  (shortened) We determine the transformation matrix T that maps multiple
images with resolved features onto one another and that is based on a
Taylor-expanded lensing potential close to a point on the critical curve within
our model-independent lens characterisation approach. From T, the same
information about the critical curve at fold and cusp points is derived as
determined by the quadrupole moment of the individual images as observables. In
addition, we read off the relative parities between the images, so that the
parity of all images is determined, when one is known. We compare all
retrievable ratios of potential derivatives to the actual ones and to those
obtained by using the quadrupole moment as observable for two and three image
configurations generated by a galaxy-cluster scale singular isothermal ellipse.
We conclude that using the quadrupole moments as observables, the properties of
the critical curve at the cusp points are retrieved to higher accuracy, at the
fold points to lower accuracy, and the ratios of second order potential
derivatives to comparable accuracy. We show that the approach using ratios of
convergences and reduced shear is equivalent to ours close to the critical
curve but yields more accurate results and is more robust because it does not
require a special coordinate system like the approach using potential
derivatives. T is determined by mapping manually assigned reference points in
the images onto each other. If the assignment of reference points is subject to
measurement uncertainties under noise, we find that the confidence intervals of
the lens parameters can be as large as the values, when the uncertainties are
larger than one pixel. Observed multiple images with resolved features are more
extended than unresolved ones, so that higher order moments should be taken
into account to improve the reconstruction.
