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A novel methodology is introduced here that exploits 2D images of arbitrary elastic body deformation instances so as to quantify mechanoelastic characteristics that are deformation invariant. Determination of such characteristics allows for developing methods offering an image of the undeformed body. General assumptions about the mechanoelastic properties of the bodies are stated which lead to two different approaches for obtaining bodies' deformation invariants. One was developed to spot a 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 of 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, 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 six families, with an accuracy rate of 97.6 percent.

In this paper, a methodology of general applicability is presented for answering the question if an artist used a number of archetypes to draw a painting or if he drew it freehand. In fact, the contour line parts of the drawn objects that potentially correspond to archetypes are initially spotted. Subsequently, the exact form of these archetypes and their appearance throughout the painting is determined. The method has been applied to celebrated Thera Late Bronze Age wall paintings with full success. It has been demonstrated that the artist or group of artists has used seven geometrical archetypes and seven corresponding well-constructed stencils (four hyperbolae, two ellipses, and one Archimedes' spiral) to draw the wall painting "Gathering of Crocus" in 1650 B.C. This method of drawing seems to be unique in the history of arts and of great importance for archaeology, and the history of mathematics and sciences, as well.

In this paper, a color image segmentation method and a pattern analysis are presented, in connection with the extraordinary 1650 B.C. wall paintings found in the Greek island of Thera. These wall paintings are usually reconstructed from thousands of fragments widely scattered in the excavated site. The fragments' depiction manifests inhomogeneous color decay, cracks, added extraneous material, etc. The proposed color image segmentation method takes into account the decay problems and offers a very good approximation of the initial fragment depiction as the artist drew it in the late Bronze Age. The algorithm performs essentially better than other standard segmentation schemes as extensive qualitative tests indicate. Moreover, it offers clear-cut color regions and region borders for each fragment depiction. The whole approach is based on classifying the pixels into a number of regions where each region is described by a normal distribution, followed by fragment-decay reduction and edge refining. Extensive pattern analysis to the obtained region borders leads to the conclusion that 3650 years ago, the artist most probably used advanced geometrical methods in order to construct handcrafted "French curves" (stencils or templates) and use them to draw certain figures. On the basis of the aforementioned results, specific pattern matching techniques are employed for the reconstruction of wall paintings, depicting spirals, from their constituent fragments. [ABSTRACT FROM AUTHOR]