Surface radiance correction for shape from shading

Abstract

It is well known that many surfaces exhibit reflectance that is not well modelled by Lambert's law. This is the case not only for surfaces that are rough or shiny, but also those that are matte and composed of materials that are particle suspensions. As a result, standard Lambertian shape-from-shading methods can not be applied directly to the analysis of rough and shiny surfaces. In order to overcome this difficulty, in this paper, we consider how to reconstruct the Lambertian component for rough and shiny surfaces when the object is illuminated in the viewing direction (retroreflection). To do this we make use of the diffuse reflectance models described by Oren and Nayar, and by Wolff. Our experiments with synthetic and real-world data reveal the effectiveness of the correction method, leading to improved surface normal and height recovery.

Generalised Perspective Shape from Shading with Oren-Nayar Reflectance

“…However, the reflectance model should not be more complicated than the one of Oren and Nayar. Otherwise a carefully controlled experimental environment is needed to achieve meaningful results; see [19].…”

“…Since model parameters in SfS are in general unknown, experiments with such real-world data are highly challenging; see e.g. [19,23]. In particular, the position of the camera relative to the position of the light source is typically not provided with such data sets, since standard SfS models are restricted to the assumption that both positions coincide (which is often not true by construction).…”

“…[3,19]. In this context, the reflectance model of Oren-Nayar turned out to be particularly useful [13,15,16].…”

“…In this context, the reflectance model of Oren-Nayar turned out to be particularly useful [13,15,16]. It is a general model for diffuse reflectance and has been studied in detail in the frameworks concerning orthographic SfS [19]. Relying on perspective instead of orthographic projection, a different class of modern SfS approaches has emerged in the last years [12], most of them formulated again in terms of PDEs [17,22,23].…”

“…[5,11,18,20]. Apart from creating a very general and flexible approach, setting up our model in this way offers a third advantage: (iii) since for (advanced) diffuse reflectance models the brightest points correspond approximately to local minima of the depth [19], it allows us to extend the efficient FM algorithm proposed in [7] to our model -although our HJEs are significantly more complex. Experiments with medical real-world input images from endoscopy allow us to verify the useful properties of our approach, see e.g.…”