Showing papers by "Andrés Bruhn published in 2015"

Variational Perspective Shape from Shading

Abstract: Many recent methods for perspective shape from shading (SfS) are based on formulations in terms of partial differential equations (PDEs). However, while the quality of such methods steadily improves, their lacking robustness is still an open issue. In this context, variational methods seem to be a promising alternative, since they allow to incorporate smoothness assumptions that have proven to be useful for many other tasks in computer vision. Surprisingly, however, such methods have hardly been considered for perspective SfS so far. In our article we address this problem and develop a novel variational model for this task. By combining building blocks of recent PDE-based methods such as a Lambertian reflectance model and camera-centred illumination with a discontinuity-preserving second-order smoothness term, we obtain a variational method for perspective SfS that offers by construction an improved degree of robustness compared to existing PDE-based approaches. Our experiments confirm the success of our strategy. They show that embedding the assumptions of PDE-based approaches into a variational model with a suitable smoothness term can be very beneficial – in particular in scenarios with noise or partially missing information.

An Efficient Linearisation Approach for Variational Perspective Shape from Shading

Abstract: Recently, variational methods have become increasingly more popular for perspective shape from shading due to their robustness under noise and missing information. So far, however, due to the strong nonlinearity of the data term, existing numerical schemes for minimising the corresponding energy functionals were restricted to simple explicit schemes that require thousands or even millions of iterations to provide accurate results. In this paper we tackle the problem by proposing an efficient linearisation approach for the recent variational model of Ju et al. [14]. By embedding such a linearisation in a coarse-to-fine Gaus-Newton scheme, we show that we can reduce the runtime by more than three orders of magnitude without degrading the quality of results. Hence, it is not only possible to apply variational methods for perspective SfS to significantly larger image sizes. Our approach also allows a practical choice of the regularisation parameter so that noise can be suppressed efficiently at the same time.

Direct Variational Perspective Shape from Shading with Cartesian Depth Parametrisation

Abstract: Most of today's state-of-the-art methods for perspective shape from shading are modelled in terms of partial differential equations (PDEs) of Hamilton-Jacobi type. To improve the robustness of such methods w.r.t. noise and missing data, first approaches have recently been proposed that seek to embed the underlying PDE into a variational framework with data and smoothness term. So far, however, such methods either make use of a radial depth parametrisation that makes the regularisation hard to interpret from a geometrical viewpoint or they consider indirect smoothness terms that require additional consistency constraints to provide valid solutions. Moreover the minimisation of such frameworks is an intricate task, since the underlying energy is typically non-convex. In our paper we address all three of the aforementioned issues. First, we propose a novel variational model that operates directly on the Cartesian depth. In this context, we also point out a common mistake in the derivation of the surface normal. Moreover, we employ a direct second-order regulariser with edge-preservation property. This direct regulariser yields by construction valid solutions without requiring additional consistency constraints. Finally, we also propose a novel coarse-to-fine minimisation framework based on an alternating explicit scheme. This framework allows us to avoid local minima during the minimisation and thus to improve the accuracy of the reconstruction. Experiments show the good quality of our model as well as the usefulness of the proposed numerical scheme.