ABSTRACT
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, 18:4, 2007) showed 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.
