Seeing edge blur: receptive fields as multiscale neural templates

Edge blur is an important perceptual cue, but how does the visual system encode the degree of blur at edges? Blur could be measured by the width of the luminance gradient profile, peak ^ trough separation in the 2nd derivative profile, or the ratio of 1st-to-3rd derivative magnitudes. In template models, the system would store a set of templates of different sizes and find which one best fits the `signature' of the edge. The signature could be the luminance profile itself, or one of its spatial derivatives. I tested these possibilities in blur-matching experiments. In a 2AFC staircase procedure, observers adjusted the blur of Gaussian edges (30% contrast) to match the perceived blur of various non-Gaussian test edges. In experiment 1, test stimuli were mixtures of 2 Gaussian edges (eg 10 and 30 min of arc blur) at the same location, while in experiment 2, test stimuli were formed from a blurred edge sharpened to different extents by a compressive transformation. Predictions of the various models were tested against the blur-matching data, but only one model was strongly supported. This was the template model, in which the input signature is the 2nd derivative of the luminance profile, and the templates are applied to this signature at the zero-crossings. The templates are Gaussian derivative receptive fields that covary in width and length to form a self-similar set (ie same shape, different sizes). This naturally predicts that shorter edges should look sharper. As edge length gets shorter, responses of longer templates drop more than shorter ones, and so the response distribution shifts towards shorter (smaller) templates, signalling a sharper edge. The data confirmed this, including the scale-invariance implied by self-similarity, and a good fit was obtained from templates with a length-to-width ratio of about 1. The simultaneous analysis of edge blur and edge location may offer a new solution to the multiscale problem in edge detection.

Binocular fusion, suppression and diplopia for blurred edges

Purpose: (1) To devise a model-based method for estimating the probabilities of binocular fusion, interocular suppression and diplopia from psychophysical judgements, (2) To map out the way fusion, suppression and diplopia vary with binocular disparity and blur of single edges shown to each eye, (3) To compare the binocular interactions found for edges of the same vs opposite contrast polarity. Methods: Test images were single, horizontal, Gaussian-blurred edges, with blur B = 1-32 min arc, and vertical disparity 0-8.B, shown for 200 ms. In the main experiment, observers reported whether they saw one central edge, one offset edge, or two edges. We argue that the relation between these three response categories and the three perceptual states (fusion, suppression, diplopia) is indirect and likely to be distorted by positional noise and criterion effects, and so we developed a descriptive, probabilistic model to estimate both the perceptual states and the noise/criterion parameters from the data. Results: (1) Using simulated data, we validated the model-based method by showing that it recovered fairly accurately the disparity ranges for fusion and suppression, (2) The disparity range for fusion (Panum's limit) increased greatly with blur, in line with previous studies. The disparity range for suppression was similar to the fusion limit at large blurs, but two or three times the fusion limit at small blurs. This meant that diplopia was much more prevalent at larger blurs, (3) Diplopia was much more frequent when the two edges had opposite contrast polarity. A formal comparison of models indicated that fusion occurs for same, but not opposite, polarities. Probability of suppression was greater for unequal contrasts, and it was always the lower-contrast edge that was suppressed. Conclusions: Our model-based data analysis offers a useful tool for probing binocular fusion and suppression psychophysically. The disparity range for fusion increased with edge blur but fell short of complete scale-invariance. The disparity range for suppression also increased with blur but was not close to scale-invariance. Single vision occurs through fusion, but also beyond the fusion range, through suppression. Thus suppression can serve as a mechanism for extending single vision to larger disparities, but mainly for sharper edges where the fusion range is small (5-10 min arc). For large blurs the fusion range is so much larger that no such extension may be needed. © 2014 The College of Optometrists.