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499
Joint MAP registration and highresolution image estimation using a sequence of undersampled images
 IEEE Transactions on Image Processing
, 1997
"... Abstract — In many imaging systems, the detector array is not sufficiently dense to adequately sample the scene with the desired field of view. This is particularly true for many infrared focal plane arrays. Thus, the resulting images may be severely aliased. This paper examines a technique for esti ..."
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Cited by 161 (2 self)
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Abstract — In many imaging systems, the detector array is not sufficiently dense to adequately sample the scene with the desired field of view. This is particularly true for many infrared focal plane arrays. Thus, the resulting images may be severely aliased. This paper examines a technique for estimating a highresolution image, with reduced aliasing, from a sequence of undersampled frames. Several approaches to this problem have been investigated previously. However, in this paper a maximum a posteriori (MAP) framework for jointly estimating image registration parameters and the highresolution image is presented. Several previous approaches have relied on knowing the registration parameters a priori or have utilized registration techniques not specifically designed to treat severely aliased images. In the proposed method, the registration parameters are iteratively updated along with the highresolution image in a cyclic coordinatedescent optimization procedure. Experimental results are provided to illustrate the performance of the proposed MAP algorithm using both visible and infrared images. Quantitative error analysis is provided and several images are shown for subjective evaluation. Index Terms—Aliased, high resolution, image registration, image sequence, MAP estimation. I.
Ranksparsity incoherence for matrix decomposition
, 2010
"... Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown lowrank matrix. Our goal is to decompose the given matrix into its sparse and lowrank components. Such a problem arises in a number of applications in model and system identification, and is intractable ..."
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Cited by 83 (10 self)
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Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown lowrank matrix. Our goal is to decompose the given matrix into its sparse and lowrank components. Such a problem arises in a number of applications in model and system identification, and is intractable to solve in general. In this paper we consider a convex optimization formulation to splitting the specified matrix into its components, by minimizing a linear combination of the ℓ1 norm and the nuclear norm of the components. We develop a notion of ranksparsity incoherence, expressed as an uncertainty principle between the sparsity pattern of a matrix and its row and column spaces, and use it to characterize both fundamental identifiability as well as (deterministic) sufficient conditions for exact recovery. Our analysis is geometric in nature with the tangent spaces to the algebraic varieties of sparse and lowrank matrices playing a prominent role. When the sparse and lowrank matrices are drawn from certain natural random ensembles, we show that the sufficient conditions for exact recovery are satisfied with high probability. We conclude with simulation results on synthetic matrix decomposition problems.
A Frequency Analysis of Light Transport
, 2005
"... We present a signalprocessing framework for light transport. We study the frequency content of radiance and how it is altered by phenomena such as shading, occlusion, and transport. This extends previous work that considered either spatial or angular dimensions, and it offers a comprehensive treatm ..."
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Cited by 78 (11 self)
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We present a signalprocessing framework for light transport. We study the frequency content of radiance and how it is altered by phenomena such as shading, occlusion, and transport. This extends previous work that considered either spatial or angular dimensions, and it offers a comprehensive treatment of both space and angle. We show that occlusion, a multiplication in the primal, amounts in the Fourier domain to a convolution by the spectrum of the blocker. Propagation corresponds to a shear in the spaceangle frequency domain, while reflection on curved objects performs a different shear along the angular frequency axis. As shown by previous work, reflection is a convolution in the primal and therefore a multiplication in the Fourier domain. Our work shows how the spatial components of lighting are affected by this angular convolution. Our framework predicts the characteristics of interactions such as caustics and the disappearance of the shadows of small features. Predictions on the frequency content can then be used to control sampling rates for rendering. Other potential applications include precomputed radiance transfer and inverse rendering.
Depth from Defocus: A Spatial Domain Approach
 International Journal of Computer Vision
, 1994
"... A new method named STM is described for determining distance of objects and rapid autofocusing of camera systems. STM uses image defocus information and is based on a new SpatialDomain Convolution/Deconvolution Transform. The method requires only two images taken with dierent camera parameters ..."
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Cited by 78 (13 self)
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A new method named STM is described for determining distance of objects and rapid autofocusing of camera systems. STM uses image defocus information and is based on a new SpatialDomain Convolution/Deconvolution Transform. The method requires only two images taken with dierent camera parameters such as lens position, focal length, and aperture diameter. Both images can be arbitrarily blurred and neither of them needs to be a focused image. Therefore STM is very fast in comparison with DepthfromFocus methods which search for the lens position or focal length of best focus. The method involves simple local operations and can be easily implemented in parallel to obtain the depthmap of a scene. STM has been implemented on an actual camera system named SPARCS. Experiments on the performance of STM and their results on realworld planar objects are presented. The results indicate that the accuracy of STM compares well with DepthfromFocus methods and is useful in practical ap...
Better Optical Triangulation through Spacetime Analysis
 In ICCV
, 1995
"... The standard methods for extracting range data from optical triangulation scanners are accurate only for planar objects of uniform reflectance illuminated by an incoherent source. Using these methods, curved surfaces, discontinuous surfaces, and surfaces of varying reflectance cause systematic disto ..."
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Cited by 76 (8 self)
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The standard methods for extracting range data from optical triangulation scanners are accurate only for planar objects of uniform reflectance illuminated by an incoherent source. Using these methods, curved surfaces, discontinuous surfaces, and surfaces of varying reflectance cause systematic distortions of the range data. Coherent light sources such as lasers introduce speckle artifacts that further degrade the data. We present a new ranging method based on analyzing the time evolution of the structured light reflections. Using our spacetime analysis, we can correct for each of these artifacts, thereby attaining significantly higher accuracy using existing technology. We present results that demonstrate the validity of our method using a commercial laser stripe triangulation scanner. 1 Introduction Active optical triangulation is one of the most common methods for acquiring range data. Although this technology has been in use for over twenty years, its speedandaccuracyhas increasedd...
Parallel Depth Recovery by Changing Camera Parameters
, 1992
"... A new method is described for recovering the distance of objects in a scene from images formed by lenses. The recovery is based on measuring the change in the scene's image due to a known change in the three intrinsic camera parameters: (i) distance between the lens and the image detector, (ii) ..."
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Cited by 74 (14 self)
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A new method is described for recovering the distance of objects in a scene from images formed by lenses. The recovery is based on measuring the change in the scene's image due to a known change in the three intrinsic camera parameters: (i) distance between the lens and the image detector, (ii) focal length of the lens, and (iii) diameter of the lens aperture. The method is parallel involving simple local computations. In comparison with stereo vision and structurefrommotion methods, the correspondence problem does not arise. This method for depthmap recovery may also be used for (i) obtaining focused images (i.e. images having large depth of field) from two images having finite depth of field, and (ii) rapid autofocusing of computer controlled video cameras. 1. Introduction Here we describe a new passive ranging method which in principle is fast and involves relatively weak assumptions that are generally valid. The method is basically a generalized version of the `depthfromfocu...
In Search of a General Picture Processing Operator
 Computer Graphics and Image Processing
, 1978
"... INTRODUCTION Pictorial pattern recognition systems are often described as consisting of three parts: a preprocessing part, a feature extraction part, and a classification part. The preprocessing is used to enhance or sharpen the image to be processed. This is usually done using linear operations or ..."
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Cited by 54 (3 self)
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INTRODUCTION Pictorial pattern recognition systems are often described as consisting of three parts: a preprocessing part, a feature extraction part, and a classification part. The preprocessing is used to enhance or sharpen the image to be processed. This is usually done using linear operations or operations on the gray scale such as thresholding [13] The classification part is fairly well understood [4,5]. The feature extractor, on the other hand, is very much dependent upon the actual problem and no general theory has emerged on how to deal with it. Feature extraction procedures so far have been ad hoc, often referred to as "a bag of tricks." The present work grew out of an interest in finding a single picture operator that could in parallel perform a number of useful operations and that could work on several levels in a hierarchy. One background to this interest is the feeling that the eyes and brains of humans and animals are likely to have such standard operators, as the micro
4D frequency analysis of computational cameras for depth of field extension
 MIT CSAIL TR
, 2009
"... latticefocal lens. The defocus kernel of this lens is designed to preserve high frequencies over a wide depth range. Right: An allfocused image processed from the latticefocal lens input. Since the defocus kernel preserves high frequencies, we achieve a good restoration over the full depth range. ..."
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Cited by 30 (7 self)
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latticefocal lens. The defocus kernel of this lens is designed to preserve high frequencies over a wide depth range. Right: An allfocused image processed from the latticefocal lens input. Since the defocus kernel preserves high frequencies, we achieve a good restoration over the full depth range. Depth of field (DOF), the range of scene depths that appear sharp in a photograph, poses a fundamental tradeoff in photography— wide apertures are important to reduce imaging noise, but they also increase defocus blur. Recent advances in computational imaging modify the acquisition process to extend the DOF through deconvolution. Because deconvolution quality is a tight function of the frequency power spectrum of the defocus kernel, designs with high spectra are desirable. In this paper we study how to design effective extendedDOF systems, and show an upper bound on the maximal power spectrum that can be achieved. We analyze defocus kernels in the 4D light field space and show that in the frequency domain, only a lowdimensional 3D manifold contributes to focus. Thus, to maximize the defocus spectrum, imaging systems should concentrate their limited energy on this manifold. We review several computational imaging systems and show either that they spend energy outside the focal manifold or do not achieve a high spectrum over the DOF. Guided by this analysis we introduce the latticefocal lens, which concentrates energy at the lowdimensional focal manifold and achieves a higher power spectrum than previous designs. We have built a prototype latticefocal lens and present extended depth of field results.
Programmable imaging using a digital micromirror array
 In Proc. CVPR
, 2004
"... In this paper, we introduce the notion of a programmable imaging system. Such an imaging system provides a human user or a vision system significant control over the radiometric and geometric characteristics of the system. This flexibility is achieved using a programmable array of micromirrors. The ..."
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Cited by 29 (2 self)
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In this paper, we introduce the notion of a programmable imaging system. Such an imaging system provides a human user or a vision system significant control over the radiometric and geometric characteristics of the system. This flexibility is achieved using a programmable array of micromirrors. The orientations of the mirrors of the array can be controlled with high precision over space and time. This enables the system to select and modulate rays from the light field based on the needs of the application at hand. We have implemented a programmable imaging system that uses a digital micromirror device (DMD), which is used in digital light processing. Although the mirrors of this device can only be positioned in one of two
ThreeDimensional Object Reconstruction Using PhaseOnly Information From a Digital Hologram
"... We present the initial results of a novel technique that uses only phase information from a digital hologram for the reconstruction of threedimensional (3D) objects. Our holograms are created using phaseshift digital holography. Perspectives of the 3D object are usually reconstructed numerically o ..."
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Cited by 26 (19 self)
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We present the initial results of a novel technique that uses only phase information from a digital hologram for the reconstruction of threedimensional (3D) objects. Our holograms are created using phaseshift digital holography. Perspectives of the 3D object are usually reconstructed numerically on a computer. For large holograms this can be a computationally intensive task. We believe that the proposed reconstruction technique is promising for 3D display because the phaseencoded digital holograms admit optical, and therefore realtime, reconstructions that use commercially available display devices such as liquid crystal spatial light modulators. Numerical evaluation of the reconstructed 3D object and an experimental demonstration are presented.