New set of non-separable 2D and 3D invariant moments for image representation and recognition

Abstract

The extraction of feature vectors of the images is the most important step in image recognition, because it allows a good description of the forms to be recognized. This step is an operation that makes it possible to convert an image into a vector of real or complex values that can serve as a signature for this image. For an accurate recognition system, the used feature vector must be invariant to the three image transformations (translation, rotation and scale), which means that, the descriptor vectors of the image and the transformed image by translation, rotation or scale must be equal. Given the importance of moments and their invariants in pattern recognition and imaging, based on Newton’s binomial and trinomial formulas and the normalized central moments, we construct in this paper four new series of moments for 2D and 3D image recognition, which are invariant to translation, scaling and rotation (TSR): the first is a set of non-orthogonal moment invariants for 2D images (2dMIs), the second is a set of orthogonal moment invariants for 2D images (2dOMIs), the third is a set of non-orthogonal moment invariants for 3D images (3dMIs) and the fourth is a set of orthogonal moment invariants for 3D images (3dOMIs). Using the proposed invariant moments (2dMIs), (2dOMIs), (3dMIs) and (3dOMIs), we construct two types of image descriptor vectors for 2D images and two types for 3D images, which are invariant to translation, rotation and scale. A series of experiments is performed to validate this new set of invariant moments and compare its performance with the existing invariants moments. The obtained results ensure the superiority of the proposed moments over all existing moments in image recognition. Experiments on processing time show that the proposed method is faster than the existing orthogonal invariant moments.