Intrinsic image decomposition from pair-wise shading ordering

An image is composed by several intrinsic images including the reflectance and the shading. In this paper, we propose a novel approach to infer the shading image from shading orders between pairs of pixels. The pairwise shading orders are measured by two types of methods: the brightness order and the low-order fittings of local shading field. The brightness order is a non-local measure, which does not rely on local gradients, and can be applied to any pair of pixels. In contrast, the loworder fittings are effective for pixel pairs within local regions of smooth shading. These methods are complementary, and they together can capture both the local smoothness and non-local order structure of shading. Further, we evaluate the reliability of these methods by their robustness to perturbations, including the errors in reflectance clustering, the variations of reflectance and shading, and the spatial distances. We adopt a strategy of local competition and global Angular Embedding to integrate pairwise orders into a globally consistent order, taking their reliability into account. Experiments on the MIT Intrinsic Image dataset and the UIUC Shadow dataset show that our model can effectively recover the shading image including those deeply shadowed areas.