Application of geometric models to letter recognition: distance and density

This article reviews studies in which a single letter is visually presented under adverse conditions and the subject's task is to identify the letter. The typical results for such studies are (a) certain pairs of letters are more often confused than other pairs of letters; (b) certain letters are more easily recognized than others; and (c) confusion errors for a letter pair are often asymmetric, the number of errors differing depending on which letter of the pair is presented as the stimulus. A geometric model incorporating the properties of distance and spatial density (after Krumhansl) is presented to account for these results. The present application of the distance-density model assumes that each letter is constructed in a typical 5 X 7 dot matrix. Each letter is represented in 35-dimensional space based on its constituent dots. A central idea behind the model, embodied in the property of spatial density, is that an explanation of typical results must take into account the relationship of the entire stimulus set to both the presented letter and the responded letter. Specifically, according to the model, (a) pairs of letters that are close in geometric space are more often confused than pairs of letters that are distant; (b) letters that are in less spatially dense regions are more easily recognized than letters that are in more spatially dense regions; and (c) asymmetric confusion errors result when one member of a letter pair is in a denser region than the other member of the letter pair. The distance-density model is applied to published and unpublished results of the authors as well as published results from two other laboratories. Alternative explanations of the three typical letter recognition results are also considered. The most successful alternative explanations are (a) confusions are an increasing function of the number of dots that two letters share; (b) letters constructed from fewer dots are easier to recognize; and (c) asymmetries arise when one member of a letter pair is more easily recognized, since that letter then has fewer confusion errors to give to the other letter of the pair. The model is discussed in terms of the distinction between template matching and feature analysis. An alternative classification of letter recognition models is proposed based on the global versus local qualities of features and the spatial information associated with each feature. The model is extended to explain reaction time study results. It is suggested that the distance-density model can be used to create optimal letter fonts by minimizing interletter confusions and maximizing letter recognizability.