A single-lobe photometric stereo approach for heterogeneous material

Shape from shading with multiple light sources is an active research area, and a diverse range of approaches have been proposed in recent decades. However, devising a robust reconstruction technique still remains a challenging goal, as the image acquisition process is highly nonlinear. Recent Photometric Stereo variants rely on simplifying assumptions in order to make the problem solvable: light propagation is still commonly assumed to be uniform, and the Bidirectional Reflectance Distribution Function is assumed to be diffuse, with limited interest for specular materials. In this work, we introduce a well-posed formulation based on partial differential equations (PDEs) for a unified reflectance function that can model both diffuse and specular reflections. We base our derivation on ratio of images, which makes the model independent from photometric invariants and yields a well-posed differential problem based on a system of quasi-linear PDEs with discontinuous coefficients. In addition, we directly solve a differential problem for the unknown depth, thus avoiding the intermediate step of approximating the normal field. A variational approach is presented ensuring robustness to noise and outliers (such as black shadows), and this is confirmed with a wide range of experiments on both synthetic and real data, where we compare favorably to the state of the art.Roberto Mecca is a Marie Curie fellow of the “Istituto Nazionale di Alta Matematica” (Italy) for a project shared with University of Cambridge, Department of Engineering and the Department of Mathematics, University of Bologna

Tone mapping for high dynamic range images

Tone mapping is an essential step for the reproduction of "nice looking" images. It provides the mapping between the luminances of the original scene to the output device's display values. When the dynamic range of the captured scene is smaller or larger than that of the display device, tone mapping expands or compresses the luminance ratios. We address the problem of tone mapping high dynamic range (HDR) images to standard displays (CRT, LCD) and to HDR displays. With standard displays, the dynamic range of the captured HDR scene must be compressed significantly, which can induce a loss of contrast resulting in a loss of detail visibility. Local tone mapping operators can be used in addition to the global compression to increase the local contrast and thus improve detail visibility, but this tends to create artifacts. We developed a local tone mapping method that solves the problems generally encountered by local tone mapping algorithms. Namely, it does not create halo artifacts, nor graying-out of low contrast areas, and provides good color rendition. We then investigated specifically the rendition of color and confirmed that local tone mapping algorithms must be applied to the luminance channel only. We showed that the correlation between luminance and chrominance plays a role in the appearance of the final image but a perfect decorrelation is not necessary. Recently developed HDR monitors enable the display of HDR images with hardly any compression of their dynamic range. The arrival of these displays on the market create the need for new tone mapping algorithms. In particular, legacy images that were mapped to SDR displays must be re-rendered to HDR displays, taking best advantage of the increase in dynamic range. This operation can be seen as the reverse of the tone mapping to SDR. We propose a piecewise linear tone scale function that enhances the brightness of specular highlights so that the sensation of naturalness is improved. Our tone scale algorithm is based on the segmentation of the image into its diffuse and specular components as well as on the range of display luminance that is allocated to the specular component and the diffuse component, respectively. We performed a psychovisual experiment to validate the benefit of our tone scale. The results showed that, with HDR displays, allocating more luminance range to the specular component than what was allocated in the image rendered to SDR displays provides more natural looking images