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Looking at Op Art from a computational viewpoint.

Arts history tells an exciting story about repeated attempts to represent features that are crucial for the understanding of our environment and which, at the same time, go beyond the inherently two-dimensional nature of a flat painting surface: depth and motion. In the twentieth century, Op artists such as Bridget Riley began to experiment with simple black and white patterns that do not represent motion in an artistic way but actually create vivid dynamic illusions in static pictures. The cause of motion illusions in such paintings is still a matter of debate. The role of involuntary eye movements in this phenomenon is studied here with a computational approach. The possible consequences of shifting the retinal image of synthetic wave gratings, dubbed as 'riloids', were analysed by a two-dimensional array of motion detectors (2DMD model), which generates response maps representing the spatial distribution of motion signals generated by such a stimulus. For a two-frame sequence reflecting a saccadic displacement, these motion signal maps contain extended patches in which local directions change only little. These directions, however, do not usually precisely correspond to the direction of pattern displacement that can be expected from the geometry of the curved gratings as an instance of the so-called 'aperture problem'. The patchy structure of the simulated motion detector response to the displacement of riloids resembles the motion illusion, which is not perceived as a coherent shift of the whole pattern but as a wobbling and jazzing of ill-defined regions. Although other explanations are not excluded, this might support the view that the puzzle of Op Art motion illusions could potentially have an almost trivial solution in terms of small involuntary eye movement leading to image shifts that are picked up by well-known motion detectors in the early visual system. This view can have further consequences for our understanding of how the human visual system usually compensates for eye movements, in order to let us perceive a stable world despite continuous image shifts generated by gaze instability.