Object recognition using a neural network and invariant Zernike features

Khotanzad, A.; Lu, J.-H.

doi:10.1109/cvpr.1989.37850

Cited by 15 publications

(6 citation statements)

References 9 publications

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“…Traditionally the most popular method of achieving scale invariance of Zernike moments [15][16][17][18] is based on normalizing the area that is the zero order of geometric moments, to a constant value; however there are several drawbacks: first, the changes in area are not always linearly dependent on changes of size for the same image; second, when the order of moments becomes larger, the dynamic range increases, which in turn amplify the numerical errors; third, the conversion from geometric moments to Zernike moments adds more computation complexity. In [1], Belkasim used the zero order and the second order of Zernike moments to develop several scale invariance parameters.…”

Section: Introductionmentioning

confidence: 99%

Improving stability and invariance of Cartesian Zernike moments

Zhao

Belkasim

2012

2012 IEEE Southwest Symposium on Image Analysis and Interpretation

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Zernike moments are widely used in shape retrieval, recognition and classification. The rotational invariance property of Zernike moments is very simple to achieve, due to their separable magnitude-phase property. However, Zernike moments are not directly invariant to scale and translation. Recently Cartesian Zernike moments invariants (CZMI) were introduced to directly make Zernike moments invariant under translation and scale. Although CZMI reduced scale error considerably, they are inconsistent and scale error increases for high aspect ratio images. In this paper, we propose a new scale invariance parameter, which reduces scale errors, improves the stability of scale invariance and is more consistent and stable for processing all images including the ones with large aspect ratios.

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Section: Introductionmentioning

confidence: 99%

Improving stability and invariance of Cartesian Zernike moments

Zhao

Belkasim

2012

2012 IEEE Southwest Symposium on Image Analysis and Interpretation

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“…It is usually unreasonable due to both time and space constraints to replicate each image many times at different rotations and to compute the resulting covariance matrix for eigenvector decomposition. To cope with this, Teague, [19] and then Khotanzad and Lu [10], developed a means of creating rotation-invariant image approximations based on Zernike polynomials. While Zernike polynomials are not adaptive to the data, PCA produces an optimal data adaptive basis (in the least squares sense).…”

Section: Introductionmentioning

confidence: 99%

Computing Steerable Principal Components of a Large Set of Images and Their Rotations

Ponce

Singer

2011

IEEE Trans. on Image Process.

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We present here an efficient algorithm to compute the Principal Component Analysis (PCA) of a large image set consisting of images and, for each image, the set of its uniform rotations in the plane. We do this by pointing out the block circulant structure of the covariance matrix and utilizing that structure to compute its eigenvectors. We also demonstrate the advantages of this algorithm over similar ones with numerical experiments. Although it is useful in many settings, we illustrate the specific application of the algorithm to the problem of cryo-electron microscopy.

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“…Several years after, Teague used orthogonal polynomials to propose a new kind of moments called today, Zernike and Legendre moments [2]. Many authors have demonstrated that the moments of an image are useful features for pattern recognition and object classification [3][4][5][6][7][8][9][10][11]. In all these researches have been demonstrated that image moments based on different nature of polynomials can be efficiently combined in an algebraic way to define invariants to the orientation [12], scale [13], shift [14], blur [15][16][17], and the contrast changes [18] on the vision field of an image.…”

Section: Introductionmentioning

confidence: 99%

Classification of motion-blurred images using Zernike and wavelet-Fourier moments

2007

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In this paper, we consider the use of circular moments for invariant classification of images which have been blurred by motion. The test images used here have been acquired when the objects are vibrating at different frequencies. A comparative analysis using Zernike and Wavelet-Fourier moment sets is presented. An intensity normalization of the input images is done to homogenize them due to inhomogeneous illumination produced by the acquisition. The classification method is tested using images from objects which have intrinsically little differences between them. Experimental results show that, the proposed classification method based in Zernike and Wavelet-Fourier moments can be well addressed to grade images smeared by motion, from objects under high frequency vibrations.

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Object recognition using a neural network and invariant Zernike features

Cited by 15 publications

References 9 publications

Improving stability and invariance of Cartesian Zernike moments

Improving stability and invariance of Cartesian Zernike moments

Computing Steerable Principal Components of a Large Set of Images and Their Rotations

Classification of motion-blurred images using Zernike and wavelet-Fourier moments

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