Rotation scaling and translation invariants by a remediation of Hu’s invariant moments

Abstract

Due to the invariance to translation, rotation and scaling, the seven invariant moments presented by Hu (Visual pattern recognition by moment invariants, IRE Transactions on Information Theory, vol. 8, February 1962, pp. 179–187) are widely used in the field of pattern recognition. The set of these moments is finite; therefore, they do not comprise a complete set of image descriptors. To solve this problem, we introduce in this paper a new set of invariant moments of infinite order. The non-orthogonal property causes the redundancy of information. For this reason, we propose a new set of orthogonal polynomials in two variables, and we present a set of orthogonal moments, which are invariant to rotation, scale and translation. The presented approaches are tested by the invariability of the moments, the image retrieval and the classification of the objects. In this framework, using the proposed orthogonal moments, we present two classification systems. The first based on the Fuzzy C-Means Clustering algorithm (FCM) and the second based on the Radial Basis Functions Neural Network (RBF). The performance of our invariant moments is compared with Legendre invariant moments, Tchebichef-Krawtchouk (TKIM), Tchebichef-Hahn (THIM), Krawtchouk-Hahn (KHIM), Hu invariant moments, the descriptor of histogram of oriented gradients (HOG), the adaptive hierarchical density histogram features (AHDH) and with descriptors of color and texture Hist, HSV, FOS and SGLD. The experimental tests are performed on seven image databases: Columbia Object Image Library (COIL-20) database, MPEG7-CE shape database, MNIST handwritten digit database, MNIST fashion image database, ImageNet database, COIL-100 database and ORL database. The obtained results show the efficiency and superiority of our orthogonal invariant moments.