Combined Invariants to Similarity Transformation and to Blur Using Orthogonal Zernike Moments

• Published in: IEEE transactions on image processing Vol. 20; no. 2; pp. 345 - 360
• Main Authors: Beijing Chen, Huazhong Shu, Hui Zhang, Coatrieux, G, Limin Luo, Coatrieux, J L
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.02.2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Bioengineering; Blurred; Cameras; Circularly symmetric blur; combined invariants; Construction; Convolution; Deconvolution; Degradation; Derivation; Exact sciences and technology; Image processing; Information, signal and communications theory; Invariants; Layout; Life Sciences; Object recognition; Pattern matching; Pattern recognition; Radiometry; Robustness; Signal processing; Similarity; Telecommunications; Telecommunications and information theory; template matching; Transformations; Zernike moments; Performance evaluation; Similarity; Moment method; template matching; Symmetric function; Pattern recognition; Blurred image; Zernike polynomial; Point spread function; Accuracy; Circularly symmetric blur; Convolution; Zernike moments; Robustness; combined invariants; Pattern matching; circularly symmetric blur; pattern recognition
• ISSN: 1057-7149; 1941-0042
• DOI: 10.1109/TIP.2010.2062195

The derivation of moment invariants has been extensively investigated in the past decades. In this paper, we construct a set of invariants derived from Zernike moments which is simultaneously invariant to similarity transformation and to convolution with circularly symmetric point spread function (PSF). Two main contributions are provided: the theoretical framework for deriving the Zernike moments of a blurred image and the way to construct the combined geometric-blur invariants. The performance of the proposed descriptors is evaluated with various PSFs and similarity transformations. The comparison of the proposed method with the existing ones is also provided in terms of pattern recognition accuracy, template matching and robustness to noise. Experimental results show that the proposed descriptors perform on the overall better.