  A novel methodology is introduced here that exploits 2D images of arbitrary
elastic body deformation instances, so as to quantify mechano-elastic
characteristics that are deformation invariant. Determination of such
characteristics allows for developing methods offering an image of the
undeformed body. General assumptions about the mechano-elastic properties of
the bodies are stated, which lead to two different approaches for obtaining
bodies' deformation invariants. One was developed to spot deformed body's
neutral line and its cross sections, while the other solves deformation PDEs by
performing a set of equivalent image operations on the deformed body images.
Both these processes may furnish a body undeformed version from its deformed
image. This was confirmed by obtaining the undeformed shape of deformed
parasites, cells (protozoa), fibers and human lips. In addition, the method has
been applied to the important problem of parasite automatic classification from
their microscopic images. To achieve this, we first apply the previous method
to straighten the highly deformed parasites and then we apply a dedicated curve
classification method to the straightened parasite contours. It is demonstrated
that essentially different deformations of the same parasite give rise to
practically the same undeformed shape, thus confirming the consistency of the
introduced methodology. Finally, the developed pattern recognition method
classifies the unwrapped parasites into 6 families, with an accuracy rate of
97.6 %.
