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A novel methodology is introduced here that exploits 2D images of arbitraryelastic body deformation instances, so as to quantify mechano-elasticcharacteristics that are deformation invariant. Determination of suchcharacteristics allows for developing methods offering an image of theundeformed body. General assumptions about the mechano-elastic properties ofthe bodies are stated, which lead to two different approaches for obtainingbodies' deformation invariants. One was developed to spot deformed body'sneutral line and its cross sections, while the other solves deformation PDEs byperforming a set of equivalent image operations on the deformed body images.Both these processes may furnish a body undeformed version from its deformedimage. This was confirmed by obtaining the undeformed shape of deformedparasites, cells (protozoa), fibers and human lips. In addition, the method hasbeen applied to the important problem of parasite automatic classification fromtheir microscopic images. To achieve this, we first apply the previous methodto straighten the highly deformed parasites and then we apply a dedicated curveclassification method to the straightened parasite contours. It is demonstratedthat essentially different deformations of the same parasite give rise topractically the same undeformed shape, thus confirming the consistency of theintroduced methodology. Finally, the developed pattern recognition methodclassifies the unwrapped parasites into 6 families, with an accuracy rate of97.6 %.

A General Methodology for the Determination of 2D Bodies Elastic Deformation Invariants. Application to the Automatic Identification of Parasites