#### Introduction

Zernike moments are the mappings of an image onto a set of complex Zernike polynomials [1]. Since Zernike polynomials are orthogonal to eachother, Zernike moments can represent the properties of an image with no redundancy or overlap of information between the moments. Zernike moments are significantly dependent on the scaling and translation of the object in an ROI. Nevertheless, their magnitudes are independent of the rotation angle of the object [1], [2]. Hence, we can utilize them to describe shape characteristics of the objects. For instance, in [1], we took the advantage of Zernike moments to extract the shape information of benign and malignant breast masses.

#### Software support

The following file includes a function to calculate the radial polynomials (radialpoly.m), a function to calculate the Zernike moments (Zernikmoment.m) and a demo to illustrate how the functions work (Zernike_main.m). For more information, please study [1].

Download Matlab code for Zernike moments

Copyright © 2012 Amir Tahmasbi: You are free to use this code in your scientific research but you should cite [1].

#### Mammography CADx system (2010)

Despite the recent advances in the fields of mammography, thermography, optical tomography and other screening methodologies, breast cancer is still a prominent problem. Women have about a 1 in 8 lifetime risk of developing invasive breast cancer. Hence, in this research I tried to develop several Computer-aided diagnosis (CADx) systems for classification of breast masses. I utilized different types of features namely Zernike moments [1]-[3] and FTRD [4] as well as different classifiers like CWLA [5] and Opposition-based MLP [6] in order to enhance the accuracy and false negative rate (FNR).

#### References

[1] A. Tahmasbi, F. Saki, S. B. Shokouhi, "Classification of Benign and Malignant Masses Based on Zernike Moments," J. Computers in Biology and Medicine, vol. 41, no. 8, pp. 726-735, 2011.

[2] A. Tahmasbi, F. Saki, H. Aghapanah, S. B. Shokouhi, "A Novel Breast Mass Diagnosis System based on Zernike Moments as Shape and Density Descriptors," in Proc. IEEE, 18th Iranian Conf. on Biomedical Engineering (ICBME'2011), Tehran, Iran, 2011, pp. 100-104.

[3] A. Tahmasbi, F. Saki, S. B. Shokouhi, "An Effective Breast Mass Diagnosis System using Zernike Moments," in Proc. IEEE, 17th Iranian Conf. on Biomedical Engineering (ICBME'2010), Isfahan, Iran, 2010, pp. 1-4.

[4] A. Tahmasbi, F. Saki, S. B. Shokouhi, "Mass Diagnosis in Mammography Images using Novel FTRD Features," in Proc. IEEE, 17th Iranian Conf. on Biomedical Engineering (ICBME'2010), Isfahan, Iran, 2010, pp. 1-5.

[5] A. Tahmasbi, F. Saki, S. B. Shokouhi, "CWLA: A Novel Cognitive Classifier for Breast Mass Diagnosis," in Proc. IEEE, 18th Iranian Conf. on Biomedical Engineering (ICBME'2011), Tehran, Iran, 2011, pp. 255-259.

[6] F. Saki, A. Tahmasbi, S. B. Shokouhi, "A Novel Opposition-based Classifier for Mass Diagnosis in Mammography Images," in Proc. IEEE, 17th Iranian Conf. on Biomedical Engineering (ICBME'2010), Isfahan, Iran, 2010, pp. 1-4.

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