# Quantifying Writer Variance Through Rainbow Triangle Graph Decomposition of the Common Word “the”

Conference/Workshop:
Published: 2023
Primary Author: Alexandria Arabio
Secondary Authors: Danica Ommen, Alicia Carriquiry
Type: Poster

Handwriting comparative analysis is based on the principle that no two individuals can produce the same writing and that an individual cannot exactly reproduce his/her handwriting. This project aims to assess and quantify the natural variations produced by a distinct writer. In an attempt to support traditional examination with objective measures, this project provides results from a study where features of handwriting are examined through graph decomposition and rainbow triangulation. Using this method to examine handwriting samples, more specific information can be obtained from each exemplar and can be standardized to be compared both within a writer and between different writers. Each type of characteristic or landmark of each handwriting sample are marked as a different color node in a graph, including the location that a pen stroke begins (blue), the location that a pen stroke ends (orange), any location where a pen line overlaps itself (pink), the highest location that a pen stroke reaches (green), and the lowest location that a pen stroke reaches (purple). Triangles can provide information on angles, edge slopes, edge lengths, and areas that all prove useful for quantitative and comparative analysis. By forming rainbow triangles over these samples, it is possible to gauge the variation within a single writer and to compare these quantitative values to other samples of unknown sources. Rainbow triangles are formed so that each vertex or node within a triangle set has a unique color, and each edge is unique to its triangle so that it is not to be used to form a different triangle in another set. Using this information, the study aims to form a quantitative analysis of handwriting samples and to calculate how similar or dissimilar two samples are from one another. One of the study’s main goals is to form these triangles from multiple samples from several different writers and to group, identify, and accurately determine what samples came from which writer. Finally, multiple summary statistics are explored to determine whether any can be used to discriminate between inclusions and exclusions using data where ground truth is known, such as a true match. This project hopes to impact the forensic community by demonstrating a new method for analyzing handwriting that could be used in conjunction with current practices to better quantify and support results regarding the source of a questioned document.

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