Abstract
Personalizing the three-dimensional atlas model (template) of an organ under analysis based on the data of patient’s three-dimensional examination is an important task for modern digital medicine. The template should be represented by a set of points Y and marked with the key points for the model (landmarks). The template is personalized by the non-rigid registration of the set Y with the set of points X that represents patient’s tomogram. Presently, the coherent point drift (CPD) is the most popular method for solving the problem of non-rigid alignment. In this paper, we propose and explore an approach that substantially improves the CPD result in the problem of automatic registration of cephalometric points (CPs). The proposed algorithm remains robust in the presence of significant skull deformations. Traditionally, 3D cephalometry uses the geometric descriptor of a CP, which refines the position of the point on the bone surface. However, the result of applying the descriptor depends significantly on the accuracy of its anatomical basis reconstruction. The proposed approach solves this problem by clarifying the basis of geometric descriptors, the supporting elements of which are orbital planes and the Frankfurt (orbital-ear) horizontal. For this purpose, additionally marked points of the orbitals (YO) are included into the template Y. Once Y and X are aligned by the CPD method, the plane positions of the orbitals are refined by solving a linear regression problem on the subsets of YO for the left and right orbitals. Cases of refinement with and without use of Tikhonov regularization (ridge-regression) are analyzed. The effect of the increase in the cardinality of the set X relative to Y on the registration accuracy is investigated. It is found that the condition |X| < |Y| has a negative effect on the accuracy, which increases when the cardinality of X relative to Y decreases. The refinement of CPs by the geometric descriptor is carried out on tomogram data in the region around CPs that is found by the CPD method. The dimensions of this region along three coordinates are determined by the anatomical domain of a particular CP descriptor. The quality of the algorithm is measured by the Euclidean distance between hand-marked and automatically found points. The template Y for the algorithm is built on a trauma-deformed skull. The algorithm is quantitatively verified by registering the CPs of orbitals and cheekbones from the data of four tomograms for the deformed skull. A key feature and source of high accuracy of the approach is the use of linear regression with Tikhonov regularization to refine it. As a result, 81.25% of the points found fall within a radius of 2 mm from the hand-marked points and 100% of the points fall within a radius of 4 mm.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.REFERENCES
Myronenko, A., Song, X., and Carreira-Perpinan, M.A., Non-rigid point set registration: Coherent point drift, Proc. NIPS, 2007, pp. 1009–1016.
Myronenko, A. and Song, X., Point set registration: Coherent point drift, IEEE Trans. Pattern Anal. Mach. Intell., 2010, vol. 32, no. 12, pp. 2262–2275.
Jacobson, A. and Jacobson, R.L., Radiographic cephalometry: From basics to videoimaging, Quintessence Pub., 1995, pp. 53–63.
Yue, W., Yin, D., Li, C., Wang, G., and Xu, T., Automated 2-D cephalometric analysis on X-ray images by a model-based approach, IEEE Trans. Biomed. Eng., 2006, vol. 53, no. 8, pp. 1615–1623.
Chu, C., et al., Fully automatic cephalometric X-ray landmark detection using random forest regression and sparse shape composition, Proc. ISBI Automatic Cephalometric X-Ray Landmark Detection Challenge, 2014.
Wang, C.-W., Evaluation and comparison of anatomical landmark detection methods for cephalometric X‑ray images: A grand challenge, IEEE Trans. Med. Imaging, 2015.
Swennen, G.R.J., Schutyser, F., and Hausamen, J.-E., Three-Dimensional Cephalometry: A Color Atlas and Manual, Berlin: Springer-Verlag, 2006, pp. 116–185.
Shahidi, S., Bahrampour, E., Soltanimehr, E., Zamani, A., Oshagh, M., Moattari, M., and Mehdizadeh, A., The accuracy of a designed software for automated localization of craniofacial landmarks on CBCT images, BMC Med. Imaging, 2014, vol. 14, no. 1, pp. 1471–2342.
Gupta, A., Kharbanda, O.P., Sardana, V., Balachandran, R., and Sardana, H.K., A knowledge-based algorithm for automatic detection of cephalometric landmarks on CBCT images, Int. J. Comput.-Assisted Radiology Surgery, 2015, vol. 10, no. 11, pp. 1737–1752.
Koch, M., et al., Towards deformable shape modeling of the left atrium using non-rigid coherent point drift registration, Bildverarbeitung für die Medizin, 2013, pp. 332–337.
Delavari, M., Foruzan, A.H., and Chen, Y.-W., Improvement of statistical shapemodels for soft tissues using modified-coherent point drift, IFAC-PapersOnLine, 2015, vol. 48, pp. 36–41.
Peng, L., Li, G., Xiao, M., and Xie, L., Robust CPD algorithm for non-rigid point set registration based on structure information, PLOS One, 2016, vol. 11, no. 2, pp. 1–17.
Mansoory, M.S., Allahverdy, A., and Jafari, A.H., Mitral valve prolapse classification from an echocardiography sequence using coherent point drift method based on fractal dimension, J. Biomed. Phys. Eng., 2016.
Ravikumar, N., Gooya, A., Frangi, A.F., and Taylor, Z.A., Generalized coherent point drift for group-wise registration of multi-dimensional point sets, Proc. Int. Conf. Medical Image Computing and Computer-Assisted Intervention (MICCAI), Quebec, 2017, pp. 309–316.
Gadomski, P.J., Measuring glacier surface velocities with LiDAR: A comparison of three-dimensional change detection methods, Master’s thesis, University of Houston, 2016. http://www.researchgate.net/publication/315773214_Measuring_Glacier_Surface_ Velocities_With_LiDAR_A_Comparison_of_Three-Dimensional_Change_Detection_Methods.
Senyukova, O.V. and Zubov, A.Yu., Full anatomical labeling of magnetic resonance images of human brain by registration with multiple atlases, Program. Comput. Software, 2016, vol. 42, no. 6, pp. 356–360.
Kvostikov, A.V., Krylov, A.S., and Kamalov, U.R., Ultrasound image texture analysis for liver fibrosis stage diagnostics, Program. Comput. Software, 2015, vol. 41, no. 5, pp. 273–278.
Tikhonov, A.N., On incorrect linear algebra problems and a robust method for their solution, Dokl. Akad. Nauk SSSR, 1965, vol. 163, no. 3, pp. 97–102.
Lindeberg, T., Scale selection properties of generalized scale-space interest point detectors, J. Math. Imaging Vis., 2013, vol. 46, no. 2, pp. 177–210.
Kharinov, M.V., Pixel clustering for color image segmentation, Program. Comput. Software, 2015, vol. 41, no. 5, pp. 258–266.
Gavrilov, N.I. and Turlapov, V.E., Novel approach to development of direct volume rendering algorithms based on visualization quality assessment, Program. Comput. Software, 2014, vol. 40, no. 4, pp. 174–184.
Mamaev, N.V., Lukin, A.S., and Yurin, D.V., HeNLM-LA: A locally adaptive non-local means algorithm based on Hermite functions expansion, Program. Comput. Software, 2014, vol. 40, no. 4, pp. 199–207.
ACKNOWLEDGMENTS
This work was supported by the Russian Foundation for Basic Research, project no. 18-37-00383.
Author information
Authors and Affiliations
Corresponding authors
Additional information
Translated by Yu. Kornienko
Rights and permissions
About this article
Cite this article
Lachinov, D.A., Getmanskaya, A.A. & Turlapov, V.E. Refinement of the Coherent Point Drift Registration Results by the Example of Cephalometry Problems. Program Comput Soft 44, 248–257 (2018). https://doi.org/10.1134/S0361768818040084
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0361768818040084