| Image feature extraction is the key problem in the areas of image processing, pattern recognition and computer vision. It is the process of extracting a set of features which will most efficiently and meaningfully represent the image information that is significant for image analysis and classification.Moments and the corresponding moment invariants (translation, rotation, scaling, and intensity invariants) play a very important role as image features. They were first introduced to the image processing community in1962, and considerable progress has been made during the past50years. Much recent research has focused on the orthogonal moments, which comprises two types:continuous orthogonal moments and discrete orthogonal moments. Both types of the orthogonal moments have their own advantages and disadvantages, but the relationship between them has rarely been studied. Orthogonal moments and their invariants own good image description ability, and have been widely used.This dissertation concerns with the theory and application of orthogonal moments. The specific work and innovations of this dissertation can be summarized as follows:(1) Discretization process in the numerical calculation of continuous orthogonal moments affects the orthogonality of the kernel function, and then affects the properties of the moments. Therefore, in this paper, a novel discretization idea was induced, and a general method has been considered. Inspired by this idea, the discrete orthogonal moments which are discrete analogues of the continuous orthogonal moments were constructed.(2) A generic discrete orthogonal moments:Discrete Jacobi-Fourier Moments were proposed. The discrete Jacobi polynomials which are discrete analogues of the Jacobi polynomials and satisfy the discrete orthogonality property were constructed firstly. Based on the discrete Jacobi polynomials, Discrete Jacobi-Fourier Moments which are the discrete analogues of Jacobi-Fourier Moments can be obtained. Discrete Jacobi-Fourier Moments are a generic discrete orthogonal moments with two parameters. The variation of the parameters can form various classes of discrete orthogonal moments:Discrete Legendre-Fourier Moments, Discrete Chebyshev-Fourier Moments, Discrete Orthogonal Fourier-Mellin Moments, Discrete Zernike Moments, Discrete Pseudo-Zernike Moments, etc, which respectively are the discrete analogues of the special case of Jacobi-Fourier Moments with the same parameters:Legendre-Fourier Moments, Chebyshev-Fourier Moments, Orthogonal Fourier-Mellin Moments, Zernike Moments, Pseudo-Zernike Moments, etc. The experimental results demonstrate that the Discrete Jacobi-Fourier Moments outperform the Jacobi-Fourier Moments in terms of the image reconstruction ability.(3) Discrete Radial-Harmonic-Fourier Moments were proposed. Radial-Harmonic-Fourier Moments are different from other continuous orthogonal moments that the continuous orthogonal triangular function is chosen to be a radial function. Therefore, Discrete Radial-Harmonic-Fourier Moments which are the discrete analogues of Radial-Harmonic-Fourier Moments can be constructed, when the continuous orthogonal triangular function is replaced by a discrete orthogonal triangular function. The relationship between Discrete Radial-Harmonic-Fourier Moments and Radial-Harmonic-Fourier Moments was also analyzed. The experimental results indicate that the Discrete Radial-Harmonic-Fourier Moments have excellent image description ability.(4)Some conventional moments such as Hu invariants and Zernike Moments have been used in many application areas, however Jacobi-Fourier Moments and Radial-Harmonic-Fourier Moments are rarely applied. Therefore, some applications of these moments as well as Discrete Jacobi-Fourier Moments and Discrete Radial-Harmonic-Fourier Moments proposed in this dissertation were discussed. Translation and rotation invariants of these moments were constructed firstly and then exploited in rotated Chinese character recognition and product image retrieval respectively. The experimental results confirm the effectiveness of these moments in rotated Chinese character recognition, and also show that these moments can be employed as new shape descriptors for content-based image retrieval. |
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