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Incorporating approximate rotational invariance into two-dimensional S-transform

The discrete two-dimensional (2D) S-transform (ST-2D) is a space-frequency representation that provides the local spectrum at each pixel in an image. The inherent localisation properties of the ST-2D make it a preferred candidate for space-frequency analysis. However, the ST-2D is sensitive to the image rotation. This limits its use in many image processing applications such as texture analysis. This study describes the rotational sensitivity of the ST-2D, and explains how this limits its application. To overcome these problems, a novel rotationally invariant S-transform (RIST) is formulated, and its rotational invariance is investigated. The RIST can provide approximate rotational invariance for magnitudes and complex values over a wide range of rotation angles, but with a trade-off of higher computation time. The RIST may be useful for many medical, scientific and industrial applications.