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We introduce a novel learning-based method to reconstruct the high-quality geometry and complex, spatially-varying BRDF of an arbitrary object from a sparse set of only six images captured by wide-baseline cameras under collocated point lighting. We first estimate per-view depth maps using a deep multi-view stereo network; these depth maps are used to coarsely align the different views. We propose a novel multi-view reflectance estimation network architecture that is trained to pool features from these coarsely aligned images and predict per-view spatially-varying diffuse albedo, surface normals, specular roughness and specular albedo. We do this by jointly optimizing the latent space of our multi-view reflectance network to minimize the photometric error between images rendered with our predictions and the input images. While previous state-of-the-art methods fail on such sparse acquisition setups, we demonstrate, via extensive experiments on synthetic and real data, that our method produces high-quality reconstructions that can be used to render photorealistic images.