Incomplete Figure Perception and Invisible Masking

The Gollin test (measuring recognition thresholds for fragmented line drawings of everyday objects and animals) has traditionally been regarded as a test of incomplete figure perception or ‘closure’, though there is a debate about how such closure is achieved. Here, figural incompleteness is considered to be the result of masking, such that absence of contour elements of a fragmented figure is the result of the influence of an ‘invisible’ mask. It is as though the figure is partly obscured by a mask having parameters identical to those of the background. This mask is ‘invisible’ only consciously, but for the early stages of visual processing it is real and has properties of multiplicative noise. Incomplete Gollin figures were modeled as the figure covered by the mask with randomly distributed transparent and opaque patches. We adjusted the statistical characteristics of the contour image and empty noise patches and processed those using spatial and spatial-frequency measures. Across 73 figures, despite inter-subject variability, mean recognition threshold was always approximately 15% of total contour in naive observers. Recognition worsened with increasing spectral similarity between the figure and the ‘invisible’ mask. Near threshold, the spectrum of the fragmented image was equally similar to that of the ‘invisible’ mask and complete image. The correlation between spectral parameters of figures at threshold and complete figures was greatest for figures that were most easily recognised. Across test sessions, thresholds reduced when either figure or mask parameters were familiar. We argue that recognition thresholds for Gollin stimuli in part reflect the extraction of signal from noise.

Complexity of Images: Experimental and Computational Estimates Compared

We tested whether visual complexity can be modeled through the use of parameters relevant to known mechanisms of visual processing. In psychophysical experiments observers ranked the complexity of two groups of stimuli: 15 unfamiliar Chinese hieroglyphs and 24 outline images of well-known common objects. To predict image complexity, we considered: (i) spatial characteristics of the images, (ii) spatial-frequency characteristics, (iii) a combination of spatial and Fourier properties, and (iv) the size of the image encoded as a JPEG file. For hieroglyphs the highest correlation was obtained when complexity was calculated as the product of the squared spatial-frequency median and the image area. This measure accounts for the larger number of lines, strokes, and local periodic patterns in the hieroglyphs. For outline objects the best predictor of the experimental data was complexity estimated as the number of turns in the image, as Attneave (1957 Journal of Experimental Psychology53 221–227) obtained for his abstract outlined images. Other predictors of complexity gave significant but lower correlations with the experimental ranking. We conclude that our modeling measures can be used to estimate the complexity of visual images but for different classes of images different measures of complexity may be required.