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

TL;DR

This paper introduces a new methodology to extract deformation-invariant characteristics from 2D images of elastic bodies, enabling the reconstruction of undeformed shapes and improving parasite classification accuracy.

Contribution

The paper presents two novel approaches for determining deformation invariants and applies them to accurately reconstruct undeformed shapes and classify parasites from deformed images.

Findings

Successfully reconstructed undeformed shapes of parasites, cells, fibers, and lips.

Achieved 97.6% accuracy in parasite classification after deformation correction.

Confirmed consistency of deformation invariants across different deformation instances.

Abstract

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 %.