figure2.png

Figure 2: From an impulse to a Motion Cloud. (A) The movie corresponding to a typical edge", i.e., a moving Gabor patch that corresponds to a localized grating. The Gabor patch being relatively small, for clarity, we zoomed 8 times into the non-zeros values of the image. (B): By densely mixing multiple copies of the kernel shown in (A) at random positions, we obtain a Random Phase Texture (RPT), see Supplemental Movie 1. (C): We show here the envelope of the Fourier transform of kernel $K$: inversely, $K$ is the impulse response in image space of the filter defined by this envelope. Due to the linearity of the Fourier transform, apart from a multiplicative constant that vanishes by normalizing the energy of the RPT to $1$, the spectral envelope of the RPT in (B) is the same as the one of the kernel K shown in (A): $\mathcal{E}_{\bar{\beta}}=\mathcal{F}(K)$. Note that, the spectral energy envelope of a classical" grating would result in a pair of Dirac delta functions centered on the peak of the patches in (C) (the orange hot-spots"). Motion Clouds are defined as the subset of such RPTs whose main motion component is a full-field translations and thus characterized by spectral envelopes concentrated on a plane.}

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