The conformal monogenic signal is a novel rotational invariant approach for analyzing i(ntrinsic)1D and i2D local features of two-dimensional signals (e.g. images) without the use of any heuristics. It contains the monogenic signal as a special case for i1D signals and combines scale-space, phase, orientation, energy and isophote curvature in one unified algebraic framework. The conformal monogenic signal will be theoretically illustrated and motivated in detail by the relation of the Radon and the Riesz transform. One of the main ideas is to lift up two-dimensional signals to a higher dimensional conformal space where the signal can be analyzed with more degrees of freedom. The most interesting result is that isophote curvature can be calculated in a purely algebraic framework without the need of any derivatives.
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