30 June 2015 Surface reconstruction from photometric normals with reference height measurements
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Abstract
In the dome imaging system at UCL, sets of pixel-registered images can be captured, with a different direction of illumination for each image. A new method has been developed to estimate surface normals more accurately by solving the photometric normal equations as a regression over a set of illumination angles and intensities selected from the subset corresponding to the diffuse component of reflection from the object surface (the 'body colour'). The gradients are integrated to reconstruct a digital terrain map, using a Fourier transform to regularise (i.e. enforce integrability of) the gradients in the frequency domain. This yields a 3D surface that is continuous but distorted over the whole area with the height greatly amplified. The problem is that although the gradients give a good representation of the spatial frequencies in the surface, right up to the Nyquist frequency, they are not accurate for very low frequencies of a few cycles over the full object diameter. Such frequencies are represented in the Fourier plane by only a few sample points close to the (shifted) origin. Errors in these frequencies can result in 'curl' or 'heave' in the baseplane, even though the superimposed higher spatial frequencies may be accurate. The solution is to replace the inaccurate low frequencies of the photometric normals by the more accurate low frequencies of a surface constructed from a few known heights. This is conveniently achieved from the values measured by a digital height gauge by interpolating to produce a smooth ‘hump’ and then transforming into the frequency domain by an FFT.
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Lindsay W. MacDonald, Lindsay W. MacDonald, } "Surface reconstruction from photometric normals with reference height measurements", Proc. SPIE 9527, Optics for Arts, Architecture, and Archaeology V, 952706 (30 June 2015); doi: 10.1117/12.2184980; https://doi.org/10.1117/12.2184980
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