Tomography

Active Contour and Segmentation Models using Geometric PDE's for medical imaging

This paper is devoted to the analysis and the extraction of information from bio-medical images. Our technique is based on object and contour detection, curve evolution and segmentation. We present a particular active contour model for 2D and 3D images, formulated using the level set method, and based on a 2-phase segmentation. We then show how this model can be generalized to segmentation of images with more than two segments. Our techniques are based on the mumford-Shuh model. By our proposed models, we can extract in addition measurements of the detected objects, such as average intensity, perimeter, area, or volume. Such information are useful when in particular a time evolution of the subject is known, or when we need to make comparisons between different subjects, for instance between a normal subject and as abnormal one. Finally, all these will give more informations about the dynamic of a disease, or about how the human body growths. We illustrate our method by calculations on two- dimensional and three-dimensional bio-medical images. (from CAM 00-41 Abstract, Dec 2000) Report by Chan and Vese .

Total Variation Regularization in Positron Emission Tomography

We propose computational algorithms for incorporating total variation regularization in positron emission tomography (PET). The motivation for using TV is that it has been shown to suppress noise effectively while capturing sharp edges without oscillations. This feature makes it particularly attractive for those applications of PET where the objective is to identify the shape of objects (e.g. tumors ) that are distinguished from the background by sharp edges. We show that the standard EM algorithm can be modified to incorporate the TV regularization, resulting in an algorithm that is robust independent of the amount of regularization. (from CAM 98-48 Abstract, Nov 98)