Micromorphology of gold jewels: a novel algorithm for 3D reconstruction and its quality assessment

The development of a reliable algorithm for 3D reconstruction of jewel surfaces and the relative accuracy evaluation, are the main issues of this paper. They rely on the estimation of the depth and 3D shape of an object from a sequence of images taken at different focus settings (shape from focus). Assuming the focal plane be identified by the best local sharpness, it turns out that the criterion for sharpness evaluation is crucial for obtaining an accurate 3D reconstruction. We present for the first time a novel algorithm for sharpness evaluation, which is based on a particular combination of sum of square differences (SSD). The images processed with SSD have been captured using a novel homemade microscope prototype. The implementation of this technique allows computing the best-focus map (and, consequently, image) from the whole set of images. The assessment of the 3D reconstruction quality has been carried out by considering the structural similarity index (SSIM), since thanks to its effectiveness in measuring the quality of natural images distorted by a large variety of biases. Hence, the novel algorithm has been applied to study micro-morphological features of a modern replica of an Etruscan gold jewel. The granulation ornament on the jewel has been characterized through a geometrical model which can be introduced to illustrate the grains solder quality. The developed geometrical model has been used to analyze also the granulation on an original Etruscan bauletto earring.