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T.J. Atherton, S.J. Hinds, K. Langley; Orientation-texture-defined edges: a computational model. Journal of Vision 2002;2(7):236. doi: https://doi.org/10.1167/2.7.236.
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© ARVO (1962-2015); The Authors (2016-present)
A two-stage model of second order processing is proposed. The model is an extension of the familiar “filter-rectify-filter” scheme. There are two stages; stage 1, filter(1)-nonlinearity-orientation_pooling(1), followed by a second stage applied to each of the outputs of the first stage, filter(2)-nonlinearity-orientation_pooling(2). This unifies second-order processes for the detection of spatial location, orientation of contrast modulations, and texture defined form. The first stage of the model; filter(1) is a bank of linear bandpass filters of equal spatial frequency but different orientations. The non-linearity finds the energy response of each of these first stage filter outputs, which are passed through a Fourier transform, that “pools” over orientation. The magnitude and phase of these Fourier coefficients enables detection of the presence and orientation, respectively, of, eg, lines and edges. Each complex response from the first stage is passed to a separate second stage of processing whose purpose is to detect second-order structure. The second stage; filter(2) is similar to the first, but with the peak tuning frequency reduced by at least two octaves. Two symmetries from the first stage Fourier transform over orientation are examined, E0 and E2. The first, E0, refers to the total energy of the image signal. The second stage processing of this signal leads to the detection of spatial contrast variations. The second, E2, refers to the oriented energy present in the image signal. The second stage processing of this signal leads to the detection of orientation-texture-defined form. In respect of luminance boundaries, contrast variation boundaries and boundaries of orientation-texture-defined form, the model explains the condition when these boundaries are most salient, it occurs when the phase differences in the outputs of the first stage across a boundary is at 180 degrees, whether luminance defined, or texture defined.
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