Rotation of 2D orthogonal polynomials

© 2017 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license: http://creativecommons.org/licenses/by-nc-nd/4.0/ This author accepted manuscript is made available following 24 month embargo from date of publication (Dec 2017) in accordance with the publisher’s archiving policyOrientation-independent object recognition mostly relies on rotation invariants. Invariants from moments orthogonal on a square have favorable numerical properties but they are difficult to construct. The paper presents sufficient and necessary conditions, that must be fulfilled by 2D separable orthogonal polynomials, for being transformed under rotation in the same way as are the monomials. If these conditions have been met, the rotation property propagates from polynomials to moments and allows a straightforward derivation of rotation invariants. We show that only orthogonal polynomials belonging to a specific class exhibit this property. We call them Hermite-like polynomials

Face Recognition with Degraded Images

After more than two decades of research on the topic, automatic face recognition is finding its applications in our daily life; banks, governments, airports and many other institutions and organizations are showing interest in employing such systems for security purposes. However, there are so many unanswered questions remaining and challenges not yet been tackled. Despite its common occurrence in images, blur is one of the topics that has not been studied until recently. There are generally two types of approached for dealing with blur in images: (1) identifying the blur system in order to restore the image, (2) extracting features that are blur invariant. The first category requires extra computation that makes it expensive for large scale pattern recognition applications. The second category, however, does not suffer from this drawback. This class of features were proposed for the first time in 1995, and has attracted more attention in the last few years. The proposed invariants are mostly developed in the spatial domain and the Fourier domain. The spatial domain blur invariants are developed based on moments, while those in the Fourier domain are defined based on the phase\u27 properties. In this dissertation, wavelet domain blur invariants are proposed for the first time, and their performance is evaluated in different experiments. It is also shown that the spatial domain blur invariants are a special case of the proposed invariants. The second contribution of this dissertation is blur invariant descriptors that are developed based on an alternative definition for ordinary moments that is proposed in this dissertation for the first time. These descriptors are used forface recognition with blurred images, where excellent results are achieved. Also, in a comparison with the state-of-art, the superiority of the proposed technique is demonstrated