Michail Panagopoulos | Searcharxiv

arXiv2013

New Mathematical and Algorithmic Schemes for Pattern Classification with Application to the Identification of Writers of Important Ancient Documents

In this paper, a novel approach is introduced for classifying curves into proper families, according to their similarity. First, a mathematical quantity we call plane curvature is introduced and a number of propositions are stated and proved. Proper similarity measures of two curves are introduced and a subsequent statistical analysis is applied. First, the efficiency of the curve fitting process has been tested on 2 shapes datasets of reference. Next, the methodology has been applied to the very important problem of classifying 23 Byzantine codices and 46 Ancient inscriptions to their writers, thus achieving correct dating of their content. The inscriptions have been attributed to ten individual hands and the Byzantine codices to four writers.

cs.CV↗

arXiv2010

Characterizing Complex Particle Morphologies Through Shape Matching: Descriptors, Applications, and Algorithms

Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for characterizing the unique and highly complex structures often encountered in the emerging field of nano and microscale self-assembly, or other disciplines involving complex structures such as computational biology. Computer science algorithms known as "shape matching" methods pose a unique solution to this problem by providing robust metrics for quantifying the similarity between pairs of arbitrarily complex structures. This pairwise matching operation, either implicitly or explicitly, lies at the heart of most standard structural characterization schemes for particle systems. By substituting more robust "shape descriptors" into these schemes we extend their applicability to structures formed from more complex building blocks. Here, we describe several structural characterization schemes and shape descriptors that can be used to obtain various types of structural information about particle systems. We demonstrate the application of shape matching algorithms to a variety of example problems, for topics including local and global structure identification and classification, automated phase diagram mapping, and the construction of spatial and temporal correlation functions. The methods are applicable to a wide range of systems, both simulated and experimental, provided particle positions are known or can be accurately imaged.

cond-mat.soft↗