Abstract
Minimization techniques are widely used for retrieving a 3D surface starting from a single shaded image i.e., for solving the shape from shading problem. Such techniques are based on the assumption that expected surface to be retrieved coincides with the one that minimize a properly developed functional, consisting of several contributions. Among the possible contributes defining the functional, the so called “smoothness constraint” is always used since it guides the convergence of the minimization process towards a more accurate solution. Unfortunately, in areas where actually brightness changes rapidly, it also introduces an undesired over-smoothing effect. The present work proposes two simple yet effective strategies for avoiding the typical over-smoothing effect, with regards to the image regions in which this effect is particularly undesired (e.g., areas where surface details are to be preserved in the reconstruction). Tested against a set of case studies the strategies prove to outperform traditional SFS-based methods.
Highlights
One of the most used methods to retrieve the threedimensional surface of the object represented in a single image is the Shape-from-Shading (SFS) method
Brightness Constraint (BC) is directly derived from the image irradiance and indicates the total brightness error of the retrieved surface compared with the input image: BC = ∫∫(I ( x, y) − R( x, y))2 dxdy ≅ ∑ ( I (i, j) − R(i, j))2 (5) (i, j)∈Ω
The present paper described two simple yet effective strategies for avoiding the over-smoothing effect typically arising using the smoothness constraint for solving the SFS problem with minimization techniques
Summary
One of the most used methods to retrieve the threedimensional surface of the object represented in a single image is the Shape-from-Shading (SFS) method. Under these hypotheses it is possible to formulate a relation between the surface normal N , the unknown of the reconstruction problem and the light unit-vector for each pixel of the image: L ⋅ N (i, j) =
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