The reflections caused by common semi-reflectors, such as glass windows, can impact the performance of computer vision algorithms. State-of-the-art methods can remove reflections on synthetic data and in controlled scenarios. However, they are based on strong assumptions and do not generalize well to real-world images. Contrary to a common misconception, real-world images are challenging even when polarization information is used. We present a deep learning approach to separate the reflected and the transmitted components of the recorded irradiance, which explicitly uses the polarization properties of light. To train it, we introduce an accurate synthetic data generation pipeline, which simulates realistic reflections, including those generated by curved and non-ideal surfaces, non-static scenes, and high-dynamic-range scenes.
offer a third venue to tackle this problem. Assuming that images taken at different polarization angles offer independent measurements of the same scene, reflection and transmission can be separated using independent component analysis @cite_31 @cite_3 @cite_18 . An additional prior that can be leveraged is given by double reflections, when the semi-reflective surface generates them @cite_24 . Under ideal conditions, and leveraging polarization information, a solution can also be found in closed form @cite_26 @cite_4 . In our experiments, we found that most of the pictures captured in unconstrained settings break even the well-founded assumptions used by these papers, as shown in Figure .
@cite_18 @cite_26 @cite_4 @cite_3 @cite_24 @cite_31
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We propose a physically-based approach to separate reflection using multiple polarized images with a background scene captured behind glass. The input consists of three polarized images, each captured from the same view point but with a different polarizer angle separated by 45 degrees. The output is the high-quality separation of the reflection and background layers from each of the input images. A main technical challenge for this problem is that the mixing coefficient for the reflection and background layers depends on the angle of incidence and the orientation of the plane of incidence, which are spatially varying over the pixels of an image. Exploiting physical properties of polarization for a double-surfaced glass medium, we propose a multiscale scheme which automatically finds the optimal separation of the reflection and background layers. Through experiments, we demonstrate that our approach can generate superior results to those of previous methods. We address the problem of recovering a scene recorded through a semireflecting medium (i.e. planar lens), with a virtual reflected image being superimposed on the image of the scene transmitted through the semirefelecting lens. Recent studies propose imaging through a linear polarizer at several orientations to estimate the reflected and the transmitted components in the scene. In this study we extend the sparse ICA (SPICA) technique and apply it to the problem of separating the image of the scene without having any a priori knowledge about its structure or statistics. Recent novel advances in the SPICA approach are discussed. Simulation and experimental results demonstrate the efficacy of the proposed methods.© 2005 Wiley Periodicals, Inc. © 2005 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 15, 84–91, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002 ima.20042 We present an approach to recover scenes deteriorated by reflections off a semireflecting medium (e.g., a glass window). The method, based on imaging through a polarizer at two or more orientations, separates the reflected and transmitted scenes and determines which is which. We analyze the polarization effects, taking into account internal reflections within the medium. The scene reconstruction requires the estimation of the orientation (inclination and tilt angles) of the transparent (invisible) surface. The inclination angle is estimated by seeking the value that leads to the minimal mutual information of the estimated scenes. The limitations and the consequences of noise and angle error are discussed, including a fundamental ambiguity in the determination of the plane of incidence. Experimental results demonstrate the success of angle estimation and consequent scene separation and labeling. We present a novel process for acquiring detailed facial geometry with high resolution diffuse and specular photometric information from multiple viewpoints using polarized spherical gradient illumination. Key to our method is a new pair of linearly polarized lighting patterns which enables multiview diffuse-specular separation under a given spherical illumination condition from just two photographs. The patterns -- one following lines of latitude and one following lines of longitude -- allow the use of fixed linear polarizers in front of the cameras, enabling more efficient acquisition of diffuse and specular albedo and normal maps from multiple viewpoints. In a second step, we employ these albedo and normal maps as input to a novel multi-resolution adaptive domain message passing stereo reconstruction algorithm to create high resolution facial geometry. To do this, we formulate the stereo reconstruction from multiple cameras in a commonly parameterized domain for multiview reconstruction. We show competitive results consisting of high-resolution facial geometry with relightable reflectance maps using five DSLR cameras. Our technique scales well for multiview acquisition without requiring specialized camera systems for sensing multiple polarization states. Photographs taken through glass windows often contain both the desired scene and undesired reflections. Separating the reflection and transmission layers is an important but ill-posed problem that has both aesthetic and practical applications. In this work, we introduce the use of ghosting cues that exploit asymmetry between the layers, thereby helping to reduce the ill-posedness of the problem. These cues arise from shifted double reflections of the reflected scene off the glass surface. In double-pane windows, each pane reflects shifted and attenuated versions of objects on the same side of the glass as the camera. For single-pane windows, ghosting cues arise from shifted reflections on the two surfaces of the glass pane. Even though the ghosting is sometimes barely perceptible by humans, we can still exploit the cue for layer separation. In this work, we model the ghosted reflection using a double-impulse convolution kernel, and automatically estimate the spatial separation and relative attenuation of the ghosted reflection components. To separate the layers, we propose an algorithm that uses a Gaussian Mixture Model for regularization. Our method is automatic and requires only a single input image. We demonstrate that our approach removes a large fraction of reflections on both synthetic and real-world inputs. Vision in scattering media is important but challenging. Images suffer from poor visibility due to backscattering and attenuation. Most prior methods for scene recovery use active illumination scanners (structured and gated), which can be slow and cumbersome, while natural illumination is inapplicable to dark environments. The current paper addresses the need for a non-scanning recovery method, that uses active scene irradiance. We study the formation of images under widefield artificial illumination. Based on the formation model, the paper presents an approach for recovering the object signal. It also yields rough information about the 3D scene structure. The approach can work with compact, simple hardware, having active widefield, polychromatic polarized illumination. The camera is fitted with a polarization analyzer. Two frames of the scene are taken, with different states of the analyzer or polarizer. A recovery algorithm follows the acquisition. It allows both the backscatter and the object reflection to be partially polarized. It thus unifies and generalizes prior polarization-based methods, which had assumed exclusive polarization of either of these components. The approach is limited to an effective range, due to image noise and illumination falloff. Thus, the limits and noise sensitivity are analyzed. We demonstrate the approach in underwater field experiments. The images taken through glass often capture a target transmitted scene as well as undesired reflected scenes. In this paper, we propose a low-rank matrix completion algorithm to remove reflection artifacts automatically from multiple glass images taken at slightly different camera locations. We assume that the transmitted scenes are more dominant than the reflected scenes in typical glass images. We first warp the multiple glass images to a reference image, where the gradients are consistent in the transmission images while the gradients are varying across the reflection images. Based on this observation, we compute a gradient reliability such that the pixels belonging to the salient edges of the transmission image are assigned high reliability. Then we suppress the gradients of the reflection images and recover the gradients of the transmission images only, by solving a low-rank matrix completion problem in gradient domain. We reconstruct an original transmission image using the resulting optimal gradient map. Experimental results show that the proposed algorithm removes the reflection artifacts from glass images faithfully and outperforms the existing algorithms on typical glass images. By using mirror reflections of a scene, stereo images can be captured with a single camera (catadioptric stereo). In addition to simplifying data acquisition single camera stereo provides both geometric and radiometric advantages over traditional two camera stereo. In this paper, we discuss the geometry and calibration of catadioptric stereo with two planar mirrors. In particular, we will show that the relative orientation of a catadioptric stereo rig is restricted to the class of planar motions thus reducing the number of external calibration parameters from 6 to 5. Next we derive the epipolar geometry for catadioptric stereo and show that it has 6 degrees of freedom rather than 7 for traditional stereo. Furthermore, we show how focal length can be recovered from a single catadioptric image solely from a set of stereo correspondences. To test the accuracy of the calibration we present a comparison to Tsai camera calibration and we measure the quality of Euclidean reconstruction. In addition, we will describe a real-time system which demonstrates the viability of stereo with mirrors as an alternative to traditional two camera stereo. 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. In this paper, we address the problem of the simultaneous recovery of the shape and refractive index of an object from a spectro-polarimetric image captured from a single view. Here, we focus on the diffuse polarisation process occuring at dielectric surfaces due to subsurface scattering and transmission from the object surface into the air. The diffuse polarisation of the reflection process is modelled by the Fresnel transmission theory. We present a method for estimating the azimuth angle of surface normals from the spectral variation of the phase of polarisation. Moreover, we estimate the zenith angle of surface normals and index of refraction simultaneously in a well-posed optimisation framework. We achieve well-posedness by introducing two additional constraints to the problem, including the surface integrability and the material dispersion equation. This yields an iterative solution which is computationally efficient due to the use of closed-form solutions for both the zenith angle and the refractive index in each iteration. To demonstrate the effectiveness of our approach, we show results of shape recovery and surface rendering for both real-world and synthetic imagery. We present a method for acquiring the per-pixel diffuse albedo, specular albedo, and surface normal maps of a subject at a single instant in time. The method is single-shot, requiring no optical flow, and per-pixel, making no assumptions regarding albedo statistics or surface connectivity. We photograph the subject inside a spherical illumination device emitting a static lighting pattern of vertically polarized RGB color gradients aligned with the XYZ axes, and horizontally polarized RGB color gradients inversely aligned with the XYZ axes. We capture simultaneous photographs using one of two possible setups: a single-view setup using a coaxially aligned camera pair with a polarizing beam splitter, and a multi-view stereo setup with different orientations of linear polarizing filters placed on the cameras, enabling high- quality geometry reconstruction. From this lighting we derive full-color diffuse albedo, single-channel specular albedo suitable for dielectric materials, and polarization-preserving surface normals which are free of corruption from subsurface scattering. We provide simple formulae to estimate the diffuse albedo, specular albedo, and surface normal maps in the single-view and multi-view cases and show error bounds which are small for many common subjects including faces. This paper presents a novel method for 3D surface reconstruction that uses polarization and shading information from two views. The method relies on the polarization data acquired using a standard digital camera and a linear polarizer. Fresnel theory is used to process the raw images and to obtain initial estimates of surface normals, assuming that the reflection type is diffuse. Based on this idea, the paper presents two novel contributions to the problem of surface reconstruction. The first is a technique to enhance the surface normal estimates by incorporating shading information into the method. This is done using robust statistics to estimate how the measured pixel brightnesses depend on the surface orientation. This gives an estimate of the object material reflectance function, which is used to refine the estimates of the surface normals. The second contribution is to use the refined estimates to establish correspondence between two views of an object. To do this, surface patches are extracted from each view, which are then aligned by minimising an energy functional based on the surface normal estimates and local topographic properties. The optimum alignment parameters for different patch pairs are then used to establish stereo correspondence. This process results in an unambiguous field of surface normals, which can be integrated to recover the surface depth. Our technique is most suited to smooth nonmet allic surfaces. It complements existing stereo algorithms since it does not require salient surface features to obtain correspondences. An extensive set of experiments, yielding reconstructed objects and reflectance functions, are presented and compared to ground truth. A method was recently devised for the recovery of an invariant image from a 3-band colour image. The invariant image, originally 1D greyscale but here derived as a 2D chromaticity, is independent of lighting, and also has shading removed: it forms an intrinsic image that may be used as a guide in recovering colour images that are independent of illumination conditions. Invariance to illuminant colour and intensity means that such images are free of shadows, as well, to a good degree. The method devised finds an intrinsic reflectivity image based on assumptions of Lambertian reflectance, approximately Planckian lighting, and fairly narrowband camera sensors. Nevertheless, the method works well when these assumptions do not hold. A crucial piece of information is the angle for an “invariant direction” in a log-chromaticity space. To date, we have gleaned this information via a preliminary calibration routine, using the camera involved to capture images of a colour target under different lights. In this paper, we show that we can in fact dispense with the calibration step, by recognizing a simple but important fact: the correct projection is that which minimizes entropy in the resulting invariant image. To show that this must be the case we first consider synthetic images, and then apply the method to real images. We show that not only does a correct shadow-free image emerge, but also that the angle found agrees with that recovered from a calibration. As a result, we can find shadow-free images for images with unknown camera, and the method is applied successfully to remove shadows from unsourced imagery. An image acquired through a glass window is a super-position of two sources: a scene behind the window, and a reflection of a scene in front of the window. Light rays incident on the window are reflected back and forth inside the glass. Such internal reflections affect the radiance of both sources: a spatial effect is created of dimmed and shifted replications. Our work generalizes the treatment of transparent scenes to deal with this effect. First, we present a physical model of the image formation. It turns out that each of the transmitted and reflected scenes undergoes a convolution with a particular point spread function (PSF), composed of distinct delta functions. Therefore, scene recovery involves inversion of these PSFs. We analyze the fundamental limitations faced by any attempt to solve this inverse problem. We then present a solution approach. The approach is based on deconvolution by linear filtering and simple optimization. The input to the algorithm is a pair of frames, taken through a polarizing filter. The method is demonstrated experimentally. Convolutive mixtures of images are common in photography of semi-reflections. They also occur in microscopy and tomography. Their formation process involves focusing on an object layer, over which defocused layers are superimposed. We seek blind source separation (BSS) of such mixtures. However, achieving this by direct optimization of mutual information is very complex and suffers from local minima. Thus, we devise an efficient approach to solve these problems. While achieving high quality image separation, we take steps that make the problem significantly simpler than a direct formulation of convolutive image mixtures. These steps make the problem practically convex, yielding a unique global solution to which convergence can be fast. The convolutive BSS problem is converted into a set of instantaneous (pointwise) problems, using a short time Fourier transform (STFT). Standard BSS solutions for instantaneous problems suffer, however, from scale and permutation ambiguities. We overcome these ambiguities by exploiting a parametric model of the defocus point spread function. Moreover, we enhance the efficiency of the approach by exploiting the sparsity of the STFT representation as a prior. We apply our algorithm to semi-reflections, and demonstrate it in experiments. We propose a new application of « Shape from Polarization » method to reconstruct surface shapes of specular met allic objects. Studying the polarization state of the reflected light is very useful to get information on the surface normals. After reflection, an unpolarized light wave becomes partially linearly polarized. Such a wave, can be described by its three parameters: intensity, degree of polarization, and angle of polarization. By using the refractive index of the surface, a relationship between the degree of polarization and the reflection angle can be established. Unfortunately, the relation commonly used for dielectrics, cannot be applied since the refractive index of met allic surfaces is complex. To get a similar relation, we apply a usual approximation valid in the visible region. The Fresnel reflectance model can also provide a relationship between the angle of polarization and the incidence plane orientation. Thus, the reflection angle and the incidence plane orientation give the surface normals. The shape is finally computed by integrating the normals with a relaxation algorithm. Applications on met allic objects made by stamping and polishing are also described, and show the efficiency of our system to discriminate shape defects. Future works will consist in integrating the system into an automatic process of defects detection. 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. This paper presents a general approach for the simultaneous tracking of multiple moving targets using a generic active stereo setup. The problem is formulated on the plane, where cameras are modeled as “line scan cameras,” and targets are described as points with unconstrained motion. We propose to control the active system parameters in such a manner that the images of the targets in the two views are related by a homography. This homography is specified during the design stage and, thus, can be used to implicitly encode the desired tracking behavior. Such formulation leads to an elegant geometric framework that enables a systematic and thorough analysis of the problem at hand. The benefits of the approach are illustrated by applying the framework to two distinct stereo configurations. In the first case, we assume two pan-tilt-zoom cameras, with rotation and zoom control, which are arbitrarily placed in the working environment. It is proved that such a stereo setup can track up to N = 3 free-moving targets, while assuring that the image location of each target is the same for both views. The second example considers a robot head with neck pan motion and independent eye rotation. For this case, it is shown that it is not possible to track more than N = 2 targets because of the lack of zoom. The theoretical framework is used to derive the control equations, and the implementation of the tracking behavior is described in detail. The correctness of the results is confirmed through simulations and real tracking experiments. In this paper we consider the localization of a collection of small, three-dimensional bounded homogeneous inclusions via time-harmonic electromagnetic means, typically using arrays of electric or magnetic dipole transmitters and receivers with given polarization(s) at some distance from the collection, possibly also lying in the far field. The inclusions, somewhat apart or closely spaced, are buried within a homogeneous medium, and are of arbitrary contrast of permittivity, conductivity, and permeability vis-ag-vis this embedding medium. The problem is formulated as an inverse scattering problem for the full Maxwell equations and it involves a robust asymptotic modeling of the multistatic response matrix. No specific application is studied at this stage, but characterization of obstacles in subsoils, nondestructive evaluation of man-made structures, and medical imaging are primary fields of application envisaged. The proposed approach uses a MUSIC (multiple signal classification)-type algorithm, and it yields fast numbering, accurate localization, and estimates of the electromagnetic and geometric parameters (polarization tensors) of the inclusions. The mathematical machinery is detailed first, some specific attention being given to triaxial ellipsoidal inclusions and degenerate spherical shapes (for the latter known results are retrieved). Then, the viability of this algorithm—which would be easily extended to planarly layered environments by introduction of their Green’s functions—is documented by a variety of numerical results from synthetic, noiseless, and severely noisy field data. In this paper, polar codes for the m-user multiple access channel (MAC) with binary inputs are constructed. It is shown that Arikan's polarization technique applied individually to each user transforms independent uses of an m-user binary input MAC into successive uses of extremal MACs. This transformation has a number of desirable properties: 1) the “uniform sum-rate” of the original MAC is preserved, 2) the extremal MACs have uniform rate regions that are not only polymatroids but matroids, and thus, 3) their uniform sum-rate can be reached by each user transmitting either uncoded or fixed bits; in this sense, they are easy to communicate over. A polar code can then be constructed with an encoding and decoding complexity of O(n log n) (where n is the block length), a block error probability of o(exp (- n1 2 - e)), and capable of achieving the uniform sum-rate of any binary input MAC with arbitrary many users. Applications of this polar code construction to channels with a finite field input alphabet and to the additive white Gaussian noise channel are also discussed.