Image Segmentation with a Statistical Appearance Model and a Generic Mumford-Shah Inspired Outside Model

We present a novel statistical-model-based segmentation algorithm that addresses a recurrent problem in appearance model fitting and model-based segmentation: the "shrinking problem". When statistical appearance models are fitted to an image in order to segment an object, they have the tendency not to cover the full object, leaving a gap between the real and the detected boundary. This is due to the fact that the cost function for fitting the model is evaluated only on the inside of the object and the gap at the boundary is not detected. The state-of-the-art approach to overcome this shrinking problem is to detect the object edges in the image and force the model to adhere to these edges. Here, we introduce a region-based approach motivated by the Mumford-Shah functional that does not require the detection of edges. In addition to the appearance model, we define a generic model estimated from the input image for the outside of the appearance model. Shrinking is prevented because a misaligned boundary would create a large discrepancy between the image and the inside/outside model. The method is independent of the dimensionality of the image. We apply it to 3-dimensional CT images.