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Synthetic scene generation models depend on the repeated evaluation or iteration of often computationally expensive functions to create 'texture' or structure in a modeled natural scene. The computational burden of 'texture' function evaluation is dependent upon the spatial frequency response characteristics of the optical system through which the modeled scene is to be 'propagated.' All real 'cameras' utilize detector elements of finite size to transduce the resulting MXN pixels of the image. Two general situations arise in modeling the effects of cameras (sensors) on the imaged scene. The first is the 'oversampled' case where the Nyquist frequency of the detector spacing exceeds the cutoff of the optics transfer (aperture) function. The 'undersampled' case is when such Nyquist frequency is below the aperture cutoff spatial frequency, which results in aliasing. The application of brute force in the oversampled case results in MXN scene 'texture' function evaluations, while for the undersampled case, (mM)X(nN) (m, n > 1) points are required. Several computationally efficient methods significantly reduce the stated brute force computational burden for these two cases. This paper discusses three such methods. For the oversampled case, a correct and efficient method is 2D sample 'interpolation,' in the multirate digital signal processing sense. This method expressly avoids signal aliasing caused by simpler but inappropriate bilinear interpolation of the sparser set of (mM)+(nN) (m, n fractions < 1) scene samples onto the MXN imaged scene. The second and third techniques discussed are applicable to the undersampled case. Each relies upon MXN scene 'texture' function evaluations. The second technique extrapolates the frequency spectrum of the MXN grid with a synthetic spectrum beyond Nyquist which follows the 1/f(beta ) decrease in power typical of natural (fractal) textures. The third technique, 'fractal interpolation,' operates in the spatial domain where spatial detail, generated from the computed ('texture' function) MXN grid onto a larger (nM)X(nN) grid, is synthesized at the same local fractal dimension as that of the MXN 'undersampled' data. In both cases, the synthesized frequencies above the camera Nyquist are 'folded back' in the spectral domain to approximate the aliasing of spatial frequencies into the transduced image.
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