Optical mapping is an integrated system for the analysis of single DNA molecules. It constructs restriction maps (noted as "optical map" ) from individual DNA molecules presented on surfaces after they are imaged by fluorescence microscopy. Because restriction digestion and fluorochrome staining are performed after molecules are mounted, resulting restriction fragments retain their order. Maps of fragment sizes and order are constructed by image processing techniques employing integrated fluorescence intensity measurements. Such analysis, in place of molecular length measurements, obviates need for uniformly elongated molecules, but requires samples containing small fluorescent reference molecules for accurate sizing. Although robust in practice, elimination of internal reference molecules would reduce errors and extend single molecule analysis to other platforms. In this paper, we introduce a new approach that does not use reference molecules for direct estimation of restriction fragment sizes, by the exploitation of the quantiles associated with their expected distribution. We show that this approach is comparable to the current reference-based method as evaluated by map alignment techniques in terms of the rate of placement of optical maps to published sequence.