Hilbert wavelet transform for recognition of image rotation

In the previous paper [2] we demonstrated the usefulness of complex frequency scaling of Fourier Transform in identifying amount of rotation angle between two objects. Using the complex frequency scaling property of Fourier transform, an image and its Hilbert transform can be used to find the exact angle of rotation between the images [24]. In order to find the correct angle between the two different images, we need to find the Hilbert transform of the function f(x,y) to construct an analytically extended function f'(x,y) . However, our approach does not perform satisfactorily for identification of rotation angle between two similar objects [2]. A considerable amount of research has been performed on wavelet based signal processing by utilizing a pair of wavelet transforms where the wavelets form the Hilbert transform pair. In this paper we describe the design procedure based on spectral factorization in the generation of the Hilbert transform pair of wavelet bases. [1], [3], [4], [5]. The one-dimensional wavelets are then used to generate two-dimensional wavelets. The two-dimensional wavelets thus generated are then used in the determination of correct angle between the images. The intention behind taking the above approach using the wavelets is to find if the wavelets help in discriminating the different images. In this paper we use the Hilbert transform pair of wavelet bases instead in constructing the analytically extended function. In generating the filter, orthogonal solutions are presented [3]. The solution depends on the all pass filter having a flat delay response [10]. We use the infrared images to validate our algorithm.

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