text: We address the problem of decomposing a single image into reflectance and shading. The difficulty comes from the fact that the components of image---the surface albedo, the direct illumination, and the ambient illumination---are coupled heavily in observed image. We propose to infer the shading by ordering pixels by their relative brightness, without knowing the absolute values of the image components beforehand. The pairwise shading orders are estimated in two ways: brightness order and low-order fittings of local shading field. The brightness order is a non-local measure, which can be applied to any pair of pixels including those whose reflectance and shading are both different. The low-order fittings are used for pixel pairs within local regions of smooth shading. Together, they can capture both global order structure and local variations of the shading. We propose a Consistency-aware Selective Fusion (CSF) to integrate the pairwise orders into a globally consistent order. The iterative selection process solves the conflicts between the pairwise orders obtained by different estimation methods. Inconsistent or unreliable pairwise orders will be automatically excluded from the fusion to avoid polluting the global order. Experiments on the MIT Intrinsic Image dataset show that the proposed model is effective at recovering the shading including deep shadows. Our model also works well on natural images from the IIW dataset, the UIUC Shadow dataset and the NYU-Depth dataset, where the colors of direct lights and ambient lights are quite different.
  @cite_22: 
  @cite_46: 
  @cite_41: Intrinsic images represent the underlying properties of a scene such as illumination (shading) and surface reflectance. Extracting intrinsic images is a challenging, ill-posed problem. Human performance on tasks such as shadow detection and shape-from-shading is improved by adding colour and texture to surfaces. In particular, when a surface is painted with a textured pattern, correlations between local mean luminance and local luminance amplitude promote the interpretation of luminance variations as illumination changes. Based on this finding, we propose a novel feature, local luminance amplitude, to separate illumination and reflectance, and a framework to integrate this cue with hue and texture to extract intrinsic images. The algorithm uses steerable filters to separate images into frequency and orientation components and constructs shading and reflectance images from weighted combinations of these components. Weights are determined by correlations between corresponding variations in local luminance, local amplitude, colour and texture. The intrinsic images are further refined by ensuring the consistency of local texture elements. We test this method on surfaces photographed under different lighting conditions. The effectiveness of the algorithm is demonstrated by the correlation between our intrinsic images and ground truth shading and reflectance data. Luminance amplitude was found to be a useful cue. Results are also presented for natural images.
  @cite_17: Interpreting real-world images requires the ability distinguish the different characteristics of the scene that lead to its final appearance. Two of the most important of these characteristics are the shading and reflectance of each point in the scene. We present an algorithm that uses multiple cues to recover shading and reflectance intrinsic images from a single image. Using both color information and a classifier trained to recognize gray-scale patterns, given the lighting direction, each image derivative is classified as being caused by shading or a change in the surface's reflectance. The classifiers gather local evidence about the surface's form and color, which is then propagated using the generalized belief propagation algorithm. The propagation step disambiguates areas of the image where the correct classification is not clear from local evidence. We use real-world images to demonstrate results and show how each component of the system affects the results.
  @cite_44: Sensations of color show a strong correlation with reflectance, even though the amount of visible light reaching the eye depends on the product of reflectance and illumination. The visual system must achieve this remarkable result by a scheme that does not measure flux. Such a scheme is described as the basis of retinex theory. This theory assumes that there are three independent cone systems, each starting with a set of receptors peaking, respectively, in the long-, middle-, and short-wavelength regions of the visible spectrum. Each system forms a separate image of the world in terms of lightness that shows a strong correlation with reflectance within its particular band of wavelengths. These images are not mixed, but rather are compared to generate color sensations. The problem then becomes how the lightness of areas in these separate images can be independent of flux. This article describes the mathematics of a lightness scheme that generates lightness numbers, the biologic correlate of reflectance, independent of the flux from objects
  @cite_49: Intrinsic images are a useful midlevel description of scenes proposed by H.G. Barrow and J.M. Tenenbaum (1978). An image is de-composed into two images: a reflectance image and an illumination image. Finding such a decomposition remains a difficult problem in computer vision. We focus on a slightly, easier problem: given a sequence of T images where the reflectance is constant and the illumination changes, can we recover T illumination images and a single reflectance image? We show that this problem is still imposed and suggest approaching it as a maximum-likelihood estimation problem. Following recent work on the statistics of natural images, we use a prior that assumes that illumination images will give rise to sparse filter outputs. We show that this leads to a simple, novel algorithm for recovering reflectance images. We illustrate the algorithm's performance on real and synthetic image sequences.
  @cite_15: We present a method for decomposing an image into its intrinsic reflectance and shading components. Different from previous work, our method examines texture information to obtain constraints on reflectance among pixels that may be distant from one another in the image. We observe that distinct points with the same intensity-normalized texture configuration generally have the same reflectance value. The separation of shading and reflectance components should thus be performed in a manner that guarantees these non-local constraints. We formulate intrinsic image decomposition by adding these non-local texture constraints to the local derivative analysis employed in conventional techniques. Our results show a significant improvement in performance, with better recovery of global reflectance and shading structure than by previous methods.
  @cite_11: Images can be represented as the composition of multiple intrinsic component images, such as shading, albedo, and noise images. In this paper, we present a method for estimating intrinsic component images from a single image, which we apply to the problems of estimating shading and albedo images and image denoising. Our method is based on learning estimators that predict filtered versions of the desired image. Unlike previous approaches, our method does not require unnatural discretizations of the problem. We also demonstrate how to learn a weighting function that properly weights the local estimates when constructing the estimated image. For shading estimation, we introduce a new training set of real-world images. The accuracy of our method is measured both qualitatively and quantitatively, showing better performance on the shading albedo separation problem than previous approaches. The performance on denoising is competitive with the current state of the art.
summary: Different constraints often result in quite different shading orders. How to fuse them remains an open problem. Edge-based methods classify each edge into a reflectance edge or a shading edge. Accordingly, the shading order between the two sides of the edge can be decided. In particular, Retinex classified the edges by the magnitude of gradients @cite_44 . This classification method is risky. Some shadow edges are quite strong, while the reflectance edges between similar colors are relatively weak. Extensions of Retinex introduced several new features, including texture similarity @cite_15 , classifiers over local features @cite_46 or patches @cite_17 @cite_11 , correlation between the mean luminance and luminance amplitude @cite_41 , and image sequences under different illumination directions @cite_49 @cite_22 . These features improved the accuracy of classification, but none of them are robust enough to handle all kinds of scenes. CSF faces a similar problem of selecting the optimal pairwise order from several estimates. The difference is that CSF incorporates consistency between the pairwise orders and global order into the selection criteria, which can rectify the inconsistent selections made by noisy image features.