The sense of touch is important to human to understand shape, texture, and hardness of the objects. An object under grip, i.e. object exploration by enclosure, provides a unique pressure distribution on the different regions of palm depending on its shape. This paper utilizes the above experience for recognition of object shapes by tactile image analysis. The high pressure regions (HPRs) are segmented and analyzed for object shape recognition rather than analyzing the entire image. Tactile images are acquired by capacitive tactile sensor while grasping a particular object. Geometrical features are extracted from the chain codes obtained by polygon approximation of the contours of the segmented HPRs. Two-level classification scheme using linear support vector machine (LSVM) is employed to classify the input feature vector in respective object shape classes with an average classification accuracy of 93.46% and computational time of 1.19 s for 12 different object shape classes. Our proposed two-level LSVM reduces the misclassification rates, thus efficiently recognizes various object shapes from the tactile images.