Various types of moments have been used to recognize planar shapes. The algorithms are mostly based upon extracting moment features and train the machine to match these features with a database of templates. The shapes could be represented by a polygon whose vertices lie on the boundary. The computational complexity of algorithm is a function of number of vertices of polygon. We have implemented three descriptors to recognize hand drawn shapes. The descriptors are mostly based upon extracting moment features and train the machine to match these features with two-database of templates. The robustness of the descriptors based upon the moment features has been exhibited by matching a test shape that is a distortion of one of template stored in the database. An optimization technique using E1 and E2 error norms is used to calculate optimal vertices. The time as well as space complexity is improved by the optimization steps that discards most of the redundant vertices and retain only the points where the bend is sufficient to contribute towards the appearance of the shapes. We have also studied the behavior of the shapes under reasonable noise.