We explore the application to underwater imagery of the photometric stereo technique- the recovery of 3-D shape from three or more images of the same scene acquired under different lighting conditions. Ignoring back-scatter effects, we generalize McGlamery's model - expressing the image in terms of two direct and small-angle forward-scattered components- to devise a recursive 3-D shape reconstruction technique. By correction for certain range-dependent effects in underwater imagery- e.g., due to the medium attenuation, point source spreading loss, and irradiance gain from small-angle forward scattering- that are responsible for deviations from the land model, we construct rectified images in order to apply a closed-form solution based on the land image model of a Lambertian surface under collimated-source illumination. The method requires knowledge of the medium attenuation coefficient- readily measured from standard instruments (e.g., AC-9 )- and is relatively robust with respect to rought estimates of two other empirical parameters that approximated by the tabulated values of the absorption and total scattering coefficients for different bodies of water. Experimental results with images acquired under a variety of medium conditions are presented to demonstrate performance.
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