Orthogonal Moments And Its Application In The Image Analysis

Moment function is an important tool in image processing and analysis and has been widely used in the field of computer vision, pattern recognition, image processing, digital watermarking and texture retrieval and so on. A classification of moment based feature descriptors is going from the geometric moments, complex moments, rotational moments, to orthogonal moments. Geometric moments appear to be the earliest moment function and has simple form that has been well studied. Orthogonal moments has good properties and very simple inverse transform, can be easily to reconstruct image directly. Because of describing image with a minimal amount of information redundancy and small noisy sensibility, made orthogonal moments attract the interest among the pattern recognition and image processing researchers. Discrete orthogonal moments satisfying all the required analytical properties without any numerical approximation errors that have been widely used in the field of image analysis.This paper discusses orthogonal moment function used in the field of image analysis, including based on discrete tchebichef transform for image compression, A comparison between based on discrete tchebichef transform compression and JPEG compression is conducted. According to JPEG standard quantization table, using information entropy made quantization table of algorithm of based on discrete tchebichef transform for image compression. A comparison for color image between based on discrete tchebichef transform and JPEG image compression and reconstruction using MATLAB R2010B. Based on discrete tchebichef transform compression provides a more compact support to real digital image than JPEG.This chapter provides a novel approach based on discrete tchebichef transform for digital watermarking. A comparison for gray image between based on discrete tchebichef transform and DCT for digital watermarking using MATLAB R2010B. The experimental results show that, the algorithm based on DCT for digital watermarking close to based on discrete tchebichef transform in the performance. The PSNR has a very small difference in the embedded watermarking of image, but the algorithm based on discrete tchebichef transform extracted digital watermark has higher PSNR than based on DCT for digital watermarking.Scaling, rotation and translation invariant texture retrieval using Bessel-Fourier moments. It is a set of moments that based on the Bessel function of the first kind. Compared with the others moments based methods, the radial polynomials of Bessel-Fourier moments have more zeros and these zeros are more evenly distributed. It makes Bessel-Fourier moments more suitable for invariant texture retrieval as a generalization of orthogonalized complex moments. The correct classification percentages are compared with that of orthogonal Fourier-Mellin moments and Zernike moments based methods in noise-free and noisy condition. BFM performs better in recognition capability and noise robustness in terms of texture retrieval under both noise-free and noisy condition when compared with orthogonal Fourier-Mellin moments and Zernike moments based methods.