The quickhull algorithm for convex hulls
ACM Transactions on Mathematical Software (TOMS)
Computational anatomy: an emerging discipline
Quarterly of Applied Mathematics - Special issue on current and future challenges in the applications of mathematics
Analysis of Planar Shapes Using Geodesic Paths on Shape Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms
International Journal of Computer Vision
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
A Bayesian approach to bandwidth selection for multivariate kernel density estimation
Computational Statistics & Data Analysis
Non-rigid registration of 3d multi-channel microscopy images of cell nuclei
MICCAI'06 Proceedings of the 9th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
Deformable templates using large deformation kinematics
IEEE Transactions on Image Processing
A graph-based method for detecting characteristic phenotypes from biomedical images
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
Principles of bioimage informatics: focus on machine learning of cell patterns
ISMB/ECCB'09 Proceedings of the 2009 workshop of the BioLink Special Interest Group, international conference on Linking Literature, Information, and Knowledge for Biology
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Biological shape modeling is an essential task that is required for systems biology efforts to simulate complex cell behaviors. Statistical learning methods have been used to build generative shape models based on reconstructive shape parameters extracted from microscope image collections. However, such parametric modeling approaches are usually limited to simple shapes and easily-modeled parameter distributions. Moreover, to maximize the reconstruction accuracy, significant effort is required to design models for specific datasets or patterns. We have therefore developed an instance-based approach to model biological shapes within a shape space built upon diffeomorphic measurement. We also designed a recursive interpolation algorithm to probabilistically synthesize new shape instances using the shape space model and the original instances. The method is quite generalizable and therefore can be applied to most nuclear, cell and protein object shapes, in both 2D and 3D.