Isophotes on a smooth surface related to scene geometry

It is shown, through elementary differential geometry, how the shape of the isophotes on a smooth surface is related to the underlying object and the location of the light source. Taking advantage of the principal directions, several characteristics of the isophotes are expressed, among which the geodesic curvature is emphasized. From these results, a variational method is discussed to estimate the surface shape from the image irradiance, subject to a geodesicity constraint on the isophotes. Finally, a local solid shape characteristic based on the principal curvatures ratio is offered.

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