A Closed-Form, Consistent and Robust Solution to Uncalibrated Photometric Stereo Via Local Diffuse Reflectance Maxima

Images of an object under different illumination are known to provide strong cues about the object surface. A mathematical formalization of how to recover the normal map of such a surface leads to the so-called uncalibrated photometric stereo problem. In the simplest instance, this problem can be reduced to the task of identifying only three parameters: the so-called generalized bas-relief (GBR) ambiguity. The challenge is to find additional general assumptions about the object, that identify these parameters uniquely. Current approaches are not consistent, i.e., they provide different solutions when run multiple times on the same data. To address this limitation, we propose exploiting local diffuse reflectance (LDR) maxima, i.e., points in the scene where the normal vector is parallel to the illumination direction (see Fig. 1). We demonstrate several noteworthy properties of these maxima: a closed-form solution, computational efficiency and GBR consistency. An LDR maximum yields a simple closed-form solution corresponding to a semi-circle in the GBR parameters space (see Fig. 2); because as few as two diffuse maxima in different images identify a unique solution, the identification of the GBR parameters can be achieved very efficiently; finally, the algorithm is consistent as it always returns the same solution given the same data. Our algorithm is also remarkably robust: It can obtain an accurate estimate of the GBR parameters even with extremely high levels of outliers in the detected maxima (up to 80 % of the observations). The method is validated on real data and achieves state-of-the-art results.

Global pulses of organic carbon burial in deep-sea sediments during glacial maxima

The burial of organic carbon in marine sediments removes carbon dioxide from the ocean–atmosphere pool, provides energy to the deep biosphere, and on geological timescales drives the oxygenation of the atmosphere. Here we quantify natural variations in the burial of organic carbon in deep-sea sediments over the last glacial cycle. Using a new data compilation of hundreds of sediment cores, we show that the accumulation rate of organic carbon in the deep sea was consistently higher (50%) during glacial maxima than during interglacials. The spatial pattern and temporal progression of the changes suggest that enhanced nutrient supply to parts of the surface ocean contributed to the glacial burial pulses, with likely additional contributions from more efficient transfer of organic matter to the deep sea and better preservation of organic matter due to reduced oxygen exposure. These results demonstrate a pronounced climate sensitivity for this global carbon cycle sink.