Identification confusions among letters of the alphabet

Black, uppercase letters, subtending 6.0' of arc in height, were presented tachistoscopically to 6 subjects. An exposure duration was chosen to keep the subject's identification performance at about 50% correct. On each trial a single letter was presented, and the subject was required to identify the letter by verbal response. The resulting 26 X 26 confusion matrix was based on 3,900 trials (150 trials per letter). Several models of visual processing were used to generate predicted confusions among letter pairs. Models based on template overlap, geometric features, and two-dimensional spatial frequency content (Fourier transforms) were tested. The highest correlation (.70) between actual and predicted confusions was attained by the model based on the Fourier transformed letters filtered by the human contrast sensitivity function. These results demonstrate that the spatial frequency content of visual patterns can provide a valuable metric for predicting their psychological similarity. The results further suggest that spatial frequency models of visual processing are competitive with feature analysis models.     

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.     

Inverse discrimination time as a perceptual distance for alphabetic characters

Reaction times to discriminate lower‐case letters were collected in an experiment. The inverse discrimination times were used to build metrics on the space of letters. These metrics were found to be significantly correlated with various well‐known letter confusability measures, and a meaningful dimensional analysis of the alphabet was performed. This methodology is mathematically well founded, it requires fewer data than common methods, and it appears to be highly sensitive to visual similarity between letters, which allows visual letter features to be effectively analysed.     

Visual image analysis by square wavelets: empirical evidence supporting a theoretical agreement between wavelet analysis and receptive field organization of visual cortical neurons

It was proposed that the human visual system analyzes images into square wavelets. To test this view, comparisons were made between the perceived similarity-dissimilarity of alphabet letters and the wavelet analyses of those same letters. For the proposal to be considered tenable, the coefficients of the wavelet analysis of similar letters must be similar, and the coefficients of the wavelet analysis of dissimilar letters must be dissimilar. From a selection of 12 letters, four pairs of letters had been reported by Van der Heijden, Mathas, and Van den Roovaart as very similar, and four other pairs of letters dissimilar. Each of the 12 letters was separately depicted in 8 x 8 matrices, and the signal represented by each of the matrices was analyzed into square wavelets using a new and original procedure which yielded a single set of coefficients for each matrix. Correlations between sets of coefficients were high (r ranged from .88 to .58) for those letter pairs judged high in similarity; correlations were low (r ranged from -.02 to .29) for those letter pairs judged low in similarity. When the correlations between the coefficients of wavelets of all eight-letter pairs were compared with the judged similarity-dissimilarity of all eight-letter pairs, the linear agreement was statistically significant. Agreement was found between the neurophysiological mapping of receptive fields of visual cortical neurons and the vectors or the pattern of pluses and minuses which characterized the wavelet analysis. Furthermore, regeneration of the visual image, or the pattern of neural activity representing the image, could be described by a tree-like flow of information among visual cortical neurons which received response data from visual receptive fields, the response data being wavelet coefficients. Results indicate the analysis accurately produces reliable transformations of visual patterns and may be a process used by the visual system.     

Letter identification as a function of type of perceptual limitation and type of attribute

It is argued that the distribution of errors in letter identification depends on two factors: (a) whether the set of letters is defined by features that exist or do not exist or by dimensions that exist at some positive value, and (b) whether errors are produced by process limitation in which the letter patterns are distorted or by state limitation in which there is inadequate energy. A specific hypothesis tested was that error distributions reflect the attribute structure under both types of limitation if dimensions define the letter set, but only under a process limitation if features define the letter set. Under a state limitation, feature set errors are primarily produced by a loss of features, so that a letter with more features is called a letter with fewer features more often than conversely. An experiment completely validated the hypothesis under test. In addition, the relative discriminabilities of two dimensions defining a dimension set of letters was reversed from state to process limitation. Thus the attribute structure derived from error distributions is not invariant across types of perceptual limitation, nor are distances between letter pairs always symmetric.     

A letter visual-similarity matrix for Latin-based alphabets

Indicators of letter visual similarity have been used for controlling the design of empirical and neuropsychological studies and for rigorously determining the factors that underlie reading ability and literacy acquisition. Additionally, these letter similarity/confusability matrices have been useful for studies examining more general aspects of human cognition, such as perception. Despite many letter visual-similarity matrices being available, they all have two serious limitations if they are to be used by researchers in the reading domain: (1) They have been constructed using atypical reading data obtained from speeded reading-aloud tasks and/or under degraded presentation conditions; (2) they only include letters from the English alphabet. Although some letter visual-similarity matrices have been constructed using data gathered from normal reading conditions, these either are based on old fonts, which may not resemble the letters found in modern print, or were never published. For the first time, this article presents a comprehensive letter visual-similarity/confusability matrix that has been constructed based on untimed responses to clearly presented upper- and lowercase letters that are present in many languages that use Latin-based alphabets, including Catalan, Dutch, English, French, Galician, German, Italian, Portuguese, and Spanish. Such a matrix will be useful for researchers interested in the processes underpinning reading and literacy acquisition.     

Cognitive precedence for local information in hierarchical stimulus processing by pigeons

Four experiments investigated the processing of hierarchical stimuli by pigeons. Using a 4 alternative divided-attention task, 4 pigeons were food-reinforced for accurately identifying letters arranged as either hierarchical global- or local-relevant stimuli or as size-matched filled stimuli. Experiment 1 found that task acquisition was faster with local-relevant than global-relevant stimuli. This difference was not due to letter size. Experiment 2 demonstrated successful transfer to a novel irrelevant letter configuration. Experiments 3 and 4 tested pigeons' responses to conflict probe stimuli composed of equally discriminable relevant letters at each level. These tests revealed that all of the pigeons showed a cognitive precedence for local information early in processing, with the pigeons using different cues to initiate the processing of global information. This local advantage contrasts with previously reported results for humans and pigeons but is similar to that reported for nonhuman primates. Alternatives attempting to reconcile these contrasting comparative results are considered.     

Processing of sequentially presented letters

The effect on the number of letters S can report of the duration of each sequentially presented letter was compared with that of processing time, defined as the time from the onset of a letter to the onset of the next letter. Four Ss were each shown 1250 common English words, from four to eight letters long, one letter at a time. Each letter acted as a visual noise field for the preceding letter. The duration of each letter and the interval between letters was varied independently. The S reported the letters he saw after each word was displayed. It was found that the processing time (onset to onset) predicted the number of letters correctly reported, regardless of the partition between on time and off time. A calculation was made of the number of milliseconds of on plus off time that are needed to ensure correct report of each letter. This time was independent of the duration of the processing time, but was positively correlated with the number of letters in the word. This correlation is probably in part artifactual, so that no claim can be made that it takes longer to process a letter of a long as compared to a short word.     

Processing of tachistoscopic displays with controlled order of characters and spaces

The task used was designed to force Ss consistently to process the letters of a tachistoscopic display in the same spatial order, if Ss are able to process the letters in a brief display serially and if Ss have enough voluntary control over the selection of a processing order to use the order chosen by the E. In the main series of experiments the set of slides shown in each session included slides having a blank space in some position in the linear array of letters. For control, no-blank slides, a sharp, monotonic decrease in the percentage of correct detections of a signal letter with distance of the signal letter from the focusing dot was obtained. An unexpected result from the slides having a blank space was that detection of the signal letter was considerably more accurate on the slides having a blank space immediately following the signal letter than on the control slides having no blank space or the slides having a blank space immediately before the signal letter in the processing order. In one experiment blank spaces were replaced by black rectangles with no substantial change in the pattern of results. The results from the slides having a blank space or a black rectangle were interpreted as indicating that the onset of processing the image of a letter was determined by the distance in the display from the focusing dot to the letter and that the duration of processing an image of a letter was determined by the distance in the display from the letter to the next letter in the processing order.     

Short-term retention of visually presented stimuli: some evidence of visual encoding.

Subjects saw two visual stimuli on each trial, separated by an interval ranging from 0 to 8 sec. Each stimulus was composed of a subset of the dots of a 7 × 5 dot matrix. In particular, it was a composite of two patterns, one of which formed a capital English letter and the other of which was an arrangement formed by 8 randomly selected dots. The task was to decide as quickly as possible whether the two stimuli contained the same letter. Under one condition (correlated noise) the same noise pattern was used with both letters; thus the decision as to whether the letters were the same could be based on a test of congruence of the two stimuli, noise and all. Under another condition (uncorrelated noise) the noise patterns differed, assuring that the composite patterns differed, and thus precluding congruence testing as an adequate way to determine whether the two letters were the same. Performance was better (RTs and error rates were smaller) with the correlated noise than with the uncorrelated noise. The result was taken as evidence that visual information was retained in memory, and used to advantage, when the situation clearly warranted the direct comparison of visual patterns.     

A comparison of tactile and blurred visual form perception

Two experiments were performed to assess the similarity of tactile form perception and visual form perception under conditions of extreme visual blurring. In the first experiment, resolution and relative localization tasks were performed by five subjects under both tactile and blurred visual presentation. The results obtained here were the same for the two modalities. In the second experiment, all 26 block letters were presented to each of four subjects in two distinct methods of presentation, using both tactile and blurred visual displays. In one method, the full-field letter was flashed for 1.0 sec; in the other, a vertical slit scanned the letter from left to right. For all method comparisons, a strong similarity was found between the patterns of correct responses as a function of letter. In addition, there was a definite similarity between the two modalities in terms of which letters improved in recognizability in the change from the full-field to the slit mode of presentation. However, the overall superiority of the slit method found for tactile recognition was not obtained visually. The two experiments indicate that recognition with blurred vision is similar to recognition using the intact cutaneous sense, although some differences remain.     

Learning of letter names follows similar principles across languages: Evidence from Hebrew

Letter names play an important role in early literacy. Previous studies of letter name learning have examined the Latin alphabet. The current study tested learners of Hebrew, comparing their patterns of performance and types of errors with those of English learners. We analyzed letter-naming data from 645 Israeli children who had not begun formal reading instruction: a younger group (mean age 5 years 2 months) and an older group (mean age 6 years 2 months). Children's errors often involved letters with similar shapes or letters adjacent to one another in the alphabet. Most Hebrew letter names are not very similar to one another phonologically, and there were fewer phonologically based confusions than in English. We found both general frequency effects and frequency effects that reflected the letters in individual children's names. On average, girls knew more letter names than did boys. The results suggest that letter name learning follows similar principles across languages.     

Reaction time as a measure of inter- and intraobject visual similarity: Letters of the alphabet

Interobject visual similarity is often measured by the time that subjects require to say that two objects are not identical, with long RTs indicating high similarity. In Experiment 1, using a complete set of uppercase alphabetic stimuli, we show: (1) RTs correlate strongly with direct ratings of visual similarity. (2) Stimuli that are similar as measured by RT or by direct judgment have the same profile of similarity to all other stimuli in the set as measured by correlational analysis. (3) The order in which the stimuli are compared has only a small effect on measured similarity. All of these results indicate desirable properties of any measure of similarity.Intraobject similarity is a concept pertinent to the relation of an object to itself. In Experiments 1 and 2 we show: (1) All letters are not equally similar to themselves, since RT for the “same” response is different for different letters. (2) The relation between RT and intraobject similarity is opposite to that for interobject similarity, with short RTs indicating high intraobject similarity. (3) Even though intraobject similarities differ, each letter is more similar to itself than to any other letter in the set. We discuss the implications of these results in terms of assumed proximity constraints underlying similarity data.     

Second-order mappings in grapheme–color synesthesia

Typically, the search for order in grapheme–color synesthesia has been conducted by looking at the frequency of certain letter–color associations. Here, we report stronger associations when second-order similarity mappings are examined—specifically, mappings between the synesthetic colors of letters and letter shape, frequency, and position in the alphabet. The analyses demonstrate that these relations are independent of one other. More strikingly, our analyses show that each of the letter–color mappings is restricted to one dimension of color, with letter shape and ordinality linked to hue, and letter frequency linked to luminance. These results imply that synesthetic associations are acquired as the alphabet is learned, with associations involving letter shape, ordinality, and frequency being made independently and idiosyncratically. Because these mappings of similarity structure between domains (letters and colors) are similar to those found in numerous other cognitive and perceptual domains, they imply that synesthetic associations operate on principles common to many aspects of human cognition.     

Sources of interference in the attentional blink: target-distractor similarity revisited

Observers monitored streams of words or letters (10 items/sec) for one or two targets. An attentional blink (AB) effect was observed in which identification of the first target temporarily impaired identification of the second target. Target identification was impaired when the distractors were composed of either letters or false-font characters (cf. Maki, Couture, Frigen, & Lien, 1997). An asymmetrical AB effect was observed with letters and mathematical symbols; the AB effect was largest for symbol targets and letter distractors. The characters used in these experiments were rated on their meaningfulness, familiarity, and other stimulus properties. The rating data showed that pixel density best accounted for the asymmetrical target-distractor similarity effects. Modulation of the AB effect by target-distractor similarity appears to result partly from low-level masking. But masking effects may be reduced by attentional capture by target features.     

Discrimination of intentional and random motion paths by pigeons

Twelve pigeons (Columba livia) were trained on a go/no-go schedule to discriminate between two kinds of movement patterns of dots, which to human observers appear to be "intentional" and "non-intentional" movements. In experiment 1, the intentional motion stimulus contained one dot (a "wolf") that moved systematically towards another dot as though stalking it, and three distractors ("sheep"). The non-intentional motion stimulus consisted of four distractors but no stalker. Birds showed some improvement of discrimination as the sessions progressed, but high levels of discrimination were not reached. In experiment 2, the same birds were tested with different stimuli. The same parameters were used but the number of intentionally moving dots in the intentional motion stimulus was altered, so that three wolves stalked one sheep. Despite the enhanced difference of movement patterns, the birds did not show any further improvement in discrimination. However, birds for which the non-intentional stimulus was associated with reward showed a decline in discrimination. These results indicated that pigeons can discriminate between stimuli that do and do not contain an element that human observer see as moving intentionally. However, as no feature-positive effect was found in experiment 1, it is assumed that pigeons did not perceive or discriminate these stimuli on the basis that the intentional stimuli contained a feature that the non-intentional stimuli lacked, though the convergence seen in experiment 2 may have been an effective feature for the pigeons. Pigeons seem to be able to recognise some form of multiple simultaneously goal-directed motions, compared to random motions, as a distinctive feature, but do not seem to use simple "intentional" motion paths of two geometrical figures, embedded in random motions, as a feature whose presence or absence differentiates motion displays. Electronic Publication     

Naming and locating simultaneously and sequentially presented letters

Two letters varying in level of confusability were presented either simultaneously for 75 msec or sequentially for 75 msec each in adjacent retinal locations. The retinal locus of presentation varied from trial to trial, and subjects both identified and located the presented letters. Identification accuracy was higher on nonconfusable than on confusable letter pairs in the simultaneous condition, but not in the sequential condition. This result is interpreted as support for the notion that inhibition between similar or identical features shared by confusable letters occurs only when letters are presented simultaneously. A relative position effect, with performance on the peripheral letter higher than on the central letter, was found for simultaneously and second sequentially presented letters, but not for first sequentially presented letters. This result is interpreted in terms of the assumption that feature perturbations, with foveal perturbations more likely than peripheral perturbations, affect simultaneously and secondpresented letters, but not first-presented letters. The pattern of results for relative location accuracy showed many of the same effects as identification performance. A model assuming location errors reflect feature transpositions is outlined and is able to account for the absolute and relative location results and the correlation between relative location and identification accuracy.     

Letter Interactions in Brief Visual Displays

Three experiments were conducted to examine the influence of non-target letters on target detection performance. It was hypothesised that letters which are similar would exert a stronger masking influence on each other than letters which have a low level of feature similarity. The results indicate, however, that every letter has the same inhibitory potential regardless of its similarity rating to other letters. The highly significant letter interactions which did occur in the study were interpreted as evidence for an additive, rather than a subtractive, influence by the non-targets. It is proposed that when a target has an ambiguous identity, due to an impoverished representation, it may be disambiguated by the addition of feature information from the immediate letter context. The effect of filling in the target representation with a feature value from a non-target letter will be to weight the final representation towards the target which has the value most similar to the one substituted. In a sense, then, non-targets which are similar to a target can actually enhance target detection scores.     

Features versus redundancy: comments on Massaro, Venezky, and Taylor's "Orthographic regularity, positional frequency, and visual processing of letter strings"

Massaro, Venezky, and Taylor (1979) found only a modest effect of familiarity on letter search, apparently because they pitted pseudowords (rather than real words) against nonwords and used lowercase rather than uppercase letters. Precuing the target letter seemed to reduce the familiarity effect they found yet further, but this conclusion is clouded by the fact that reaction time data were compared with accuracy data. Because similarity between target and nontarget letters tended to have more of an effect when familiarity had less of an effect. Massaro et al. proposed a successive model, with features being detected in the first stage and orthographic structure being used in a second stage. However, a concurrent model, with a self-terminating race between lower and higher level processes, can account for the data just as well. Data from Massaro et al. and from Krueger decisively demonstrate that there is a familiarity effect based on sequential redundancy over and above any effect based on spatial redundancy (Mason 1975). The Massaro et al. data also indicate that the relative familiarity effect is constant across various age groups (Krueger, Keen & Rublevich, 1974).     

Wholistic and analytic stimulus processing: The development of selective perceptual strategies

This experiment reports an investigation of the development of selective processing strategies as subjects become increasingly more practised at a serial self-paced RT task. It demonstrates the effect a preceding stimulus can have on the analysis of a current signal and the development of active analytic strategies in favour of passive wholistic processing, with practice. The stimuli used were letters with irrelevant visual noise dot patterns superimposed on them. The letter, or the dot pattern, or both, could be repeated on successive trials. Early in practice repetition of both stimulus components simultaneously produced short reponse latencies relative to repetition of the letter alone. The number of noise dots markedly affected RT. Late in practice, however, letter repetition RTs were small, irrespective of whether or not the noise dot pattern was repeated. Furthermore, the number of noise dots no longer had an effect on the RT to these stimulus transitions. The results suggest that subjects appear to be able to select relevant information to process as they become progressively more practised, even though there is evidence that they compare the current stimulus with an iconic representation of the immediately preceding one.