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We investigate the use of photometric invariance and deep learning to compute intrinsic images (albedo and shading). We propose albedo and shading gradient descriptors which are derived from physics-based models. Using the descriptors, albedo transitions are masked out and an initial sparse shading map is calculated directly from the corresponding RGB image gradients in a learning-free unsupervised manner. Then, an optimization method is proposed to reconstruct the full dense shading map. Finally, we integrate the generated shading map into a novel deep learning framework to refine it and also to predict corresponding albedo image to achieve intrinsic image decomposition. By doing so, we are the first to directly address the texture and intensity ambiguity problems of the shading estimations. Large scale experiments show that our approach steered by physics-based invariant descriptors achieve superior results on MIT Intrinsics, NIR-RGB Intrinsics, Multi-Illuminant Intrinsic Images, Spectral Intrinsic Images, As Realistic As Possible, and competitive results on Intrinsic Images in the Wild datasets while achieving state-of-the-art shading estimations.