spread function[J]. Ultrasonics, 2010, 50(3):373-386.
然而，塊匹配方法不能表示高度表征局部的可變形的運動，因為它們假設在局部區域塊中位移是剛性的。
B：稠密運動長場估計
為了解決1中遇到的問題，可以利用形變模型估計稠密運動場。典型的形變模型：
分段彷射模型：Royer, L., Marchal, M., Le Bras, A., Dardenne, G., Krupa, A., 2015. Real-time tracking
of deformable target in 3d ultrasound images. In: Proceedings of IEEE International Conference on Robotics and Automation.
薄板樣條模型：Lee, D., Krupa, A., 2011. Intensity-based visual servoing for non-rigid motion compensation of soft tissue structures due to physiological motion using 4d ultrasound. In: Proceedings of IEEE International Conference on Intelligent Robots and Systems, pp. 2831–2836.
自由形變：Heyde, B., Claus, P., Jasaityte, R., Barbosa, D., Bouchez, S., Vandenheuvel, M., Wouters, P., Maes, F., Hooge, J.D., 2012. Motion and deformation estimation of cardiac ultrasound sequences using an anatomical B-spline transformation model. In: Proceedings of IEEE International Symposium on Biomedical Imaging, pp. 266–269.
為了確保魯棒性，可以為這些方法添加時間-空間魯棒性約束（或者是采用由粗到精的優化策略）。
時間-空間約束：Somphone, O., Allaire, S., Mory, B., Dufour, C., 2014. Live feature tracking in ultrasound liver sequences with sparse demons. In: Proceedings of MICCAI Workshop on Challenge on Liver Ultrasound Tracking, p. 53.、
由粗到精的優化策略：Mukherjee, R., Sprouse, C., Abraham, T., Hoffmann, B., McVeigh, E., Yuh, D., Burlina, P., 2011. Myocardial motion computation in 4d ultrasound. In: Proceedings of IEEE International Symposium on Biomedical Imaging. IEEE, pp. 1070–1073.
2.5 形變模型拓展研究
正反向配準方法提升跟蹤精度:
Ledesma-Carbayo, M.J., Kybic, J., Desco, M., Santos, A., Unser, M., 2001. Cardiac motion analysis from ultrasound sequences using non-rigid registration. In: Proceedings of International Conference on Medical Image Computing and Computer-Assisted Intervention. Springer, pp. 889–896.
分組優化管理提升跟蹤精度：
Metz, C., Klein, S., Schaap, M., van Walsum, T., Niessen, W., 2011. Nonrigid registration of dynamic medical imaging data using nD+t B-splines and a groupwise optimization approach. Med. Image Anal. 15 (2), 238–249.
Vijayan, S., Klein, S., Hofstad, E.F., Lindseth, F., Ystgaard, B., Lango, T., 2013. Validation of a non-rigid registration method for motion compensation in 4d ultrasound of the liver. In: Proceedings of IEEE International Symposium on Biomedical Imaging, pp. 792–795.
使用特定的網格代替標準化的矩形網格：
Heyde, B., Claus, P., Jasaityte, R., Barbosa, D., Bouchez, S., Vandenheuvel, M., Wouters, P., Maes, F., Hooge, J.D., 2012. Motion and deformation estimation of cardiac ultrasound sequences using an anatomical B-spline transformation model. In: Proceedings of IEEE International Symposium on Biomedical Imaging, pp. 266–269.
離群排斥（避免噪聲干擾）：
Banerjee, J., Klink, C., Peters, E.D., Niessen, W.J., Moelker, A., van Walsum, T., 2015. Fast and robust 3d ultrasound registration block and game theoretic matching. Med. Image Anal. 20 (1), 173–183.
2.6 基于力學模型
除了這些僅基于視覺標準優化的技術之外，還提出了基于機械的跟蹤方法，用于二維超聲圖像。
Loosvelt, M., Villard, P.-F., Berger, M.-O., 2014. Using a biomechanical model for tongue tracking in ultrasound images. In: Proceedings of IEEE Symp. on Biomedical Simulation. Springer, pp. 67–75.
Marami, B., Sirouspour, S., Fenster, A., W. Capson, D., 2014. Dynamic tracking of a deformable tissue based on 3d-2d MR-US image registration. Proceedings of SPIE Medical Imaging.
但是這種2D的力學模型無法解決out-of-plane運動。
為了解決這個問題，Yipeng Hu, Carter, T.J., Ahmed, H.U., Emberton, M., Allen, C., Hawkes, D.J., Barratt, D.C., 2011. Modelling prostate motion for data fusion during image-guided interventions. IEEE Trans. Med. Imaging 30 (11), 1887–1900.采用生物建模解決3D跟蹤問題 (前列腺很簡單，所以簡單建模是可以的)。
然而，他們的方法需要在每個超聲圖像中手動識別前列腺的一些表面點，以驅動模型。總而言之，我們根據表1中的主要特性，提出了跟蹤方法的分類。
據我們所知，目前還沒有針對三維超聲圖像設計的實時跟蹤方法，將魯棒稠密運動估計和力學模型結合在一起。
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