Abstract
Large-scale deformations of a tubular object, or generalized cylinder, are often defined by a target shape for its center curve, typically using a parametric target curve. This task is non-trivial for free-form deformations or direct manipulation methods because it is hard to manually control the centerline by adjusting control points. Most skeleton-based methods are no better, again due to the small number of manually adjusted control points. In this paper, we propose a method to deform a generalized cylinder based on its skeleton composed of a centerline and orthogonal cross sections. Although we are not the first to use such a skeleton, we propose a novel skeletonization method that tries to minimize the number of intersections between neighboring cross sections by means of a relative curvature condition to detect intersections. The mesh deformation is first defined geometrically by deforming the centerline and mapping the cross sections. Rotation minimizing frames are used during mapping to control twisting. Secondly, given displacements on the cross sections, the deformation is decomposed into finely subdivided regions. We limit distortion at these vertices by minimizing an elastic thin shell bending energy, in linear time. Our method can handle complicated generalized cylinders such as the human colon.
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Acknowledgements
We gratefully thank Dr. Saad Nadeem and Dr. Arie Kaufman from Stony Brook University and Dr. Sarah McGill from UNC Medical School for sharing their results, data, and suggestions. This work was supported by National Institutes of Health grant R01 CA158925.
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Ruibin Ma is a Ph.D. candidate in the Department of Computer Science, University of North Carolina at Chapel Hill. His research focuses on medical image analysis and computer vision. He received his bachelor degree from the Department of Electronic Engineering, Tsinghua University, in 2016.
Qingyu Zhao received his Ph.D. degree from the Computer Science Department at the University of North Carolina at Chapel Hill in 2017. He is currently a postdoctoral research fellow in the Department of Psychiatry and Behavioral Sciences, Stanford University. His research focuses on geometric modeling, non-linear statistics, and machine learning from medical images, with emphasis on neuroimaging applications.
Rui Wang received his bachelor and master degrees in computer science from the University of Missouri at Columbia in 2010 and 2012, respectively. He is currently a Ph.D. candidate in the Department of Computer Science, University of North Carolina at Chapel Hill. His primary research is on the combination of 3D vision and deep learning, and on their applications in endoscopic image analysis.
James Damon received his Ph.D. degreee in mathematics from Harvard University in 1972. He is an Emeritus Professor in Mathematics at the University of North Carolina at Chapel Hill, and a Fellow of the Amer. Math. Soc. He has also been a Simons Fellow, a Fulbright Lecturer (Santiago, Chile), an SERC Senior Visiting Fellow (Univ. Liverpool), and a Fulbright Scholar (Math. Inst. of Univ. Warwick). His areas of interest include singularity theory and its applications to bifurcation theory, computer imaging, and shape and position modeling for medical imaging.
Julian Rosenman is a Professor of Radiation Oncology at the University of North Carolina at Chapel Hill, and a cancer doctor (M.D.) who has treated cancer patients there since 1981. Before going to medical school, he received his Ph.D. degree from the University of Texas in Theoretical Physics. He has had an adjunct appointment in Computer Science since 1984. His major interest is in medical image analysis and display to improve cancer diagnosis and treatment. His major academic accomplishment was as part of a small team that developed and employed a fully 3D radiation treatment planning system that has been widely copied by commercial systems. 3D treatment planning is now standard-of-care around the world.
Stephen Pizer is a Kenan Professor at the University of North Carolina at Chapel Hill in Computer Science, Radiation Oncology, Biomedical Engineering, and Radiology and also has active collaborations in Psychiatry there. At UNC since 1967, he was also co-founder of Morphormics, Inc. (now part of Accuray), which specializes in software for segmentation and registration for radiation oncology. His research, centered since 1962 on medical image computing and display, presently focuses on image and object shape statistics, segmentation, registration, and 3D visualization of medical images. Other research directions have included interactive 3D graphics, human vision, image quality analysis, contrast enhancement, and image restoration. He is co-author of a book on medial representations and author of 2 books on numerical computing, as well as over 360 published chapters and journal and proceedings articles. He is a Fellow of the MICCAI Society.
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Ma, R., Zhao, Q., Wang, R. et al. Deforming generalized cylinders without self-intersection by means of a parametric center curve. Comp. Visual Media 4, 305–321 (2018). https://doi.org/10.1007/s41095-018-0127-7
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DOI: https://doi.org/10.1007/s41095-018-0127-7