Improving the performance of image classification by Hahn moment invariants

Abstract

The discrete orthogonal moments are powerful descriptors for image analysis and pattern recognition. However, the computation of these moments is a time consuming procedure. To solve this problem, a new approach that permits the fast computation of Hahn's discrete orthogonal moments is presented in this paper. The proposed method is based, on the one hand, on the computation of Hahn's discrete orthogonal polynomials using the recurrence relation with respect to the variable x instead of the order n and the symmetry property of Hahn's polynomials and, on the other hand, on the application of an innovative image representation where the image is described by a number of homogenous rectangular blocks instead of individual pixels. The paper also proposes a new set of Hahn's invariant moments under the translation, the scaling, and the rotation of the image. This set of invariant moments is computed as a linear combination of invariant geometric moments from a finite number of image intensity slices. Several experiments are performed to validate the effectiveness of our descriptors in terms of the acceleration of time computation, the reconstruction of the image, the invariability, and the classification. The performance of Hahn's moment invariants used as pattern features for a pattern classification application is compared with Hu [IRE Trans. Inform. Theory 8, 179 (1962)] and Krawchouk [IEEE Trans. Image Process.12, 1367 (2003)] moment invariants.

Fast and stable computation of higher-order Hahn polynomials and Hahn moment invariants for signal and image analysis

“…The following test is conducted to prove the fastness of the proposed HMIs computation method compared to the conventional one that is presented in [ 36 ]. Initially, the test image “Covid-19” is resized to 60 × 60, then HMIs are computed up to the order (20, 20) by using both methods.…”

“…( 31 ) can be expressed in terms of HPs (Eq. ( 3 )) as follows [ 36 ]: where is the normalized image.…”

“…Motivated by overcoming these problems, a fast and numerically stable computation of large-size image moment invariants is proposed in this paper. For this purpose, significant improvements are made on the conventional computation of HMIs presented in [ 36 ]. On one hand, the proposed improvements allow to compute HMIs independently of gamma and factorial functions, which guarantees the numerical stability of the computed moment invariants.…”

Image Classification Using Separable Discrete Moments of Charlier-Tchebichef

“…To use the Charlier-Tchebichef's moments for the objects classification, it is indispensable that be invariant under rotation, scaling, and translation of the image. Therefore to obtain the translation, scale and rotation invariants moments of Charlier-Tchebichef (CTMI), we adopt the same strategy used by Author et al for Hahn's moments in [12]. That is, we derive the CTMI through the geometric moments.…”

“…The orthogonal property of continuous orthogonal moments assures the robustness against noise and eliminates the redundancy of information [2][3][4], but their computation requires the discretization of continuous space and the approximation of the integrals which increases the computational complexity and causes the discretization error [5][6][7][8][9]. To eliminate this error, the discrete orthogonal moments such as Tchebichef [8], Krawtchouk [9], Charlier [10] and Hahn [11][12][13] have been introduced in image analysis and pattern recognition. The use of this set of moments satisfies exactly the orthogonal property and eliminates the need for numerical approximation [14][15].…”