Image Analysis by Conformal Embedding
 This work presents new ideas in isotropic multi-dimensional phase based
  signal theory. The novel approach, called the emph{conformal monogenic
    signal}, is a rotational invariant quadrature filter for extracting local
  features of any curved signal without the use of any heuristics or steering
  techniques. The emph{conformal monogenic signal} contains the recently
  introduced emph{monogenic signal} as a special case and combines Poisson
  scale space, local amplitude, direction, phase and curvature in one un
ified
  algebraic framework. The emph{conformal monogenic signal} will be
  theoretically illustrated and motivated in detail by the relation between
  the Radon transform and the generalized Hilbert transform. The main idea of
  the emph{conformal monogenic signal} is to lift up $n$-dimensional signals
  by emph{inverse stereographic projections} to a $n$-dimensional sphere in
  $
eals{n+1}$ where the local signal features can be analyzed with more
  degrees of freedom compared to the flat $n$-dimensional space of the
  original signal domain. As result, it delivers a novel way of computing the
  isophote curvature of signals without partial derivatives.  The philosophy
  of the emph{conformal monogenic signal} is based on the idea to use the
  direct relation between the original signal and geometric entities such as
  lines, circles, hyperplanes and hyperspheres. Furthermore, the emph{2D
    conformal monogenic signal} can be extended to signals of any
  dimension. The main advantages of the emph{conformal monogenic signal} in
  practical applications are its compatibility with intrinsically one
  dimsensional and special intrinsically two dimensional signals, the
  rotational invariance, the low computational time complexity, the easy
  implementation into existing software packages and the numerical robustness
  of calculating exact local curvature of signals without the need of any
  derivatives.  keywords{Unit sphere and signal processing and generalized
    Hilbert transform and Riesz transform and Radon transform and isotropic
    and local phase based signal analysis and Clifford analysis and
    monogenic signal and analytic signal and isophote curvature and Poisson
    scale space and stereographic projection and conformal space}