We present a generalized method for reconstructing the shape of an object from measured gradient data. A certain class of optical sensors does not measure the shape of an object but rather its local slope. These sensors display several advantages, including high information efficiency, sensitivity, and robustness. For many applications, however, it is necessary to acquire the shape, which must be calculated from the slopes by numerical integration. Existing integration techniques show drawbacks that render them unusable in many cases. Our method is based on an approximation employing radial basis functions. It can be applied to irregularly sampled, noisy, and incomplete data, and it reconstructs surfaces both locally and globally with high accuracy.
In general, it is crucial to note that the reconstruction method depends on the slope-measuring sensor and the properties of the acquired data. For example, slope data acquired by Shape from Shading is rather noisy, exhibits curl, and is usually located on a full grid of millions of points. Here, a fast subspace approximation method like the one proposed by Frankot and Chellappa @cite_13 is appropriate. On the other hand, wavefront reconstruction deals with much smaller data sets, and the surface is known to be rather smooth and flat. In this case, a direct finite-difference solver can be applied @cite_11 . Deflectometric sensors deliver a third type of data: It consists of very large data sets with rather small noise and curl, but the data may not be complete, depending on the local reflectance of the measured surface. Furthermore, the measuring field may have an unknown, irregularly shaped boundary. These properties render most of the aforementioned methods unusable for deflectometric data. In the following sections, we will describe a surface reconstruction method which is especially able to deal with slope data acquired by sensors such as Phase-measuring Deflectometry.
@cite_13 @cite_11
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One of the potentially effective means for large-scale 3D scene reconstruction is to reconstruct the scene in a global manner, rather than incrementally, by fully exploiting available auxiliary information on the imaging condition, such as camera location by Global Positioning System (GPS), orientation by inertial measurement unit (or compass), focal length from EXIF, and so on. However, such auxiliary information, though informative and valuable, is usually too noisy to be directly usable. In this paper, we present an approach by taking advantage of such noisy auxiliary information to improve structure from motion solving. More specifically, we introduce two effective iterative global optimization algorithms initiated with such noisy auxiliary information. One is a robust rotation averaging algorithm to deal with contaminated epipolar graph, the other is a robust scene reconstruction algorithm to deal with noisy GPS data for camera centers initialization. We found that by exclusively focusing on the estimated inliers at the current iteration, the optimization process initialized by such noisy auxiliary information could converge well and efficiently. Our proposed method is evaluated on real images captured by unmanned aerial vehicle, StreetView car, and conventional digital cameras. Extensive experimental results show that our method performs similarly or better than many of the state-of-art reconstruction approaches, in terms of reconstruction accuracy and completeness, but is more efficient and scalable for large-scale image data sets. Conventional compressive sensing (CS) reconstruction is very slow for its characteristic of solving an optimization problem. Convolutional neural network can realize fast processing while achieving comparable results. While CS image recovery with high quality not only depends on good reconstruction algorithms, but also good measurements. In this paper, we propose an adaptive measurement network in which measurement is obtained by learning. The new network consists of a fully-connected layer and ReconNet. The fully-connected layer which has low-dimension output acts as measurement. We train the fully-connected layer and ReconNet simultaneously and obtain adaptive measurement. Because the adaptive measurement fits dataset better, in contrast with random Gaussian measurement matrix, under the same measurement rate, it can extract the information of scene more efficiently and get better reconstruction results. Experiments show that the new network outperforms the original one. Traditional algorithms for compressive sensing recovery are computationally expensive and are ineffective at low measurement rates. In this work, we propose a data driven non-iterative algorithm to overcome the shortcomings of earlier iterative algorithms. Our solution, ReconNet, is a deep neural network, whose parameters are learned end-to-end to map block-wise compressive measurements of the scene to the desired image blocks. Reconstruction of an image becomes a simple forward pass through the network and can be done in real-time. We show empirically that our algorithm yields reconstructions with higher PSNRs compared to iterative algorithms at low measurement rates and in presence of measurement noise. We also propose a variant of ReconNet which uses adversarial loss in order to further improve reconstruction quality. We discuss how adding a fully connected layer to the existing ReconNet architecture allows for jointly learning the measurement matrix and the reconstruction algorithm in a single network. Experiments on real data obtained from a block compressive imager show that our networks are robust to unseen sensor noise. Finally, through an experiment in object tracking, we show that even at very low measurement rates, reconstructions using our algorithm possess rich semantic content that can be used for high level inference. The availability of commodity depth sensors such as Kinect has enabled development of methods which can densely reconstruct arbitrary scenes. While the results of these methods are accurate and visually appealing, they are quite often incomplete. This is either due to the fact that only part of the space was visible during the data capture process or due to the surfaces being occluded by other objects in the scene. In this paper, we address the problem of completing and refining such reconstructions. We propose a method for scene completion that can infer the layout of the complete room and the full extent of partially occluded objects. We propose a new probabilistic model, Contour Completion Random Fields, that allows us to complete the boundaries of occluded surfaces. We evaluate our method on synthetic and real world reconstructions of 3D scenes and show that it quantitatively and qualitatively outperforms standard methods. We created a large dataset of partial and complete reconstructions which we will make available to the community as a benchmark for the scene completion task. Finally, we demonstrate the practical utility of our algorithm via an augmented-reality application where objects interact with the completed reconstructions inferred by our method. Accurate signal recovery or image reconstruction from indirect and possibly undersampled data is a topic of considerable interest; for example, the literature in the recent field of compressed sensing is already quite immense. This paper applies a smoothing technique and an accelerated first-order algorithm, both from Nesterov [Math. Program. Ser. A, 103 (2005), pp. 127-152], and demonstrates that this approach is ideally suited for solving large-scale compressed sensing reconstruction problems as (1) it is computationally efficient, (2) it is accurate and returns solutions with several correct digits, (3) it is flexible and amenable to many kinds of reconstruction problems, and (4) it is robust in the sense that its excellent performance across a wide range of problems does not depend on the fine tuning of several parameters. Comprehensive numerical experiments on realistic signals exhibiting a large dynamic range show that this algorithm compares favorably with recently proposed state-of-the-art methods. We also apply the algorithm to solve other problems for which there are fewer alternatives, such as total-variation minimization and convex programs seeking to minimize the @math norm of @math under constraints, in which @math is not diagonal. The code is available online as a free package in the MATLAB language. We present a novel method to obtain fine-scale detail in 3D reconstructions generated with low-budget RGB-D cameras or other commodity scanning devices. As the depth data of these sensors is noisy, truncated signed distance fields are typically used to regularize out the noise, which unfortunately leads to over-smoothed results. In our approach, we leverage RGB data to refine these reconstructions through shading cues, as color input is typically of much higher resolution than the depth data. As a result, we obtain reconstructions with high geometric detail, far beyond the depth resolution of the camera itself. Our core contribution is shading-based refinement directly on the implicit surface representation, which is generated from globally-aligned RGB-D images. We formulate the inverse shading problem on the volumetric distance field, and present a novel objective function which jointly optimizes for fine-scale surface geometry and spatially-varying surface reflectance. In order to enable the efficient reconstruction of sub-millimeter detail, we store and process our surface using a sparse voxel hashing scheme which we augment by introducing a grid hierarchy. A tailored GPU-based Gauss-Newton solver enables us to refine large shape models to previously unseen resolution within only a few seconds. While high resolution, regularly gridded observations are generally preferred in remote sensing, actual observations are often not evenly sampled and have lower-than-desired resolution. Hence, there is an interest in resolution enhancement and image reconstruction. This paper discusses a general theory and techniques for image reconstruction and creating enhanced resolution images from irregularly sampled data. Using irregular sampling theory, we consider how the frequency content in aperture function-attenuated sidelobes can be recovered from oversampled data using reconstruction techniques, thus taking advantage of the high frequency content of measurements made with nonideal aperture filters. We show that with minor modification, the algebraic reconstruction technique (ART) is functionally equivalent to Grochenig's (1992) irregular sampling reconstruction algorithm. Using simple Monte Carlo simulations, we compare and contrast the performance of additive ART, multiplicative ART, and the scatterometer image reconstruction (SIR) (a derivative of multiplicative ART) algorithms with and without noise. The reconstruction theory and techniques have applications with a variety of sensors and can enable enhanced resolution image production from many nonimaging sensors. The technique is illustrated with ERS-2 and SeaWinds scatterometer data. We study the compressed sensing reconstruction problem for a broad class of random, band-diagonal sensing matrices. This construction is inspired by the idea of spatial coupling in coding theory. As demonstrated heuristically and numerically by Krzakala [30], message passing algorithms can effectively solve the reconstruction problem for spatially coupled measurements with undersampling rates close to the fraction of nonzero coordinates. We use an approximate message passing (AMP) algorithm and analyze it through the state evolution method. We give a rigorous proof that this approach is successful as soon as the undersampling rate δ exceeds the (upper) Renyi information dimension of the signal, d(pX). More precisely, for a sequence of signals of diverging dimension n whose empirical distribution converges to pX, reconstruction is with high probability successful from d(pX) n+o(n) measurements taken according to a band diagonal matrix. For sparse signals, i.e., sequences of dimension n and k(n) nonzero entries, this implies reconstruction from k(n)+o(n) measurements. For “discrete” signals, i.e., signals whose coordinates take a fixed finite set of values, this implies reconstruction from o(n) measurements. The result is robust with respect to noise, does not apply uniquely to random signals, but requires the knowledge of the empirical distribution of the signal pX. We investigate the problem of reconstructing a high-dimensional nonnegative sparse vector from lower-dimensional linear measurements. While much work has focused on dense measurement matrices, sparse measurement schemes can be more efficient both with respect to signal sensing as well as reconstruction complexity. Known constructions use the adjacency matrices of expander graphs, which often lead to recovery algorithms which are much more efficient than minimization. However, prior constructions of sparse measurement matrices rely on expander graphs with very high expansion coefficients which make the construction of such graphs difficult and the size of the recoverable sets very small. In this paper, we introduce sparse measurement matrices for the recovery of nonnegative vectors, using perturbations of the adjacency matrices of expander graphs requiring much smaller expansion coefficients, hereby referred to as minimal expanders. We show that when minimization is used as the reconstruction method, these constructions allow the recovery of signals that are almost three orders of magnitude larger compared to the existing theoretical results for sparse measurement matrices. We provide for the first time tight upper bounds for the so called weak and strong recovery thresholds when minimization is used. We further show that the success of optimization is equivalent to the existence of a “unique” vector in the set of solutions to the linear equations, which enables alternative algorithms for minimization. We further show that the defined minimal expansion property is necessary for all measurement matrices for compressive sensing, (even when the non-negativity assumption is removed) therefore implying that our construction is tight. We finally present a novel recovery algorithm that exploits expansion and is much more computationally efficient compared to minimization. This paper presents techniques for the merging of 3D data coming from different sensors, such as ground and aerial laser range scans. The 3D models created are reconstructed to give a photo-realistic scene enabling interactive virtual walkthroughs, measurements and scene change analysis. The reconstructed model is based on a weighted integration of all available data based on sensor-specific parameters such as noise level, accuracy, inclination and reflectivity of the target, spatial distribution of points. The geometry is robustly reconstructed with a volumetric approach. Once registered and weighed, all data is re-sampled in a multi-resolution distance field using out-of-core techniques. The final mesh is extracted by contouring the iso-surface with a feature preserving dual contouring algorithm. The paper shows results of the above technique applied to Verona (Italy) city centre. We study the compressed sensing reconstruction problem for a broad class of random, band-diagonal sensing matrices. This construction is inspired by the idea of spatial coupling in coding theory. As demonstrated heuristically and numerically by KrzakalaEtAl , message passing algorithms can effectively solve the reconstruction problem for spatially coupled measurements with undersampling rates close to the fraction of non-zero coordinates. We use an approximate message passing (AMP) algorithm and analyze it through the state evolution method. We give a rigorous proof that this approach is successful as soon as the undersampling rate @math exceeds the (upper) R 'enyi information dimension of the signal, @math . More precisely, for a sequence of signals of diverging dimension @math whose empirical distribution converges to @math , reconstruction is with high probability successful from @math measurements taken according to a band diagonal matrix. For sparse signals, i.e., sequences of dimension @math and @math non-zero entries, this implies reconstruction from @math measurements. For discrete' signals, i.e., signals whose coordinates take a fixed finite set of values, this implies reconstruction from @math measurements. The result is robust with respect to noise, does not apply uniquely to random signals, but requires the knowledge of the empirical distribution of the signal @math . 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. Accurate recovery of 3D geometrical surfaces from calibrated 2D multi-view images is a fundamental yet active research area in computer vision. Despite the steady progress in multi-view stereo (MVS) reconstruction, many existing methods are still limited in recovering fine-scale details and sharp features while suppressing noises, and may fail in reconstructing regions with less textures. To address these limitations, this paper presents a detail-preserving and content-aware variational (DCV) MVS method, which reconstructs the 3D surface by alternating between reprojection error minimization and mesh denoising. In reprojection error minimization, we propose a novel inter-image similarity measure, which is effective to preserve fine-scale details of the reconstructed surface and builds a connection between guided image filtering and image registration. In mesh denoising, we propose a content-aware @math -minimization algorithm by adaptively estimating the @math value and regularization parameters. Compared with conventional isotropic mesh smoothing approaches, the proposed method is much more promising in suppressing noise while preserving sharp features. Experimental results on benchmark data sets demonstrate that our DCV method is capable of recovering more surface details, and obtains cleaner and more accurate reconstructions than the state-of-the-art methods. In particular, our method achieves the best results among all published methods on the Middlebury dino ring and dino sparse data sets in terms of both completeness and accuracy. The goal of this paper is to present a non-iterative and more importantly an extremely fast algorithm to reconstruct images from compressively sensed (CS) random measurements. To this end, we propose a novel convolutional neural network (CNN) architecture which takes in CS measurements of an image as input and outputs an intermediate reconstruction. We call this network, ReconNet. The intermediate reconstruction is fed into an off-the-shelf denoiser to obtain the final reconstructed image. On a standard dataset of images we show significant improvements in reconstruction results (both in terms of PSNR and time complexity) over state-of-the-art iterative CS reconstruction algorithms at various measurement rates. Further, through qualitative experiments on real data collected using our block single pixel camera (SPC), we show that our network is highly robust to sensor noise and can recover visually better quality images than competitive algorithms at extremely low sensing rates of 0.1 and 0.04. To demonstrate that our algorithm can recover semantically informative images even at a low measurement rate of 0.01, we present a very robust proof of concept real-time visual tracking application. The goal of this paper is to present a non-iterative and more importantly an extremely fast algorithm to reconstruct images from compressively sensed (CS) random measurements. To this end, we propose a novel convolutional neural network (CNN) architecture which takes in CS measurements of an image as input and outputs an intermediate reconstruction. We call this network, ReconNet. The intermediate reconstruction is fed into an off-the-shelf denoiser to obtain the final reconstructed image. On a standard dataset of images we show significant improvements in reconstruction results (both in terms of PSNR and time complexity) over state-of-the-art iterative CS reconstruction algorithms at various measurement rates. Further, through qualitative experiments on real data collected using our block single pixel camera (SPC), we show that our network is highly robust to sensor noise and can recover visually better quality images than competitive algorithms at extremely low sensing rates of 0.1 and 0.04. To demonstrate that our algorithm can recover semantically informative images even at a low measurement rate of 0.01, we present a very robust proof of concept real-time visual tracking application. We consider the case in which a robot has to navigate in an unknown environment but does not have enough on-board power or payload to carry a traditional depth sensor (e.g., a 3D lidar) and thus can only acquire a few (point-wise) depth measurements. We address the following question: is it possible to reconstruct the geometry of an unknown environment using sparse and incomplete depth measurements? Reconstruction from incomplete data is not possible in general, but when the robot operates in man-made environments, the depth exhibits some regularity (e.g., many planar surfaces with only a few edges); we leverage this regularity to infer depth from a small number of measurements. Our first contribution is a formulation of the depth reconstruction problem that bridges robot perception with the compressive sensing literature in signal processing. The second contribution includes a set of formal results that ascertain the exactness and stability of the depth reconstruction in 2D and 3D problems, and completely characterize the geometry of the profiles that we can reconstruct. Our third contribution is a set of practical algorithms for depth reconstruction: our formulation directly translates into algorithms for depth estimation based on convex programming. In real-world problems, these convex programs are very large and general-purpose solvers are relatively slow. For this reason, we discuss ad-hoc solvers that enable fast depth reconstruction in real problems. The last contribution is an extensive experimental evaluation in 2D and 3D problems, including Monte Carlo runs on simulated instances and testing on multiple real datasets. Empirical results confirm that the proposed approach ensures accurate depth reconstruction, outperforms interpolation-based strategies, and performs well even when the assumption of structured environment is violated. We study the notion of compressed sensing (CS) as put forward by Donoho, Candes, Tao and others. The notion proposes a signal or image, unknown but supposed to be compressible by a known transform, (e.g. wavelet or Fourier), can be subjected to fewer measurements than the nominal number of data points, and yet be accurately reconstructed. The samples are nonadaptive and measure 'random' linear combinations of the transform coefficients. Approximate reconstruction is obtained by solving for the transform coefficients consistent with measured data and having the smallest possible l1 norm.We present initial 'proof-of-concept' examples in the favorable case where the vast majority of the transform coefficients are zero. We continue with a series of numerical experiments, for the setting of lp-sparsity, in which the object has all coefficients nonzero, but the coefficients obey an lp bound, for some p ∈ (0, 1]. The reconstruction errors obey the inequalities paralleling the theory, seemingly with well-behaved constants.We report that several workable families of 'random' linear combinations all behave equivalently, including random spherical, random signs, partial Fourier and partial Hadamard.We next consider how these ideas can be used to model problems in spectroscopy and image processing, and in synthetic examples see that the reconstructions from CS are often visually "noisy". To suppress this noise we postprocess using translation-invariant denoising, and find the visual appearance considerably improved.We also consider a multiscale deployment of compressed sensing, in which various scales are segregated and CS applied separately to each; this gives much better quality reconstructions than a literal deployment of the CS methodology.These results show that, when appropriately deployed in a favorable setting, the CS framework is able to save significantly over traditional sampling, and there are many useful extensions of the basic idea. In sparse approximation theory, the fundamental problem is to reconstruct a signal A∈ℝn from linear measurements 〈Aψi〉 with respect to a dictionary of ψi's. Recently, there is focus on the novel direction of Compressed Sensing [9] where the reconstruction can be done with very few—O(k logn)—linear measurements over a modified dictionary if the signal is compressible, that is, its information is concentrated in k coefficients with the original dictionary. In particular, these results [9, 4, 23] prove that there exists a single O(k logn) ×n measurement matrix such that any such signal can be reconstructed from these measurements, with error at most O(1) times the worst case error for the class of such signals. Compressed sensing has generated tremendous excitement both because of the sophisticated underlying Mathematics and because of its potential applications In this paper, we address outstanding open problems in Compressed Sensing. Our main result is an explicit construction of a non-adaptive measurement matrix and the corresponding reconstruction algorithm so that with a number of measurements polynomial in k, logn, 1 e, we can reconstruct compressible signals. This is the first known polynomial time explicit construction of any such measurement matrix. In addition, our result improves the error guarantee from O(1) to 1 + e and improves the reconstruction time from poly(n) to poly(k logn) Our second result is a randomized construction of O(kpolylog (n)) measurements that work for each signal with high probability and gives per-instance approximation guarantees rather than over the class of all signals. Previous work on Compressed Sensing does not provide such per-instance approximation guarantees; our result improves the best known number of measurements known from prior work in other areas including Learning Theory [20, 21], Streaming algorithms [11, 12, 6] and Complexity Theory [1] for this case Our approach is combinatorial. In particular, we use two parallel sets of group tests, one to filter and the other to certify and estimate; the resulting algorithms are quite simple to implement This paper presents a novel probabilistic foundation for volumetric 3D reconstruction. We formulate the problem as inference in a Markov random field, which accurately captures the dependencies between the occupancy and appearance of each voxel, given all input images. Our main contribution is an approximate highly parallelized discrete-continuous inference algorithm to compute the marginal distributions of each voxel's occupancy and appearance. In contrast to the MAP solution, marginals encode the underlying uncertainty and ambiguity in the reconstruction. Moreover, the proposed algorithm allows for a Bayes optimal prediction with respect to a natural reconstruction loss. We compare our method to two state-of-the-art volumetric reconstruction algorithms on three challenging aerial datasets with LIDAR ground truth. Our experiments demonstrate that the proposed algorithm compares favorably in terms of reconstruction accuracy and the ability to expose reconstruction uncertainty. Distributed sampling and reconstruction of a physical field using an array of sensors is a problem of considerable interest in environmental monitoring applications of sensor networks. Our recent work has focused on the sampling of bandlimited sensor fields. However, sensor fields are not perfectly bandlimited but typically have rapidly decaying spectra. In a classical sampling set-up it is possible to precede the A D sampling operation with an appropriate analog anti-aliasing filter. However, in the case of sensor networks, this is infeasible since sampling must precede filtering. We show that even though the effects of aliasing on the reconstruction cannot be prevented due to the "filter-less" sampling constraint, they can be suitably controlled by oversampling and carefully reconstructing the field from the samples. We show using a dither-based scheme that it is possible to estimate non-bandlimited fields with a precision that depends on how fast the spectral content of the field decays. We develop a framework for analyzing non-bandlimited fields that lead to upper bounds on the maximum pointwise error for a spatial bit rate of R bits meter. We present results for fields with exponentially decaying spectra as an illustration. In particular, we show that for fields f(t) with exponential tails; i.e., F( spl omega ) < spl pi spl alpha sup - spl alpha | spl omega | , the maximum pointwise error decays as c2e sup -a sub 1 spl radic R+ c3 1 spl radic R (e sup -2a sub 1 spl radic R) with spatial bit rate R bits meter. Finally, we show that for fields with spectra that have a finite second moment, the distortion decreases as O((1 N) sup 2 3 ) as the density of sensors, N, scales up to infinity . We show that if D is the targeted non-zero distortion, then the required (finite) rate R scales as O (1 spl radic D log 1 D).