Translation invariants of Zernike moments (original) (raw)
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IET Computer Vision, 2011
The magnitude of Zernike moments (ZMs) has been used as rotation invariant features for classification problems in the past. Their individual real and imaginary components and phase coefficients are ignored, because they change with rotation. This study presents a new method to modify the individual real and imaginary components of ZMs which change due to image rotation. The modified real and imaginary components are then used as invariant image descriptors. The performance of the proposed method and magnitude-based ZM method is analysed on grayscale face images and binary character images in application to the fields of face recognition and character recognition, respectively. Experimental results show that the proposed method is robust to image rotation. For classification, the authors use L 1 -norm as the similarity measure. It is shown that the proposed method gives better recognition rate over the magnitude-based ZM method, comparatively at low orders of moment and thus it is recommended for pose invariant face recognition and also for rotation invariant character recognition. This has been proved by comparing the results of the proposed method with existing prominent methods of feature extraction in face and character recognition. On ORL database, the proposed method achieves the highest recognition rate of 96.5%, whereas a recognition rate of 99.7% is obtained on binary Roman character images.
Feature Extraction Using Zernike Moments
—Shape identification and feature extraction are the main concern of any pattern recognition system. Object parameters are mostly dependent on spatio-temporal relationships among the pixels. However feature extraction is a complex phenomenon which needs to be addressed from the invariance property, irrespective of position and orientation. Zernike moments are used as shape descriptors and identified as rotation invariant due to Orthogonality property. However the computational complexity is high. Script as a basis for evaluation of patterns and cursive nature of script language Telugu. The present work is aimed at evaluation of Zernike moments for various patterns of objects that are cursive in nature. Therefore feature extraction of patterns like vowels and consonants in cursive script Telugu using Zernike moments is considered in comparison with Hu's seven moments.
The scale invariants of pseudo-Zernike moments
Pattern Analysis & Applications, 2003
The definition of pseudo-Zernike moments has a form of projection of the image intensity function onto the pseudo-Zernike polynomials, and they are defined using a polar coordinate representation of the image space. Hence, they are commonly used in recognition tasks requiring rotation invariance. However, this coordinate representation does not easily yield a scale invariant function because it is difficult to extract a common scale factor from the radial polynomials. As a result, vision applications generally resort to image normalisation method or using a combination of scale invariants of geometric or radial moments to achieve the corresponding invariants of pseudo-Zernike moments. In this paper, we present a mathematical framework to derive a new set of scale invariants of pseudo-Zernike moments based on pseudo-Zernike polynomials. They are algebraically obtained by eliminating the scale factor contained in the scaled pseudo-Zernike moments. They remain unchanged under equal-shape expansion, contraction and reflection of the original image. They can be directly computed from any scaled image without prior knowledge of the normalisation parameters, or assistance of geometric or radial moments. Their performance is experimentally verified using a set of Chinese and Latin characters. In addition, a comparison of computational speed between the proposed descriptors and the present methods is also presented.
A New Class of Rotational Invariants Using Discrete Orthogonal Moments
2004
This paper presents a new class of Tchebichef moments in polar coordinate form, using which rotational invariants can be easily constructed. The structure of the invariants is very similar to that of Zernike and Pseudo-Zernike moments, and their computation does not involve discrete approximation of continuous integral terms. The invariants are thus very robust in the presence of image noise, and have far better recognition capabilities when compared with Zernike/Legendre moments. The new class of moment invariants presented in this paper can be used in pattern and character recognition tasks.
Accurate pseudo Zernike moment invariants for grey-level images
The Imaging Science Journal, 2012
Pseudo Zernike moments are orthogonal moments used to represent digital images with minimum amount of information redundancy. Pseudo Zernike moment invariants are image features that are invariant to translation, scaling and rotation which play an essential role in discriminating and classifying similar images where the performance and robustness of the classifiers are highly dependent on the accuracy of these futures. In this work, a new method is presented for accurate computation of two-dimensional pseudo Zernike moment invariants. Approximation errors are removed by using exact geometric and radial geometric moments. Invariance to translation and scaling are computed, while the rotation invariance is directly achieved as direct property of pseudo Zernike moments. Numerical experiments are conducted on a set of standard images. The obtained results demonstrate the efficiency of the proposed method.
Efficient computation of Zernike and Pseudo-Zernike moments for pattern classification applications
Pattern Recognition and Image Analysis, 2010
Two novel algorithms for the fast computation of the Zernike and Pseudo Zernike moments are presented in this paper. The proposed algorithms are very useful, particularly in the case of using the com puted moments, as discriminative features in pattern classification applications, where the computation of single moments of several orders is required. The derivation of the algorithms is based on the elimination of the factorial computations, by computing recursively the fractional terms of the orthogonal polynomials being used. The newly introduced algorithms are compared to the direct methods, which are the only meth ods that permit the computation of single moments of any order. The computational complexity of the pro posed method is O(p 2 ) in multiplications, with p being the moment order, while the corresponding complex ity of the direct method is O(p 3 ). Appropriate experiments justify the superiority of the proposed recursive algorithms over the direct ones, establishing them as alternative to the original algorithms, for the fast com putation of the Zernike and Pseudo Zernike moments.
Object Classification Using Sequences of Zernike Moments
Computer Information Systems and Industrial Management, 2017
In this paper we propose a method of object classification based on the sequences of Zernike moments. The method makes use of the pattern recognition properties of Zernike moments and expands it to the problem of classification. Since the distinctive features of the classified objects are carried over to the Zernike moments, the proposed method allows for a robust, rotation and translation invariant classification of complex objects in grayscale images. In this approach, each object class has defined a reference Zernike moment sequence that is used as the prototype of the class. The object's affiliation to the class is decided with the MSE criterion calculated for the object's Zernike moments sequence and the reference Zernike moments sequence of the class. The method is tested using grayscale images of handwritten digits and microscopic sections.
Improvement of Zernike moment descriptors on affine transformed shapes
2007
In general, Zernike moments are often used efficiently as shape descriptors of image objects, such as logos or trademarks that cannot be defined by a single contour. However, because these moments are defined in a unit disk space and extracted by a polar raster sampling shape, information of skewed and stretched shapes is lost. As a result, they can be inefficient shape descriptors when there is skew and stretch distortion. In this paper, a method is proposed that addresses this issue. More specifically, Zernike moments are obtained from a transformed unit disk space that allows for the extraction of shape descriptors which are invariant to rotation, translation, and scale as well as skew and stretch, thus preserving more shape information for the feature extraction process. The experimental results demonstrate that the proposed algorithm is more accurate in relation to skew and stretch distortions when compared to other available schemes reported in the literature.