Conditional-Mean Initialization Using Neighboring Objects in Deformable Model Segmentation

摘要

Most model-based segmentation methods find a target object in a new image by constructing an objective function and optimizing it using a standard minimization algorithm. In general, the objective function has two penalty terms: 1) for deforming a template model and 2) for mismatch between the trained image intensities relative to the template model and the observed image intensities relative to the deformed template model in the target image. While it is difficult to establish an objective function with a global minimum at the desired segmentation result, even such an objective function is typically non-convex due to the complexity of the intensity patterns and the many structures surrounding the target object. Thus, it is critical that the optimization starts at a point close to the global minimum of the objective function in deformable model-based segmentation framework. For a segmentation method in maximum a posteriori framework a good objective function can be obtained by learning the probability distributions of the population shape deformations and their associated image intensities because each penalty term can be simplified to a squared function of some distance metric defined in the shape space. The mean shape and intensities of the learned probability distributions also provide a good initialization for segmentation. However, a major concern in estimating the shape prior is the stability of the estimated shape distributions from given training samples because the feature space of a shape model is usually very high dimensional while the number of training samples is limited. A lot of effort in that regard have been made to attain a stable estimation of shape probability distribution. In this paper, we describe our approach to stably estimate a shape probability distribution when good segmentations of objects adjacent to the target object are available. Our approach is to use a conditional shape probability distribution (CSPD) to take into account in the shape distribution the relation of the target object to neighboring objects. In particular, we propose a new method based on principal component regression (PCR) in reflecting in the conditional term of the CSPD the effect of neighboring objects on the target object. The resulting approach is able to give a better and robust initialization with training samples of a few cases. To demonstrate the potential of our approach, we apply it first to training of a simulated data of known deformations and second to male pelvic organs, using the CSPD in m-rep segmentations of the prostate in CT images. Our results show a clear improvement in initializing the prostate by its conditional mean given the bladder and the rectum as neighboring objects, as measured both by volume overlap and average surface distance.