Object identification is essential in several image processing and computer vision applications. Despite the fact of many existing approaches, it is still being a challenge to achieve accuracy in identification of an object. In order to identify a digital object, it has to be described by certain feature vectors. We have considered one of the shape feature vectors to describe an object in this paper. We have developed a new invariant shape descriptor, which is procured after improvisation of log-polar model. Initially, shape region of an object in the image has been considered with each and every detail with the help of centroid and maximum radius of that object. Later, a shape matrix is been generated from the proposed model and the generated shape matrix is been utilized for identification of the object. This paper also provides an overview of shape matrix descriptor along with the existing polar and log-polar mappings. A comparative analysis is made against the object mapping among existing models and the proposed model where, our model gives higher accuracy in object identification.