There are many examples of problems in pattern analysis for which it is often possible to obtain systematic characterizations, if in addition a small number of useful features or parameters of the image are known a priori or can be estimated reasonably well. Often, the relevant features of a particular pattern analysis problem are easy to enumerate, as when statistical structures of the patterns are well understood from the knowledge of the domain. We study a problem from molecular image analysis, where such a domain-dependent understanding may be lacking to some degree and the features must be inferred via machine-learning techniques. In this paper, we propose a rigorous, fully automated technique for this problem. We are motivated by an application of atomic force microscopy (AFM) image processing needed to solve a central problem in molecular biology, aimed at obtaining the complete transcription profile of a single cell, a snapshot that shows which genes are being expressed and to what degree. Reed et al. (“Single molecule transcription profiling with AFM,” Nanotechnology, vol. 18, no. 4, 2007) showed that the transcription profiling problem reduces to making high-precision measurements of biomolecule backbone lengths, correct to within 20-25 bp (6-7.5 nm). Here, we present an image processing and length estimation pipeline using AFM that comes close to achieving these measurement tolerances. In particular, we develop a biased length estimator on trained coefficients of a simple linear regression model, biweighted by a Beaton-Tukey function, whose feature universe is constrained by James-Stein shrinkage to avoid overfitting. In terms of extensibility and addressing the model selection problem, this formulation subsumes the models we studied.