In this work, the ventricles in MR brain images are segmented using edge based modified Distance Regularized Level Set Evolution (DRLSE) method and the structural changes in the disease is further analysed using Minkowski functionals (MFs). Twenty normal and abnormal Tl-weighted coronal mid slice MR image are considered for the analysis. The MR brain image is pre-processed using contrast enhancement method. The edge based modified DRLSE with a new penalty term is used to segment the ventricles from the enhanced images. The results of the level set method are compared with geodesic active contour method. The segmentation results are validated using ZSI (Zijdenbos Similarity Index) and F-score. The Minkowski functionals such as MF-area, MF-perimeter and MF-Euler number are calculated from the extracted ventricle region. The longitudinal analysis of ventricles is performed using these features. The results show that the DRLSE based level set method is able to extract the ventricle edges with less discontinuity. The F-score and ZSI is high for DRLSE (0.83 and 0.84) compared to geodesic method (0.79 and 0.80). The MF-area is able to discriminate the controls and the AD subjects with high statistical significance (p < 0.001). This analysis also shows that the MF-area increases with severity. These results could be used for the study of discrimination and progression of the Alzheimer's disease like disorders.