This article presents a novel approach of edged and edgeless object-shape recognition and 3D reconstruction from gradient-based analysis of tactile images. We recognize an object's shape by visualizing a surface topology in our mind while grasping the object in our palm and also taking help from our past experience of exploring similar kind of objects. The proposed hybrid recognition strategy works in similar way in two stages. In the first stage, conventional object-shape recognition using linear support vector machine classifier is performed where regional descriptors features have been extracted from the tactile image. A 3D shape reconstruction is also performed depending upon the edged or edgeless objects classified from the tactile images. In the second stage, the hybrid recognition scheme utilizes the feature set comprising both the previously obtained regional descriptors features and some gradient-related information from the reconstructed object-shape image for the final recognition in corresponding four classes of objects viz. planar, one-edged object, two-edged object and cylindrical objects. The hybrid strategy achieves 97.62 % classification accuracy, while the conventional recognition scheme reaches only to 92.60 %. Moreover, the proposed algorithm has been proved to be less noise prone and more statistically robust.