Computational imaging enables retrieval of the spatial information of an object with the use of single-pixel detectors. By projecting a series of known random patterns and measuring the backscattered intensity, it is possible to reconstruct a two-dimensional (2D) image. We used several single-pixel detectors in different locations to capture the 3D form of an object. From each detector we derived a 2D image that appeared to be illuminated from a different direction, even though only a single digital projector was used for illumination. From the shading of the images, the surface gradients could be derived and the 3D object reconstructed. We compare our result to that obtained from a stereophotogrammetric system using multiple cameras. Our simplified approach to 3D imaging can readily be extended to nonvisible wavebands.
An analysis of data on the duration times and waiting times for eruptions from the Old Faithful Geyser reveals an interesting time series structure. A tentative physical model, derived from Rinehart, is outlined and a corresponding first-order Markov chain examined. It is shown that a second-order model is necessary to explain the observed correlations in the data. A curious clustering effect is apparent in the autocorrelation function when plotted over a large range of lags. Similar patterns are observed in simulations from the fitted second-order model.
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