We propose a constrained version of Mumford and Shah's (1989) segmentation model with an information-theoretic point of view in order to devise a systematic procedure to segment brain magnetic resonance imaging (MRI) data for parametric T(1)-Map and T(1)-weighted images, in both 2-D and 3D settings. Incorporation of a tuning weight in particular adds a probabilistic flavor to our segmentation method, and makes the 3-tissue segmentation possible. Moreover, we proposed a novel method to jointly segment the T(1)-Map and calibrate RF Inhomogeneity (JSRIC). This method assumes the average T(1) value of white matter is the same across transverse slices in the central brain region, and JSRIC is able to rectify the flip angles to generate calibrated T(1)-Maps. In order to generate an accurate T(1)-Map, the determination of optimal flip-angles and the registration of flip-angle images are examined. Our JSRIC method is validated on two human subjects in the 2D T(1)-Map modality and our segmentation method is validated by two public databases, BrainWeb and IBSR, of T(1)-weighted modality in the 3D setting.