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_33: Flash images are known to suffer from several problems: saturation of nearby objects, poor illumination of distant objects, reflections of objects strongly lit by the flash and strong highlights due to the reflection of flash itself by glossy surfaces. We propose to use a flash and no-flash (ambient) image pair to produce better flash images. We present a novel gradient projection scheme based on a gradient coherence model that allows removal of reflections and highlights from flash images. We also present a brightness-ratio based algorithm that allows us to compensate for the falloff in the flash image brightness due to depth. In several practical scenarios, the quality of flash no-flash images may be limited in terms of dynamic range. In such cases, we advocate using several images taken under different flash intensities and exposures. We analyze the flash intensity-exposure space and propose a method for adaptively sampling this space so as to minimize the number of captured images for any given scene. We present several experimental results that demonstrate the ability of our algorithms to produce improved flash images.
  @cite_8: Our goal is to turn an intensity image into its perceived luminance without parsing it into depths, surfaces, or scene illuminations. We start with jarring intensity differences at two scales mixed according to edges, identified by a pixel-centric edge detector. We propose angular embedding as a more robust, efficient, and versatile alternative to LS, LLE, and NCUTS for obtaining a global brightness ordering from local differences. Our model explains a variety of brightness illusions with a single algorithm. Brightness of a pixel can be understood locally as its intensity deviating in the gradient direction and globally as finding its rank relative to others, particularly the lightest and darkest ones.
  @cite_45: 
  @cite_23: Given the size and confidence of pairwise local orderings, angular embedding (AE) finds a global ordering with a near-global optimal eigensolution. As a quadratic criterion in the complex domain, AE is remarkably robust to outliers, unlike its real domain counterpart LS, the least squares embedding. Our comparative study of LS and AE reveals that AE's robustness is due not to the particular choice of the criterion, but to the choice of representation in the complex domain. When the embedding is encoded in the angular space, we not only have a nonconvex error function that delivers robustness, but also have a Hermitian graph Laplacian that completely determines the optimum and delivers efficiency. The high quality of embedding by AE in the presence of outliers can hardly be matched by LS, its corresponding L1 norm formulation, or their bounded versions. These results suggest that the key to overcoming outliers lies not with additionally imposing constraints on the embedding solution, but with adaptively penalizing inconsistency between measurements themselves. AE thus significantly advances statistical ranking methods by removing the impact of outliers directly without explicit inconsistency characterization, and advances spectral clustering methods by covering the entire size-confidence measurement space and providing an ordered cluster organization.
  @cite_2: The angular synchronization problem is to obtain an accurate estimation (up to a constant additive phase) for a set of unknown angles θ1,…,θn from m noisy measurements of their offsets θi−θjmod2π. Of particular interest is angle recovery in the presence of many outlier measurements that are uniformly distributed in [0,2π) and carry no information on the true offsets. We introduce an efficient recovery algorithm for the unknown angles from the top eigenvector of a specially designed Hermitian matrix. The eigenvector method is extremely stable and succeeds even when the number of outliers is exceedingly large. For example, we successfully estimate n=400 angles from a full set of m=(4002) offset measurements of which 90 are outliers in less than a second on a commercial laptop. The performance of the method is analyzed using random matrix theory and information theory. We discuss the relation of the synchronization problem to the combinatorial optimization problem Max-2-Lin mod L and present a semidefinite relaxation for angle recovery, drawing similarities with the Goemans–Williamson algorithm for finding the maximum cut in a weighted graph. We present extensions of the eigenvector method to other synchronization problems that involve different group structures and their applications, such as the time synchronization problem in distributed networks and the surface reconstruction problems in computer vision and optics.
summary: Ranking elements from their pairwise comparisons has been extensively studied in many fields @cite_33 @cite_8 @cite_45 . Angular Embedding @cite_23 adopts a cosine error function, which is proven to be more robust to outliers than the traditional @math or @math errors used by Least Squares Embedding @cite_33 . Angular Synchronization (AS) also uses the angular space @cite_2 , but it does not consider the confidences of pairwise measures.