Visuospatial interpolation in typically developing children and in people with Williams Syndrome

Abstract

Visuospatial interpolation is the estimation of object position or contour shape computed from known "anchor" positions. We characterized the developmental profile of interpolation by measuring positional thresholds as a function of inter-element separation without (Experiment 1) and with (Experiment 2) the context of illusory contours in typically developing children, typical adults and individuals with Williams Syndrome (WS), a genetic disorder that causes impaired global visuospatial abilities. We found that typically developing children and WS individuals had more difficulty integrating information across distant elements than typical adults. However, illusory contours improved thresholds in all participant groups in a similar way. Our results suggest that in WS individuals, and in typically developing children, the grouping mechanisms that enable long-range spatial integration are immature. We hypothesize that WS individuals and young children can use stimulus-driven grouping cues for bottom-up integration, but have immature mechanisms for top-down integration of spatial information.

Figure 1

Predictions for three-point Vernier tasks. (a) Vertical translation of interpolation function without a change in slope (b) Change in the slope of the interpolation function. Solid lines represent thresholds of WS and dashed lines represent thresholds of normal adults. See text and Supplementary introduction for details.

Figure 2

Schematic of stimuli in Experiment 1 (not drawn to scale). Observers were asked which group of squares, left or right, was misaligned. We measured positional offset thresholds as a function of inter-element separation (1.5, 3.0, 4.5, 6.0 and 11.5 deg).

Figure 3

Positional thresholds as a function of inter-element separation in Experiment 1. Solid lines represent threshold functions with slopes of (a) 1.62 for WS, (b) 1.61 for 3–4 year olds, (c) 1.40 for 5–6 year olds and (d) 1.29 for 7–9 year olds. Dashed lines in all panels represent threshold function for normal adults with a slope of 1.03. Thresholds of WS and normal 3–4 year olds are not significantly different. Thresholds of normal children improve with increasing age.

Figure 4

Schematic of stimuli used in the (a) illusory contour condition and (b) control condition of Experiment 2 (not drawn to scale). Observers were asked which group of objects, left or right, was misaligned.

Figure 5

Data for WS individuals and normal adults in Experiment 2. (a) In the WS group, interpolation functions had slopes of 1.48 and 1.21 for the control and illusory contour conditions, respectively. (b) In normal adults, slopes were 1.01 and 0.77. Illusory contours improved positional thresholds at larger inter-element separations.

Figure 6

Data for normal children in Experiment 2. (a) 3–4 year olds had interpolation functions with slopes of 1.46 and 1.12 for the control and illusory contour conditions, respectively. (b) In 5–6 year olds, slopes were 1.50 and 1.15. (c) In 7–9 year olds, slopes were 1.28 and 0.79. Illusory contours improved positional thresholds at larger inter-element separations.

Figure 7

Interpolation functions in the (a) control and (b) illusory contour condition for all participants.

Figure A1

Prediction 1 shows that positional thresholds follow Weber’s Law in log-log coordinates (left) and in linear-linear coordinates (right).

Figure A1

Prediction 1 shows that positional thresholds follow Weber’s Law in log-log coordinates (left) and in linear-linear coordinates (right).

Figure A2

Normalized positional thresholds from Prediction 1 in log-log coordinates (left) and in linear-linear coordinates (right).

Figure A2

Normalized positional thresholds from Prediction 1 in log-log coordinates (left) and in linear-linear coordinates (right).

Figure A3

Prediction 2 shows that positional thresholds of typical adults follow Weber’s Law, while thresholds of WS individuals follow Power law in log-log coordinates (left) and in linear-linear coordinates (right).

Figure A3

Prediction 2 shows that positional thresholds of typical adults follow Weber’s Law, while thresholds of WS individuals follow Power law in log-log coordinates (left) and in linear-linear coordinates (right).

Figure A4

Normalized positional thresholds from Prediction 2 in log-log coordinates (left) and in linear-linear coordinates (right).

Figure A4

Normalized positional thresholds from Prediction 2 in log-log coordinates (left) and in linear-linear coordinates (right).