This paper deals with a challenging, frequently encountered, yet not properly investigated problem in two-frame optical flow estimation. That is, the input frames are compounds of two imaging layers -- one desired background layer of the scene, and one distracting, possibly moving layer due to transparency or reflection. In this situation, the conventional brightness constancy constraint -- the cornerstone of most existing optical flow methods -- will no longer be valid. In this paper, we propose a robust solution to this problem. The proposed method performs both optical flow estimation, and image layer separation. It exploits a generalized double-layer brightness consistency constraint connecting these two tasks, and utilizes the priors for both of them. Experiments on both synthetic data and real images have confirmed the efficacy of the proposed method. To the best of our knowledge, this is the first attempt towards handling generic optical flow fields of two-frame images containing transparency or reflection.
The proposed method involves solving two tasks simultaneously: optical flow field estimation, and reflection transparent layer separation. For the second task, many researches have been published previously. For example, Levin al @cite_13 @cite_36 proposed methods for separating an image into two transparent layers using local statistics priors of natural images. Single image solutions are also investigated in @cite_16 and @cite_31 . To utilize multiple frames, layer separation methods have been proposed based on aligning the frames with one layer @cite_15 @cite_39 @cite_45 or multiple layers @cite_42 @cite_26 . Sarel and Irani @cite_32 presented an information theory based approach for separating transparent layers by minimizing the correlation between the layers. Chen al @cite_38 gave a gradient domain approach for moving layer separation which is also based on information theory. Schechner al @cite_12 developed a method for layer separation using image focus as a cue. By using independent component analysis, Farid and Adelson @cite_33 proposed a layer separation method which works on multiple observations under different mixing weights. Techniques for image layer separation were also developed in the field of intrinsic image video extraction @cite_1 @cite_8 @cite_5 .
@cite_38 @cite_26 @cite_33 @cite_15 @cite_36 @cite_8 @cite_42 @cite_1 @cite_32 @cite_39 @cite_45 @cite_5 @cite_31 @cite_16 @cite_13 @cite_12
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Multi-exposure X-ray imaging can see through objects and separate different material into transparent layers. However, layer motion makes the separation task under-determined. Instead of aligning the non-rigid motion, we address the layer separation problem in gradient domain and propose an energy optimization framework to regularize it by explicitly enforcing independence constraint. It is shown that gradient domain allows more accurate and robust independence analysis between non-stationary signal using mutual information (MI) and hence achieves better separation. Furthermore, gradient fields contain sufficient information for full reconstruction of separated layers by solving the Poisson Equation. For efficient regularization of the gradient separation, energy terms based on the Taylor expansion of MI is further derived. Evaluation on both synthesized and real datasets proves the effectiveness of our algorithm and its robustness to complex tissue motion. We address the problem of blind separation of multiple source layers from their linear mixtures with unknown mixing coefficients and unknown layer motions. Such mixtures can occur when one takes photos through a transparent medium, like a window glass, and the camera or the medium moves between snapshots. To understand how to achieve correct separation, we study the statistics of natural images in the Labelme data set. We not only confirm the well-known sparsity of image gradients, but also discover new joint behavior patterns of image gradients. Based on these statistical properties, we develop a sparse blind separation algorithm to estimate both layer motions and linear mixing coefficients and then recover all layers. This method can handle general parameterized motions, including translations, scalings, rotations, and other transformations. In addition, the number of layers is automatically identified, and all layers can be recovered, even in the underdetermined case where mixtures are fewer than layers. The effectiveness of this technology is shown in experiments on both simulated and real superimposed images. When estimating foreground and background layers (or equivalently an alpha matte), it is often the case that pixel measurements contain mixed colours which are a combination of foreground and background. Object boundaries, especially at thin sub-pixel structures like hair, pose a serious problem.In this paper we present a multiple view algorithm for computing the alpha matte. Using a Bayesian framework, we model each pixel as a combined sample from the foreground and background and compute a MAP estimate to factor the two. The novelties in this work include the incorporation of three different types of priors for enhancing the results in problematic scenes. The priors used are inequality constraints on colour and alpha values, spatial continuity, and the probability distribution of alpha values.The combination of these priors result in accurate and visually satisfying estimates. We demonstrate the method on real image sequences with varying degrees of geometric and photometric complexity. The output enables virtual objects to be added between the foreground and background layers, and we give examples of this augmentation to the original sequences. When we take a picture through transparent glass, the image we obtain is often a linear superposition of two images: The image of the scene beyond the glass plus the image of the scene reflected by the glass. Decomposing the single input image into two images is a massively ill-posed problem: In the absence of additional knowledge about the scene being viewed, there are an infinite number of valid decompositions. In this paper, we focus on an easier problem: user assisted separation in which the user interactively labels a small number of gradients as belonging to one of the layers. Even given labels on part of the gradients, the problem is still ill-posed and additional prior knowledge is needed. Following recent results on the statistics of natural images, we use a sparsity prior over derivative filters. This sparsity prior is optimized using the iterative reweighted least squares (IRLS) approach. Our results show that using a prior derived from the statistics of natural images gives a far superior performance compared to a Gaussian prior and it enables good separations from a modest number of labeled gradients. 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. Many natural images contain reflections and transparency, i.e., they contain mixtures of reflected and transmitted light. When viewed from a moving camera, these appear as the superposition of component layer images moving relative to each other. The problem of multiple motion recovery has been previously studied by a number of researchers. However no one has yet demonstrated how to accurately recover the component images themselves. In this paper we develop an optimal approach to recovering layer images and their associated motions from an arbitrary number of composite images. We develop two different techniques for estimating the component layer images given known motion estimates. The first approach uses constrained least squares to recover the layer images. The second approach iteratively refines lower and upper bounds on the layer images using two novel compositing operations, namely minimum- and maximum-composites of aligned images. We combine these layer extraction techniques with a dominant motion estimator and a subsequent motion refinement stage. This results in a completely automated system that recovers transparent images and motions from a collection of input images. 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. In this paper we present an approach for separating two transparent layers in images and video sequences. Given two initial unknown physical mixtures, I 1 and I 2, of real scene layers, L 1 and L 2, we seek a layer separation which minimizes the structural correlations across the two layers, at every image point. Such a separation is achieved by transferring local grayscale structure from one image to the other wherever it is highly correlated with the underlying local grayscale structure in the other image, and vice versa. This bi-directional transfer operation, which we call the “layer information exchange”, is performed on diminishing window sizes, from global image windows (i.e., the entire image), down to local image windows, thus detecting similar grayscale structures at varying scales across pixels. We show the applicability of this approach to various real-world scenarios, including image and video transparency separation. In particular, we show that this approach can be used for separating transparent layers in images obtained under different polarizations, as well as for separating complex non-rigid transparent motions in video sequences. These can be done without prior knowledge of the layer mixing model (simple additive, alpha-mated composition with an unknown alpha-map, or other), and under unknown complex temporal changes (e.g., unknown varying lighting conditions). We present a method to decompose a video into its intrinsic components of reflectance and shading, plus a number of related example applications in video editing such as segmentation, stylization, material editing, recolorization and color transfer. Intrinsic decomposition is an ill-posed problem, which becomes even more challenging in the case of video due to the need for temporal coherence and the potentially large memory requirements of a global approach. Additionally, user interaction should be kept to a minimum in order to ensure efficiency. We propose a probabilistic approach, formulating a Bayesian Maximum a Posteriori problem to drive the propagation of clustered reflectance values from the first frame, and defining additional constraints as priors on the reflectance and shading. We explicitly leverage temporal information in the video by building a causal-anticausal, coarse-to-fine iterative scheme, and by relying on optical flow information. We impose no restrictions on the input video, and show examples representing a varied range of difficult cases. Our method is the first one designed explicitly for video; moreover, it naturally ensures temporal consistency, and compares favorably against the state of the art in this regard. Layer decomposition from a single image is an under-constrained problem, because there are more unknowns than equations. This paper studies a slightly easier but very useful alternative where only the background layer has substantial image gradients and structures. We propose to solve this useful alternative by an expectation-maximization (EM) algorithm that employs the hidden Markov model (HMM), which maintains spatial coherency of smooth and overlapping layers, and helps to preserve image details of the textured background layer. We demonstrate that, using a small amount of user input, various seemingly unrelated problems in computational photography can be effectively addressed by solving this alternative using our EM-HMM algorithm. This paper addresses extracting two layers from an image where one layer is smoother than the other. This problem arises most notably in intrinsic image decomposition and reflection interference removal. Layer decomposition from a single-image is inherently ill-posed and solutions require additional constraints to be enforced. We introduce a novel strategy that regularizes the gradients of the two layers such that one has a long tail distribution and the other a short tail distribution. While imposing the long tail distribution is a common practice, our introduction of the short tail distribution on the second layer is unique. We formulate our problem in a probabilistic framework and describe an optimization scheme to solve this regularization with only a few iterations. We apply our approach to the intrinsic image and reflection removal problems and demonstrate high quality layer separation on par with other techniques but being significantly faster than prevailing methods. Certain simple images are known to trigger a percept of transparency: the input image I is perceived as the sum of two images I(x,y) = I1(x,y) + I2(x,y). This percept is puzzling. First, why do we choose the "more complicated" description with two images rather than the "simpler" explanation I(x,y) = I1(x,y) + 0 ? Second, given the infinite number of ways to express I as a sum of two images, how do we compute the "best" decomposition? Here we suggest that transparency is the rational percept of a system that is adapted to the statistics of natural scenes. We present a probabilistic model of images based on the qualitative statistics of derivative filters and "corner detectors" in natural scenes and use this model to find the most probable decomposition of a novel image. The optimization is performed using loopy belief propagation. We show that our model computes perceptually "correct" decompositions on synthetic images and discuss its application to real images. Consider situations where the depth at each point in the scene is multi-valued, due to the presence of a virtual image semi-reflected by a transparent surface. The semi-reflected image is linearly superimposed on the image of an object that is behind the transparent surface. A novel approach is proposed for the separation of the superimposed layers. Focusing on either of the layers yields initial separation, but crosstalk remains. The separation is enhanced by mutual blurring of the perturbing components in the images. However, this blurring requires the estimation of the defocus blur kernels. We thus propose a method for self calibration of the blur kernels, given the raw images. The kernels are sought to minimize the mutual information of the recovered layers. Autofocusing and depth estimation in the presence of semi-reflections are also considered. Experimental results are presented.