Fractional Charlier moments for image reconstruction and image watermarking

Quaternion polar complex exponential transform for invariant color image description

3D image analysis by separable discrete orthogonal moments based on Krawtchouk and Tchebichef polynomials

Stable computation of higher order Charlier moments for signal and image reconstruction

Rotation-invariant feature extraction using a structural co-occurrence matrix

Fast computation of separable two-dimensional discrete invariant moments for image classification

Recently, the discrete orthogonal moments have been introduced in image analysis and pattern recognition. They have better capacities than the continuous orthogonal moments but the use of these moments as feature descriptors is limited by their high computational cost. As a solution to this problem, we present in this paper an approach for fast computation of Meixner's discrete orthogonal moments. By using the recurrence relation with respect to variable x instead of order n in computation of Meixner's discrete orthogonal polynomials and the image block representation for binary images and intensity slice representation for gray-scale images. The acceleration of the computation time of Meixner moments is due to an innovative image representation where the image is described by a number of homogenous rectangular blocks instead of individual pixels. A novel set of invariant moments based on the Meixner discrete orthogonal moments is also proposed. These invariant moments are derived algebraically from the geometric invariant momenst and their computation is accelerated using image representation scheme. The presented algorithms are tested in several well-known computer vision datasets, regarding computational time, image reconstruction, invariability, and classification. The performances of Meixner invariant moments used as pattern features for a pattern classification application are compared with Hu, Tchebichef, dual-Hahn, and Krawtchouk invariant moments.

A Fast Computation of Novel Set of Meixner Invariant Moments for Image Analysis

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. Theory8, 179 (1962)] and Krawchouk [IEEE Trans. Image Process.12, 1367 (2003)] moment invariants.

Improving the performance of image classification by Hahn moment invariants

In this paper, we propose a new method for the rapid calculation of Meixner’s discrete orthogonal moments and its inverses. In this method, we have used the notion of digital filters based on the Z transform both to accelerate the computation time of Meixner and to reduce the reconstruction error of the images. To guarantee the numerical stability and robustness with respect to the noise, we propose two algorithms that treat the images as a set of blocks where each block will be treated independently. In fact, through the first algorithm, the moments of Meixner are computed from a set of geometric blocks of fixed size. On the other hand, in the second algorithm, the images are represented by a slice set where each slice contains several homogeneous blocks of different sizes. The moments of Meixner, in this case, are calculated from each block in each slice. The application of these two algorithms allowed us to deduce a significant reduction in processed information and image space, that permits the use of Meixner moments of low order for a better description of the fine details of the images. The performances of the proposed method are demonstrated through several simulations on different image bases.

Image analysis by Meixner moments and a digital filter

In this paper, we present a new set of bivariate discrete orthogonal polynomials defined from the product of Charlier and Hahn discrete orthogonal polynomials with one variable. This bivriate polynomial is used to define other set of separable two-dimensional discrete orthogonal moments called Charlier-Hahn's moments. We also propose the use of the image slice representation methodology for fast computation of Charlier-Hahn's moments. In this approach the image is decomposed into series of non-overlapped binary slices and each slice is described by a number of homogenous rectangular blocks. Thus, the moments of Charlier-Hahn can be computed fast and easily from the blocks of each slice. A novel set of Charlier-Hahn invariant moments is also presented. These invariant moments are derived algebraically from the geometric invariant moments and their computation is accelerated using an image representation scheme. The presented approaches are tested in several well known computer vision datasets including computational time, image reconstruction, the moment's invariability and the classification of objects. The performance of these invariant moments used as pattern features for a pattern classification is compared with Charlier, Hahn, Tchebichef-Krawtchouk, Tchebichef-Hahn and Krawtchouk-Hahn invariant moments.

Abdeslam Hmimid

Papers

Fast computation of separable two-dimensional discrete invariant moments for image classification

A Fast Computation of Novel Set of Meixner Invariant Moments for Image Analysis

Improving the performance of image classification by Hahn moment invariants

Image analysis by Meixner moments and a digital filter

Image analysis using separable discrete moments of Charlier-Hahn