Combining strings and necklaces for interactive three-dimensional segmentation of spinal images using an integral deformable spine model

Segmentation of the spine directly from three-dimensional (3-D) image data is desirable to accurately capture its morphological properties. We describe a method that allows true 3-D spinal image segmentation using a deformable integral spine model. The method learns the appearance of vertebrae from multiple continuous features recorded along vertebra boundaries in a given training set of images. Important summarizing statistics are encoded into a necklace model on which landmarks are differentiated on their free dimensions. The landmarks are used within a priority segmentation scheme to reduce the complexity of the segmentation problem. Necklace models are coupled by string models. The string models describe in detail the biological variability in the appearance of spinal curvatures from multiple continuous features recorded in the training set. In the segmentation phase, the necklace and string models are used to interactively detect vertebral structures in new image data via elastic deformation reminiscent of a marionette with strings allowing for movement between interrelated structures. Strings constrain the deformation of the spine model within feasible solutions. The driving application in this work is analysis of computed tomography scans of the human lumbar spine. An illustration of the segmentation process shows that the method is promising for segmentation of the spine and for assessment of its morphological properties. Index Terms--Energy-minimization methods, functional data analysis, interactive image segmentation, landmark-based object segmentation, statistical deformable models.