Variational Perspective Shape from Shading

Direct Variational Perspective Shape from Shading with Cartesian Depth Parametrisation

“…where Ψ is the Charbonnier function [13] Ψ (s 2 ) = 2λ 2 1 + s 2 λ 2 (15) with contrast parameter λ . Such higher-order smoothness terms have already been successfully applied in the context of perspective SfS parametrised in terms of the radial depth [29], orthographic SfS [49], image denoising [31], optical lithography [21] and motion estimation [18]. Finally, the use of the confidence function c in the data term allows to exclude unreliable image regions which have been identified a priori, e.g.…”

“…by a texture detector or by a background segmentation algorithm. Such functions are particularly useful in the context of real-world images that contain texture, noise, or missing data [17,29]. Properties.…”

“…So far, however, there are only a few works in the literature that deal with this recent idea. On the one hand, there is the work of Ju et al [29] that embeds the PDE of Prados et al [39] as data term into a variational model and complements it with a discontinuity-preserving second order smoothness term. However, since the approach penalises deviations from the PDE directly and uses a parametrisation in terms of the radial depth, deviations in both the data and the smoothness term are difficult to interpret geometrically or photometrically.…”

“…This, however, contradicts the idea of introducing robustness into the estimation -in particular in the presence of noise or missing data. In contrast, the other two methods estimate the solution from scratch [29,52]. However, those methods do not provide any quantitative assessment of the reconstruction quality.…”

Two Simple Yet Effective Strategies for Avoiding Over-Smoothing in SFS Problem

“…As detailed in the following section, despite the use of a smoothness constraint in the functional is highly advisable to ensure that the minimization procedure converge to a unique solution (Zhang et al, 1999), it unfortunately also introduces possible over-smoothing effects (Worthington and Hancock, 1999). This is an undesired effect, especially for areas where, actually, brightness changes rapidly i.e., the corresponding surface is characterized by discontinuities of the shape or sharp edges (Huang and Smith, 2009;Ju et al, 2010;Chen and Dong, 2010). For this reason, the main aim of the present work is to propose two simple yet effective strategies able to avoid the typical over-smoothing effect in minimizing the SFS functional, with particular regard to the image regions in which this effect is particularly undesired (e.g., areas where brightness changes rapidly or where surface details are to be preserved in the reconstruction).…”