This chapter presents an analysis on Zernike Moments from the class of orthogonal moments which are invariant to rotation, translation and scaling. The chapter initially focuses on the review of Zernike moments as 1D, 2D and 3D based on their dimension and later investigates on the construction, characteristics of Zernike Moments and their invariants, which can be used as a shape descriptor to capture global and detailed information from the data based on their order to provide outstanding performance in various applications of image processing. Further the chapter also presents an application of 2D Zernike Moments features for plant species recognition and classification using supervised learning techniques. The performance of the learned models was evaluated with True Positive Rate, True Rejection ratio, False Acceptance Rate, False Rejection Ratio and Receiver Operating Characteristics. The simulation results indicate that the Zernike moments with its invariants was successful in recognising and classifying the images with least FAR and significant TRR.
TopIntroduction
The area of pattern recognition and classification has grown due to its emerging applications towards machine vision, biometrics, medical imaging, optical character recognition, speech recognition, remote sensing and bioinformatics. Pattern recognition and classification is a process that involves acquisition of the raw data and taking certain necessary action based on the class or category of the pattern. This process involves data sensing, preprocessing, feature extraction, recognition and classification, of which image representation and description by definite features is very important for pattern recognition and analysis problems. These set of features are the deciding factors in various classification problems. The utilization of good set of features decide the success of these methods. Shape (Loncaric,1998; Zhang & Lu, 2001) is an important visual feature that best describes and represents an image. It is extremely effective in capturing both holistic and structural information from an image. There are various shape descriptors been proposed and exist in the literature. These are broadly categorized into boundary based descriptors and region based descriptors (Zhang and Lu, 2002; Zhang and Lu, 2004) as shown in Figure 1. Boundary based descriptors exploit the boundary information. These include shape signatures (Davies, 2004), global descriptors (Niblack et al.,1993) and spectral descriptors (Folkers and Samet, 2002; Yang, Lee, and Lee, 1998). Global descriptors such as perimeter, eccentricity, circularity discriminate shape with large dissimilarities; hence they are usually suitable for filtering. With spectral descriptors (Zhang and Lu,2001), low frequency components capture global features while higher frequency components capture the enhanced features. Boundary based descriptors cannot capture the interior content of the image and they drop back when the boundaries are disjoint as the information is not completely available.
Region based descriptors (Zhang and Lu, 2004) consider all the pixels within the shape region which are considered to obtain the shape description. Region based methods make effective use of all the pixel information to represent the shape. These include area, euler number, convex hull,shape matrix and moment descriptors(Yang, Lee, and Lee, 1998; Teh and Chin, 1988; Flusser, 2006).The moment based descriptors are based on extracting statistical distribution from the image pixels. These moments have the property of being invariant to image rotation, scaling and translation which is significant for image recognition and classification methods (Teh and Chin, 1988).
The chapter is organized as follows. Section 2 provides a comprehensive review on Moment invariants. Section 3 outlines Zernike Moments (ZM) based on the dimensions as 1D, 2D and 3D; the computation of Zernike moments and their invariants and the applications of ZM in various image processing areas. Section 4 furnishes details about performance evaluation of the classifiers. Section 5 presents an application of 2D ZM in plant species recognition and classification. Finally Section 6 concludes the chapter.
Figure 1. Classification of shape descriptors