Evidence for curvilinear interpolation from dot alignment judgements.

Visual interpolation between dots responsible for rectilinear versus curvilinear contour interpretation was examined with the psychophysical forced directional response (FDR) paradigm. Regular four-dot polygon segments, together with a target dot, were presented to the subjects for 150 ms. Subjects were required to indicate the direction of deviation of the target dot from the midpoint of the intermediate line segment. Crucial variables were the outer angle of the line segments and symmetry axis orientation of the polygon segment. Logistic regression analyses showed that curvilinear interpolation occurred for angles up to 30 degrees, but emerged more pervasively under the vertical symmetry axis orientation for angles up to 60 degrees.

The perceptual centre of a stimulus as the cue for synchronization to a metronome: evidence from asynchronies.

In tasks where subjects are required to tap in synchrony to a sequence of evenly spaced uniform auditory stimuli (a metronome), tap onsets typically tend to anticipate the metronome's stimulus onsets. We investigated this phenomenon, called "negative asynchrony", as a function of (1) the duration of the stimuli (1 or 2, 50, 100, and 300 msec), (2) the rise time of the stimuli (0%, 40%, and 80% of stimulus duration), and (3) the interstimulus onset interval duration (500, 700, and 900 msec). The results from three experiments with 28 different subjects showed a significant reduction of the negative asynchrony with longer stimulus durations, and the reduction was not significantly affected by the tempo of the stimulus sequence. Also, a prolongation of the rise time of the stimuli caused an analogous reduction of the negative asynchrony. Findings were taken to suggest that subjects use the perceptual centre rather than physical onset of stimulus as the cue with which to synchronize their responses to metronome stimuli. It is concluded that perceptual processes play an important role in synchronization.

Melodic cues for metre.

A method of time-series analysis and a time-beating experiment were used to test the structural and perceptual validity of notated metre. Autocorrelation applied to the flow of melodic intervals between notes from thirty fragments of compositions for solo instruments by J S Bach strongly supported the validity of bar length specifications. Time-beating data, obtained with four stimuli from the same set, played in an expressionless mode, and presented under categorically distinct tempos to different subgroups of musically trained subjects, were rather inconsistent with respect to tapped bar lengths. However, taps were most frequently given to the events in the stimuli that corresponded with the first beats according to the score notations. No significant effects of tempo on tapping patterns were observed. The findings are discussed in comparison with other examinations of metre inference from musical compositions.

Perceived location of two-dimensional patterns.

The study attempted to test the possibility that the center of gravity of two-dimensional patterns is the cue used by a human observer for their localization. Four experiments were carried out. The first, using a matching procedure, required the localization of the center of irregular dot patterns, contour and filled polygons which varied in size and orientation. In the other three experiments the subjects had to point to briefly exposed dot patterns in which overall shape (convex and concave in Expts 2 and 3) and dot density (Expt 4) were manipulated. The performance of these direct localization tasks was found to be as accurate as the performance in previous studies of indirect localization or regular patterns. The results consistently supported the claim that information about position of the center of gravity is used for the localization of visual objects.

Size invariance in visual number discrimination.

This study deals with the observer's ability to discriminate the numerosity of two random dot-patterns irrespective of their relative size. One of these two patterns was a reference one that was always composed of 32 dots randomly distributed within a K x K invisible square window (K = 1.92 degrees). The second one was the test pattern with one of the five magnifications (K = 0.64 degrees, 1.28 degrees, 1.92 degrees, 2.56 degrees, 3.20 degrees) and the relative number of dots varied on 11 levels (N = -15, -12, -9, -6, -3, 0, 3, 6, 9, 12, or 15 dots). The observer's task was to indicate which of the two patterns contained more dots. The results show that the stimulus size, as an irrelevant stimulus attribute, can be ignored in the judgements about relative numerosity. This means that the perceived numerosity is size invariant, at least for a 1.6-times magnification and a 3-times reduction of the test pattern. The size invariance observed constrains the range of potential models, since the perceived numerosity can be identified only by means of a feature of the stimulus that will remain invariant after any change in the absolute stimulus size.

Precision and accuracy in the reproduction of simple tone sequences.

In four experiments we investigated the precision and accuracy with which amateur musicians are able to reproduce sequences of tones varied only temporally, so as to have tone and rest durations constant over sequences, and the tempo varied over the musically meaningful range of 5-0.5 tones per second. Experiments 1 and 2 supported the hypothesis of attentional bias toward having the attack moments, rather than the departure moments, precisely times. Experiment 3 corroborated the hypothesis that inaccurate timing of short interattack intervals is manifested in a lengthening of rests, rather than tones, as a result of larger motor activity during the reproduction of rests. Experiment 4 gave some support to the hypothesis that the shortening of long interattack intervals is due to mnemonic constraints affecting the rests rather than the tones. Both theoretical and practical consequences of the various findings, particularly with respect to timing in musical performance, are discussed.

The perception of continuous curves in dot stimuli.

Two categorisation experiments are reported in which the perceptual phenomenon that some simple arrays of discrete dots appear as a continuous curve whereas others are perceived as an angular contour or as consisting of separate groups of dots was investigated. Triplets of dots were presented in the first experiment, and complete or incomplete regular dot polygons (ie dots positioned on the vertices of imaginary regular polygons) in the second. In both experiments the perception of a curve versus an angle was determined mainly by the relative orientations of the dots, ie by the angles between successive virtual lines, whereas the lengths of the virtual lines had relatively little influence. In experiment 2 the number of displayed dots was shown to be a second independent factor for perceiving continuity. These results are in agreement with results from experiments on dipole textures discrimination, and suggest the psychological existence and importance of virtual lines in the visual processing of dot stimuli.

A model for the perception of curves in dot figures: the role of local salience of "virtual lines".

In many models of visual information processing the notion of a virtual line or dipole is introduced in order to represent the configurational information, notably length and relative orientation, between identical figure elements in figures with discrete elements. Virtual lines have proven to be very useful in predicting perceptual phenomena (Julesz et al. 1973; Stevens 1978). In the present study, virtual lines are utilized in a model which aims to predict the perception of (dotted) curves in dot figures. Clearly many possible curves, formed by adjacent virtual lines, can be constructed within a set of dots. It is proposed that already at the local level of the virtual lines each line has a perceptual salience which results from the function induced by the global dot figure. It is this local line salience or "connectivity" that directs further processing and determines the curves to be seen in a dot figure. The model presented is an information processing model with a clear modular design. It entails three successive levels of representation. First image functions are derived through a convolution of the input with gaussian distribution functions. Next, a discrete internal representation is extracted from the image function consisting of two primitives; blobs, representing the dots, and virtual lines, representing pairwise relations between blobs. The attributes of the blobs are their positions in the image plane, while those of the virtual lines are length, relative orientation and connectivity. At the third level, the discrete internal representation is used to predict the perceived curves. It is shown that the model has advantages over other approaches, e.g. autocorrelation and network models.

The perception of a dotted line in noise: a model of good continuation and some experimental results.

A formal model is proposed, describing how the perceptual interpretation of dot figures is guided by the Gestalt rule of good continuation. The algorithm will be restricted to figures with a collinear dot array (line) embedded in a background of randomly placed dots. The model, CODE-2, is an elaboration of the model, CODE-1, of grouping dots on the basis of the Gestalt rule of (relative) proximity, and consists of the introduction of non-circular symmetric gaussian distribution functions for the representation of the orientation dependent strength of interaction between collinear dots. Supra-threshold contours of the function, resulting from a superposition on each dot of the gaussian functions, are assumed to predict the perceptual grouping of the dots. A quantitative measure for the perceptual salience of dotted lines was defined as the contrast between the internal coherence of the line dots, and their interference with the noise dots. For 20 stimuli the CODE-2 grouping of the dots is reported, together with the results of a line-in-noise latency experiment. There was a significant correlation between the predicted saliences and the experimental results. The results support the usefulness of representing good continuation between collinear dots by non-circular symmetric gaussian distribution functions.