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Keith May, Robert Hess; Implementing curve detectors for contour integration. Journal of Vision 2009;9(8):906. doi: 10.1167/9.8.906.
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© 2016 Association for Research in Vision and Ophthalmology.
We recently presented a model of contour integration in which grouping occurs due to the overlap of filter responses to the different elements [May, K.A. & Hess, R.F. (2008). Journal of Vision, 8(13):4, 1–23]. The image receives two stages of oriented filtering, separated by a nonlinearity. Then the filter output is thresholded to create a set of zero-bounded regions (ZBRs) within each orientation channel. Finally, spatially overlapping ZBRs in neighbouring orientation channels are linked to form 3D ZBRs within the space formed by the two dimensions of the image along with a third dimension representing orientation. If the 1st and 2nd stage filters have the same orientation, the model detects snakes, in which the elements are parallel to the contour path; if the 1st and 2nd stage filters are orthogonal, the model detects ladders, in which the elements are perpendicular to the path. The model detects both straight and curved contours, and correctly predicts that detection of ladders is largely unaffected by contour smoothness, but fails to explain the finding that jagged snakes are harder to detect than smooth snakes that follow an arc of a circle. The advantage for smooth snakes, and several other findings, suggest that the primitive features detected by snake-integration mechanisms are fragments of contour with constant sign of curvature. A detector for any shape of contour can be created by summing spatially shifted outputs from different orientation channels: this is equivalent to filtering with a receptive field that matches the desired shape, and would be simple to implement physiologically. We extended our earlier model by combining filter outputs in this way to create detectors for smooth contour fragments with a range of different curvatures. This approach makes the model more robust to noise, and explains the advantage for smoothly curved snakes.
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