An approach to the 2D hilbert transform for image processing applications

Authors:
Juan Valentín Lorenzo-Ginori
Affiliations:
Center for Studies on Electronics and Information Technologies, Universidad Central de Las Villas, Cuba
Venue:
ICIAR'07 Proceedings of the 4th international conference on Image Analysis and Recognition
Year:
2007

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Abstract

The Hilbert Transform (HT) and the analytic signal (AS) are widely used in their one-dimensional version for various applications. However, in the bi-dimensional (2D) case as occur for images, the definition of the 2D-HT is not unique and several approaches to it have been developed, having as one of the main goals to obtain a meaningful 2D-AS or analytic image, which can be used for various practical applications. In this work, one particular approach to the 2D-HT is introduced that allowed the calculation of analytic images which satisfy the basic properties that these functions have in the 1D case, and that produces a 2D spectrum equal to zero in one quadrant. The methods for calculation of the discrete version of the 2D-HT and the associated AS are presented and analyzed, as well as two applications, for edge detection and for envelope detection in a 2D AM modulated radial chirp.