Recent Progress in Image Moments and Moment Invariants
GCSR Volume 7
George A. Papakostas
Chapter 1 – Moment Invariants of Vector and Tensor Fields
Jan Flusser, Tomáš Suk, Jitka Kostková, Matej Lébl, and Ibrahim Ibrahim
(pages 1-28) DOI: 10.15579/gcsr.vol7.ch1
Vector and tensor fields are multidimensional data, where in each pixel/voxel the field is assigned to a vector or a matrix. The fields describe particle velocity, optical flow, stress and conductivity tensors, and similar phenomena. One of the challenging tasks is the invariant detection of patterns of interest. Invariants to total rotation and affine transformation of the field are desirable to accomplish this task. In this chapter, we review a recent development of this research area and show several practical applications on real data.
Chapter 2 – Radial Moments Based Object Recovery Under Symmetry Constraints
Mirosław Pawlak and Gurmukh Singh Panesar
(pages 29-52) DOI: 10.15579/gcsr.vol7.ch2
In this chapter we develop a class of moment based methods for invariant image reconstruction with the selected degree of symmetry. An image function is expressed in terms of radial Zernike moments due to their invariance properties to isometry transformations and the ability to uniquely represent the salient features of the image.
The regularized ridge regression estimation strategy under symmetry constraints for estimating Zernike moments is introduced. The proposed extended regularization problem allows us to enforce the bilateral symmetry in the reconstructed object. This is achieved by the proper choice of two regularization parameters controlling the level of reconstruction accuracy and the acceptable degree of symmetry. As a byproduct of our studies, we propose an algorithm for estimating an angle of the symmetry axis which in turn is used to determine the possible asymmetry present in the image. The established image recovery under the symmetry constraints model is tested in a number of experiments involving image reconstruction and symmetry estimation.
Chapter 3 – Computation of 2D and 3D High-order Discrete Orthogonal Moments
José S. Rivera-Lopez, César Camacho-Bello, and Lucia Gutiérrez-Lazcano
(pages 53-74) DOI: 10.15579/gcsr.vol7.ch3
This chapter is about eliminating numerical instability and the error of high-order orthogonal moments by reducing terms in existing recurrence relations and the Gram-Smith orthonormalization process. Besides, the simplification of the terms of the recurrence relations with respect to n of the most used kernels is analyzed, such as Tchebycheff polynomials, Hahn polynomials, Krawtchouk polynomials, Charlier polynomials, and Meixner polynomials. Also, to guarantee the effectiveness of the proposed method, reconstructions of both 3D objects and high-resolution images are presented. The results presented in this chapter will help you utilize moments for processing, recognition, and analysis on 8K Full HD images and 3D objects with large dimensions.