\documentclass{standalone}
\usepackage{graphicx}
\usepackage{tabularx}
\def\quarterwidth{8cm}
\newcolumntype{C}[0]{>{\let\newline\\\arraybackslash\hspace{0pt}}m{\quarterwidth}}

\begin{document}
		\centering
		\begin{tabular}{C@{}C@{}}
			\includegraphics[width=\quarterwidth]{FigProtrusionDensityHistograms.pdf}
			&
			\includegraphics[width=\quarterwidth]{FigProtrusionDensityHistogramsAlternative.pdf}
		\end{tabular}
\end{document}