Improved conformal metrics for 3D geometric deformable models in medical images

The Geometric Deformable Model (GDM) is a useful segmentation method that combines the energy minimization concepts of physically deformable models and the flexible topology of implicit deformable models in a mathematically well-defined framework. The key aspect of the method is the measurement of length and area using a conformal metric derived from the image. This conformal metric, usually a monotonicly decreasing function of the gradient, defines a Riemannian space in which the surface evolves. The success of the GDM for 3D segmentation in medical applications is directly related to the definition of the conformal metric. Like all deformable models, the GDM is susceptible to poor initialization, varying contrast, partial volume, and noise. This paper addresses these difficulties via the definition of the conformal metric and describes a new method for computing the metric in 3D. This method, referred to as a confidence-based mapping, incorporates a new 3D scale selection mechanism and an a-priori image model. A comparison of the confidence-based approach and previous formulations of the conformal metric is presented using computer phantoms. A preliminary application in two clinical examples is given.