Shape analysis is a very important field in computer vision. This work presents a novel and highly discriminative shape analysis method based on the weights of a Randomized Neural Network (RNN). Two approaches are proposed to extract the contour signature: Neighborhood approach uses the distance of each contour pixel and its immediate neighboring pixels and Contour portion approach, which uses metrics computed from contour sections to model the shape as RNN. We also proposed a signature that combines the feature vectors resulting from both approaches, thus resulting in a set of features tolerant to affine transformations, such as rotation and scale. We compared our approach with other shape analysis methods in 6 different shapes datasets. We calculated the accuracy as measure performance and obtained 97.98%, 99.07%, 84.67%, 87.67%, 88.92% and 80.58% for Kimia, Fish, Leaf, Rotated Leaf, Scaled Leaf and Noised Leaf datasets, respectively. The achieved performance of our method surpassed the results of several compared methods in most of these datasets, thus proving that our proposed signature can be applied successfully in shape analysis problems.