So far the recently introduced monogenic curvature tensor has only been known in Fourier domain. In this paper the monogenic curvature tensor will be formulated in spatial domain as a concatenation of two and three Riesz transforms respectively. Furthermore it will be shown that the Riesz transform of any order can be defined by a concatenation of one dimensional Hilbert transforms in Radon space, the Radon transform of the signal and its inverse. The Riesz, Hilbert and Radon transforms provide a connection between differential geometry and signal processing so that already known results from differential geometry can be used to solve problems from phase based local image analysis of intrinsic dimension two and to interpret the monogenic curvature tensor exactly.
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