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We will use that any smooth vector field fulfills this integrability requirement to design line connection algorithms for contour completion.
This might be related to processes such as optic flow or, especially given the wide-field spread, even contour completion or interpolation.
As an alternative to simulating the neural field models an interface approach (incorporating feature space) may be more useful for understanding how local data can be integrated into global geometrical structures, as advocated in the neurogeometry framework of Petitot [33] (say for understanding models of contour completion in models of primary visual cortex where the feature space is orientation).
According to one class of explanations, the illusory contour induced by Kanizsa figure may prevent saccadic compression but the speed of illusory contour completion depends on the distance between the inducers allowing the re-mapping processes, running in parallel, to remap the visual space in the absence of illusory contours [18].
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However, these are cases of amodal interpolation, where contour or surface completion links two visually specified regions.
It has been suggested by Rubin [1] that T-junctions play a central role in monocular depth perception, surface completion, and contour matching.
Rubin investigated in psychophysical experiments how local occlusion cues, such as T-junctions and more global occlusion cues, specifically relatability and surface similarity, play a role in the emergence of amodal surface completion and illusory contour perception.
It is generally agreed that the perception of such illusory figures depends on the emergence of illusory contours and on the modal completion of the interpolated surface [1].
Consistent with this, the completion of illusory contours [9] and processes of perceptual grouping [8] are stronger when the stimuli appear within the same hemifield than when they cross hemifields.
Such illusory contours can be induced by partially occluded surfaces where the contour of the occluded object is perceptually completed (amodal completion) or where the occluding object has the same luminance than parts of the occluded background (modal completion).
Boundary completion techniques are used in [24] to complete contours that are smooth but have low contrast.
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