I. OguzI, J. Cates, M. Datar, B. Paniagua, T. Fletcher, C. Vachet, M. Styner, R. Whitaker.
Entropy-based particle correspondence for shape populations, In International Journal of Computer Assisted Radiology and Surgery, Springer, pp. 1-12. December, 2015.
Statistical shape analysis of anatomical structures plays an important role in many medical image analysis applications such as understanding the structural changes in anatomy in various stages of growth or disease. Establishing accurate correspondence across object populations is essential for such statistical shape analysis studies.
In this paper, we present an entropy-based correspondence framework for computing point-based correspondence among populations of surfaces in a groupwise manner. This robust framework is parameterization-free and computationally efficient. We review the core principles of this method as well as various extensions to deal effectively with surfaces of complex geometry and application-driven correspondence metrics.
We apply our method to synthetic and biological datasets to illustrate the concepts proposed and compare the performance of our framework to existing techniques.
Through the numerous extensions and variations presented here, we create a very flexible framework that can effectively handle objects of various topologies, multi-object complexes, open surfaces, and objects of complex geometry such as high-curvature regions or extremely thin features.
M. Datar, I. Lyu, S. Kim, J. Cates, M.A. Styner, R.T. Whitaker.
Geodesic distances to landmarks for dense correspondence on ensembles of complex shapes, In Proceedings of Medical Image Computing and Computer-Assisted Intervention (MICCAI 2011), Vol. 16(Pt. 2), pp. 19--26. 2013.
PubMed ID: 24579119
Establishing correspondence points across a set of biomedical shapes is an important technology for a variety of applications that rely on statistical analysis of individual subjects and populations. The inherent complexity (e.g. cortical surface shapes) and variability (e.g. cardiac chambers) evident in many biomedical shapes introduce significant challenges in finding a useful set of dense correspondences. Application specific strategies, such as registration of simplified (e.g. inflated or smoothed) surfaces or relying on manually placed landmarks, provide some improvement but suffer from limitations including increased computational complexity and ambiguity in landmark placement. This paper proposes a method for dense point correspondence on shape ensembles using geodesic distances to a priori landmarks as features. A novel set of numerical techniques for fast computation of geodesic distances to point sets is used to extract these features. The proposed method minimizes the ensemble entropy based on these features, resulting in isometry invariant correspondences in a very general, flexible framework.
B. Paniagua, L. Bompard, J. Cates, R.T. Whitaker, M. Datar, C. Vachet, M. Styner.
Combined SPHARM-PDM and entropy-based particle systems shape analysis framework, In Medical Imaging 2012: Biomedical Applications in Molecular, Structural, and Functional Imaging, SPIE Intl Soc Optical Eng, March, 2012.
PubMed ID: 24027625
PubMed Central ID: PMC3766973
Description of purpose: The NA-MIC SPHARM-PDM Toolbox represents an automated set of tools for the computation of 3D structural statistical shape analysis. SPHARM-PDM solves the correspondence problem by defining a first order ellipsoid aligned, uniform spherical parameterization for each object with correspondence established at equivalently parameterized points. However, SPHARM correspondence has shown to be inadequate for some biological shapes that are not well described by a uniform spherical parameterization. Entropy-based particle systems compute correspondence by representing surfaces as discrete point sets that does not rely on any inherent parameterization. However, they are sensitive to initialization and have little ability to recover from initial errors. By combining both methodologies we compute reliable correspondences in topologically challenging biological shapes. Data: Diverse subcortical structures cohorts were used, obtained from MR brain images. Method(s): The SPHARM-PDM shape analysis toolbox was used to compute point based correspondent models that were then used as initializing particles for the entropy-based particle systems. The combined framework was implemented as a stand-alone Slicer3 module, which works as an end-to-end shape analysis module. Results: The combined SPHARM-PDM-Particle framework has demonstrated to improve correspondence in the example dataset over the conventional SPHARM-PDM toolbox. Conclusions: The work presented in this paper demonstrates a two-sided improvement for the scientific community, being able to 1) find good correspondences among spherically topological shapes, that can be used in many morphometry studies 2) offer an end-to-end solution that will facilitate the access to shape analysis framework to users without computer expertise.
M. Datar, Y. Gur, B. Paniagua, M. Styner, R.T. Whitaker.
Geometric Correspondence for Ensembles of Nonregular Shapes, In Proceedings of Medical Image Computing and Computer-Assisted Intervention (MICCAI 2011), Lecture Notes in Computer Science (LNCS), Vol. 6892, pp. 368--375. 2011.
PubMed ID: 21995050
PubMed Central ID: PMC3346950
An ensemble of biological shapes can be represented and analyzed with a dense set of point correspondences. In previous work, optimal point placement was determined by optimizing an information theoretic criterion that depends on relative spatial locations on different shapes combined with pairwise Euclidean distances between nearby points on the same shape. These choices have prevented such methods from effectively characterizing shapes with complex geometry such as thin or highly curved features. This paper extends previous methods for automatic shape correspondence by taking into account the underlying geometry of individual shapes. This is done by replacing the Euclidean distance for intrashape pairwise particle interactions by the geodesic distance. A novel set of numerical techniques for fast distance computations on curved surfaces is used to extract these distances. In addition, we introduce an intershape penalty term that incorporates surface normal information to achieve better particle correspondences near sharp features. Finally, we demonstrate this new method on synthetic and biological datasets.
I. Oguz, M. Niethammer, J. Cates, R.T. Whitaker, P.T. Fletcher, C. Vachet, M. Styner.
Cortical Correspondence with Probabilistic Fiber Connectivity, In Information Processing in Medical Imaging (IPMI), Lecture Notes in Computer Science (LCNS), Vol. 5636, pp. 651--663. 2009.
J. Cates, P.T. Fletcher, M. Styner, H. Hazlett, R.T. Whitaker.
Particle-Based Shape Analysis of Multi-Object Complexes, In Proceedings of the 11th International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI '08), Lecture Notes In Computer Science (LCNS), pp. 477--485. 2008.
I. Oguz, J. Cates, P.T. Fletcher, R.T. Whitaker, D. Cool, S. Aylward, M. Styner.
Cortical Correspondence using Entropy-Based Particle Systems and Local Features, In 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro, 2008. (ISBI 2008), pp. 1637--1640. 2008.
S. Pizer, M. Styner, T. Terriberry, R. Broadhurst, S. Joshi, E. Chaney, P.T. Fletcher.
Statistical Applications with Deformable M-Reps, In Computational Imaging and Vision, Springer, pp. 269--308. 2008.
J. Cates, P.T. Fletcher, M. Styner, M. Shenton, R.T. Whitaker.
Shape Modeling and Analysis with Entropy-Based Particle Systems, In Proceedings of Information Processing in Medical Imaging (IPMI) 2007, LNCS 4584, pp. 333--345. 2007.