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Figure 1: (A) Top: a natural movie with the main motion component consisting of a horizontal, rightward full-field translation. Such a movie would be produced by an eye movement with constant mean velocity to the left (negative $x$ direction), plus some residual, centered jitter noise in the motion-compensated natural scene. We represent the movie as a cube, whose $(x,y,t=0)$ face corresponds to the first frame, the $(x,y=0,t)$ face shows the rightward translation motion as diagonal stripes. As a result of the horizontal motion direction, the $(x=54,y,t)$ face is a reflected image of the $(x,y,t=0)$ face, contracted or dilated depending on the amplitude of motion. The bottom panel shows the corresponding Fourier energy spectrum, as well as its projections onto three orthogonal planes. For any given point in frequency space, the energy value with respect to the maximum is coded by 6 discrete color iso-surfaces (i.e.: 90\%, 75\%, 50\%, 25\%, 11\% and 6\% of peak. The amplitude of the Fourier energy spectrum has been normalized to 1 in all panels and the same conventions used here apply to all following figures. (B) to (C): The image is progressively morphed (A through B to C) into a Random Phase Texture by perturbing independently the phase of each Fourier component. (upper row): Form is gradually lost in this process, whereas (lower row): most motion energy information is preserved, as it is concentrated around the same speed plane in all three cases (the spectral envelopes are nearly identical).

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