A method and software for segmentation of anatomic object ensembles by deformable m‐reps

Abstract

Deformable shape models (DSMs) comprise a general approach that shows great promise for automatic image segmentation. Published studies by others and our own research results strongly suggest that segmentation of a normal or near-normal object from 3D medical images will be most successful when the DSM approach uses (1) knowledge of the geometry of not only the target anatomic object but also the ensemble of objects providing context for the target object and (2) knowledge of the image intensities to be expected relative to the geometry of the target and contextual objects. The segmentation will be most efficient when the deformation operates at multiple object-related scales and uses deformations that include not just local translations but the biologically important transformations of bending and twisting, i.e., local rotation, and local magnification. In computer vision an important class of DSM methods uses explicit geometric models in a Bayesian statistical framework to provide a priori information used in posterior optimization to match the DSM against a target image. In this approach a DSM of the object to be segmented is placed in the target image data and undergoes a series of rigid and nonrigid transformations that deform the model to closely match the target object. The deformation process is driven by optimizing an objective function that has terms for the geometric typicality and model-to-image match for each instance of the deformed model. The success of this approach depends strongly on the object representation, i.e., the structural details and parameter set for the DSM, which in turn determines the analytic form of the objective function. This paper describes a form of DSM called m-reps that has or allows these properties, and a method of segmentation consisting of large to small scale posterior optimization of m-reps. Segmentation by deformable m-reps, together with the appropriate data representations, visualizations, and user interface, has been implemented in software that accomplishes 3D segmentations in a few minutes. Software for building and training models has also been developed. The methods underlying this software and its abilities are the subject of this paper.

Training models of anatomic shape variability

“…28 uses no image match grounds, but requires a regular sampling with tight geometric distributions. Active appearance models 12,29 require both a tight geometric distribution as well as similar local image intensities. The training method used in Refs.…”

“…See the Appendix for a summary of m-reps 12 and its governing statistical model, principal geodesic analysis. 35 Since m-reps capture not only positional information ͑i.e., of the skeleton and the implied boundary͒ but also orientational information ͑of spokes between the skeleton and the boundary͒, the parameterization handles plausible physical changes such as local twisting and bending in a way that can be easily captured by the statistical model.…”

“…11 Probabilistic segmentation is based on understanding the shape variability of the anatomic structures found in medical images. Robust probability density estimates of shape have been shown to be effective for object-based methods of probabilistic segmentation 9,12,13 for two reasons: ͑1͒ their relatively low dimensionality allows us efficiently to compute optimal solutions, and ͑2͒ the optimal solutions yield anatomically credible objects. Geometrically legal spacefilling nonrigid mappings can be derived from differential equations ͑e.g., optical flow, 14,15 elastic flow, 16 visco-elastic flow 6,17,18 or finite-element models 19,20 ͒ and then reduced to lower dimension for statistical analysis by means of control points or decomposition via basis functions.…”

Multi-figure Anatomical Objects for Shape Statistics

“…Medial description is also well suited to represent an object with parts [7,10], e.g., an object with a protrusion subfigure, i.e., additive figure to the host ( fig. 1-c), or an indentation subfigure, i.e., subtractive figure from the host ( fig.…”

“…M-reps [6] have been successfully used to represent anatomical objects and complexes of objects [7][8][9]. An m-rep consists of one or more medial sheets, with the part corresponding to each sheet called a figure.…”