The Experts below are selected from a list of 144 Experts worldwide ranked by ideXlab platform
S.j. Reeves - One of the best experts on this subject based on the ideXlab platform.
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ISBI - Reduced k-space Sampling for MR images with a limited region of support
Proceedings IEEE International Symposium on Biomedical Imaging, 2002Co-Authors: S.j. ReevesAbstract:When region of support information is available in MRI, the number of phase-encoding steps and thus time can be reduced compared to acquiring the standard Rectangular grid. This reduction can be accomplished without loss of information if the k-space locations are chosen well. We propose to select locations using a Rectangular Sampling array that is shifted to various positions in k-space to obtain the necessary Sampling density. The proposed method is fast enough to be used in real-time imaging and overcomes some of the limitations of previously proposed methods.
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Reduced k-space Sampling for MR images with a limited region of support
Proceedings IEEE International Symposium on Biomedical Imaging, 2002Co-Authors: S.j. ReevesAbstract:When region of support information is available in MRI, the number of phase-encoding steps and thus time can be reduced compared to acquiring the standard Rectangular grid. This reduction can be accomplished without loss of information if the k-space locations are chosen well. We propose to select locations using a Rectangular Sampling array that is shifted to various positions in k-space to obtain the necessary Sampling density. The proposed method is fast enough to be used in real-time imaging and overcomes some of the limitations of previously proposed methods.
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Fast k-space sample selection in MRSI with a limited region of support
IEEE Transactions on Medical Imaging, 2001Co-Authors: S.j. ReevesAbstract:One of the primary drawbacks in the application of magnetic resonance spectroscopic imaging is the long acquisition times required to obtained the desired resolution. When region of support information is available, the number of phase-encoding steps and thus time can be reduced without loss of information if the k-space locations are chosen well. The authors propose to select locations using a Rectangular Sampling array that is shifted to various positions in k-space to obtain the necessary Sampling density. This method allows multiple samples to be selected simultaneously and reduces the computation required to evaluate the selection criterion. The authors present an efficient forward selection algorithm for optimizing the shift pattern so that the image can be reconstructed as reliably as possible from a periodic nonuniform set of samples. The proposed algorithm has important practical potential in that it can finish the selection in less than half a minute for typical image sizes and can reconstruct the image with fewer samples than regular Sampling. With appropriate imaging hardware, this new algorithm makes selective Sampling possible in a real-time image acquisition setting.
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Efficient backward selection ofk-space samples in MRI on a hexagonal grid
Circuits Systems and Signal Processing, 2000Co-Authors: S.j. ReevesAbstract:Certain types of magnetic resonance imaging (MRI) such as magnetic resonance spectroscopic imaging and three-dimensional (3D) MRI require a great deal of time to acquire the image data. The acquisition time can be reduced if the image has a limited region of support, such as when imaging the brain or a cross section of the chest. Hexagonal Sampling of the spatial frequency-domain ( k -space) yields a 13.4% Sampling density reduction compared to Rectangular Sampling of the k -space for images with a circular region of support (ROS) without incurring spatial aliasing in the reconstructed image. However, certain nonuniform Sampling patterns are more efficient than hexagonal Sampling for the same ROS. Sequential backward selection (SBS) has been used in previous work to optimize a nonuniform set of k -space samples selected from a Rectangular grid. To reduce the selection time, we present SBS of samples from a hexagonal grid. A Smith normal decomposition is used to transform the nonRectangular 2D discrete Fourier transform to a standard Rectangular 2D fast Fourier transform so that the spatial-domain samples are represented directly on a Rectangular grid without interpolation. The hexagonal grid allows the SBS algorithm to begin with a smaller set of candidate samples so that fewer samples have to be eliminated. Simulation results show that a significantly reduced selection time can be achieved with the proposed method in comparison with SBS on a Rectangular grid.
A.j. Van Leest - One of the best experts on this subject based on the ideXlab platform.
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Gabor's signal expansion and the Gabor transform based on a non-orthogonal Sampling geometry
Proceedings of the Sixth International Symposium on Signal Processing and its Applications (Cat.No.01EX467), 2001Co-Authors: Mj Martin Bastiaans, A.j. Van LeestAbstract:Gabor's (1946) signal expansion and the Gabor transform are formulated on a non-orthogonal time-frequency lattice instead of on the traditional Rectangular lattice. The reason for doing so is that a non-orthogonal Sampling geometry might be better adapted to the form of the window functions (in the time-frequency domain) than an orthogonal one. OverSampling in the Gabor scheme, which is required to have mathematically more attractive properties for the analysis window, then leads to better results in combination with less overSampling. The new procedure presented in this paper is based on considering the non-orthogonal lattice as a sub-lattice of a denser orthogonal lattice that is oversampled by a rational factor. In doing so, Gabor's signal expansion on a non-orthogonal lattice can be related to the expansion on an orthogonal lattice (restricting ourselves, of course, to only those Sampling points that are part of the non-orthogonal sub-lattice), and all the techniques that have been derived for Rectangular Sampling can be used, albeit in a slightly modified form.
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Gabor's signal expansion and the Gabor transform on a non-separable time-frequency lattice
Journal of The Franklin Institute-engineering and Applied Mathematics, 2000Co-Authors: A.j. Van Leest, Mj Martin BastiaansAbstract:Abstract Gabor's signal expansion and the Gabor transform are formulated on a general, non-separable time–frequency lattice instead of on the traditional Rectangular lattice. The representation of the general lattice is based on the Rectangular lattice via a shear operation, which corresponds to a description of the general lattice by means of a lattice generator matrix that has the Hermite normal form. The shear operation on the lattice is associated with simple operations on the signal, on the synthesis and the analysis window, and on Gabor's expansion coefficients; these operations consist of multiplications by quadratic phase terms. Following this procedure, the well-known bi-orthogonality condition for the window functions in the Rectangular Sampling geometry, can be directly translated to the general case. In the same way, a modified Zak transform can be defined for the non-separable case, with the help of which Gabor's signal expansion and the Gabor transform can be brought into product forms that are identical to the ones that are well known for the Rectangular Sampling geometry.
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ISSPA - Gabor's signal expansion and a modified Zak transform for a quincunx-type Sampling geometry
ISSPA '99. Proceedings of the Fifth International Symposium on Signal Processing and its Applications (IEEE Cat. No.99EX359), 1999Co-Authors: Mj Martin Bastiaans, A.j. Van LeestAbstract:Gabor's (1946) signal expansion and the Gabor transform are formulated on a quincunx lattice instead of on the traditional Rectangular lattice; the representation of the quincunx lattice is based on the Rectangular lattice via either a shear operation or a rotation operation. A modified Zak (1972) transformation is defined with the help of which Gabor's signal expansion and the Gabor transform can be brought into product forms that are identical to the ones that are well known for the Rectangular Sampling geometry. The shear operation on the lattice is associated with an operation on the synthesis and the analysis window, consisting of a multiplication by a quadratic-phase function. Following this procedure, the well-known biorthogonality condition for the window functions in the Rectangular Sampling geometry can be directly translated to the quincunx case.
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Gabor's signal expansion and a modified Zak transform for a quincunx-type Sampling geometry
ISSPA '99. Proceedings of the Fifth International Symposium on Signal Processing and its Applications (IEEE Cat. No.99EX359), 1999Co-Authors: Mj Martin Bastiaans, A.j. Van LeestAbstract:Gabor's (1946) signal expansion and the Gabor transform are formulated on a quincunx lattice instead of on the traditional Rectangular lattice; the representation of the quincunx lattice is based on the Rectangular lattice via either a shear operation or a rotation operation. A modified Zak (1972) transformation is defined with the help of which Gabor's signal expansion and the Gabor transform can be brought into product forms that are identical to the ones that are well known for the Rectangular Sampling geometry. The shear operation on the lattice is associated with an operation on the synthesis and the analysis window, consisting of a multiplication by a quadratic-phase function. Following this procedure, the well-known biorthogonality condition for the window functions in the Rectangular Sampling geometry can be directly translated to the quincunx case.
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Product forms in Gabor analysis for a quincunx-type Sampling geometry
1998Co-Authors: Mj Martin Bastiaans, A.j. Van LeestAbstract:Recently a new Sampling lattice - the quincunx lattice - has been introduced [1] as a Sampling geometry in the Gabor scheme, which geometry is different from the traditional Rectangular Sampling geometry. In this paper we will show how results that hold for Rectangular Sampling (see, for instance, [2,3]) can be transformed to the quincunx case. In particular we will concentrate on the well-known product forms [2] of Gabor's signal expansion and the Gabor transform, in terms of the Fourier transform of the expansion coefficients and the Zak transforms of the signal and the window functions; these product forms hold in the case of critical Sampling, to which case we will confine ourselves. We will show that identical product forms can be formulated in the case of a quincunx Sampling geometry, as well, but then in terms of a modified version of the Zak transform. [1] P. Prinz, "Calculating the dual Gabor window for general Sampling sets," IEEE Trans. Signal Processing, 44 (1996) 2078-2082. [2] M.J. Bastiaans, "Gabor's signal expansion and its relation to Sampling of the sliding-window spectrum," in Advanced Topics in Shannon Sampling and Interpolation Theory, R.J. Marks II, Ed., Springer, New York (1993) 1-35. [3] H.G. Feichtinger and T. Strohmer, Eds., Gabor Analysis and Algorithms: Theory and Applications. Berlin: Birkhauser (1998).
Tsuhan Chen - One of the best experts on this subject based on the ideXlab platform.
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On Sampling of image-based rendering data
2020Co-Authors: Cha Zhang, Tsuhan ChenAbstract:Image-based rendering (IBR) generates novel views from images instead of 3D models. It can be considered as a process of Sampling the light rays in the space and interpolating the ones in novel views. The Sampling of IBR is a high-dimensional Sampling problem, and is very challenging. This thesis focuses on answering two questions related to IBR Sampling, namely how many images are needed for IBR, and if such number is limited, where should we capture them. There are three major contributions in this dissertation. First, we give a complete analysis on uniform Sampling of IBR data. By introducing the surface plenoptic function, we are able to analyze the Fourier spectrum of non-Lambertian and occluded scenes. Given the spectrum, we also apply the generalized Sampling theorem on the IBR data, which results in better rendering quality than Rectangular Sampling for complex scenes. Such uniform Sampling analysis provides general guidelines on how the images in IBR should be taken. For instance, it shows that non-Lambertian and occluded scenes often require higher Sampling rate. Second, we propose a very general Sampling framework named freeform Sampling. Freeform Sampling has three categories: incremental Sampling, decremental Sampling and rearranged Sampling. When the to-be-reconstructed function values are unknown, freeform Sampling becomes active Sampling. Algorithms of active Sampling are developed for image-based rendering and show better results than the traditional uniform Sampling approach. Third, we present a self-reconfigurable camera array that we developed, which features a very efficient algorithm for real-time rendering and the ability of automatically reconfiguring the cameras to improve the rendering quality. Both are based on active Sampling. Our camera array is able to render dynamic scenes interactively at high quality. To our best knowledge, it is the first camera array in literature that can reconfigure the camera positions automatically.
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On generalized Sampling for image-based rendering data
2003 IEEE International Conference on Acoustics Speech and Signal Processing 2003. Proceedings. (ICASSP '03)., 2003Co-Authors: Cha Zhang, Tsuhan ChenAbstract:We apply generalized Sampling to image-based rendering (IBR) data, more specifically, the lightfield. We show that, in theory, the lowest Sampling rate of a lightfield when we use generalized Sampling can be as low as half of that when we use Rectangular Sampling. However, in practice, Rectangular Sampling has several advantages over generalized Sampling. We analyze the pros and cons for each Sampling approach, and explain why, in practice, Rectangular Sampling is still preferable.
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Spectral analysis for Sampling image-based rendering data
IEEE Transactions on Circuits and Systems for Video Technology, 2003Co-Authors: Cha Zhang, Tsuhan ChenAbstract:Image-based rendering (IBR) has become a very active research area in recent years. The spectral analysis problem for IBR has not been completely solved. In this paper, we present a new method to parameterize the problem, which is applicable for general-purpose IBR spectral analysis. We notice that any plenoptic function is generated by light ray emitted/reflected/refracted from the object surface. We introduce the surface plenoptic function (SPF), which represents the light rays starting from the object surface. Given that radiance along a light ray does not change unless the light ray is blocked, SPF reduces the dimension of the original plenoptic function to 6D. We are then able to map or transform the SPF to IBR representations captured along any camera trajectory. Assuming some properties on the SPF, we can analyze the properties of IBR for generic scenes such as scenes with Lambertian or non-Lambertian surfaces and scenes with or without occlusions, and for different Sampling strategies such as lightfield/concentric mosaic. We find that in most cases, even though the SPF may be band-limited, the frequency spectrum of IBR is not band-limited. We show that non-Lambertian reflections, depth variations and occlusions can all broaden the spectrum, with the latter two being more significant. SPF is defined for scenes with known geometry. When the geometry is unknown, spectral analysis is still possible. We show that with the "truncating windows" analysis and some conclusions obtained with SPF, the spectrum expansion caused by non-Lambertian reflections and occlusions can be quantatively estimated, even when the scene geometry is not explicitly known. Given the spectrum of IBR, we also study how to sample IBR data more efficiently. Our analysis is based on the generalized periodic Sampling theory with arbitrary geometry. We show that the Sampling efficiency can be up to twice of that when we use Rectangular Sampling. The advantages and disadvantages of generalized periodic Sampling for IBR are also discussed.
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Light Field Sampling
Light Field Sampling, 1Co-Authors: Cha Zhang, Tsuhan ChenAbstract:Light field is one of the most representative image-based rendering techniques that generate novel virtual views from images instead of 3D models. The light field capture and rendering process can be considered as a procedure of Sampling the light rays in the space and interpolating those in novel views. As a result, light field can be studied as a high-dimensional signal Sampling problem, which has attracted a lot of research interest and become a convergence point between computer graphics and signal processing, and even computer vision. This lecture focuses on answering two questions regarding light field Sampling, namely how many images are needed for a light field, and if such number is limited, where we should capture them. The book can be divided into three parts. First, we give a complete analysis on uniform Sampling of IBR data. By introducing the surface plenoptic function, we are able to analyze the Fourier spectrum of non-Lambertian and occluded scenes. Given the spectrum, we also apply the generalized Sampling theorem on the IBR data, which results in better rendering quality than Rectangular Sampling for complex scenes. Such uniform Sampling analysis provides general guidelines on how the images in IBR should be taken. For instance, it shows that non-Lambertian and occluded scenes often require a higher Sampling rate. Next, we describe a very general Sampling framework named freeform Sampling. Freeform Sampling handles three kinds of problems: sample reduction, minimum Sampling rate to meet an error requirement, and minimization of reconstruction error given a fixed number of samples. When the to-be-reconstructed function values are unknown, freeform Sampling becomes active Sampling. Algorithms of active Sampling are developed for light field and show better results than the traditional uniform Sampling approach. Third, we present a self-reconfigurable camera array that we developed, which features a very efficient algorithm for real-time rendering and the ability of automatically reconfiguring the cameras to improve the rendering quality. Both are based on active Sampling. Our camera array is able to render dynamic scenes interactively at high quality. To the best of our knowledge, it is the first camera array that can reconfigure the camera positions automatically.
Mj Martin Bastiaans - One of the best experts on this subject based on the ideXlab platform.
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Gabor's signal expansion and the Gabor transform based on a non-orthogonal Sampling geometry
Proceedings of the Sixth International Symposium on Signal Processing and its Applications (Cat.No.01EX467), 2001Co-Authors: Mj Martin Bastiaans, A.j. Van LeestAbstract:Gabor's (1946) signal expansion and the Gabor transform are formulated on a non-orthogonal time-frequency lattice instead of on the traditional Rectangular lattice. The reason for doing so is that a non-orthogonal Sampling geometry might be better adapted to the form of the window functions (in the time-frequency domain) than an orthogonal one. OverSampling in the Gabor scheme, which is required to have mathematically more attractive properties for the analysis window, then leads to better results in combination with less overSampling. The new procedure presented in this paper is based on considering the non-orthogonal lattice as a sub-lattice of a denser orthogonal lattice that is oversampled by a rational factor. In doing so, Gabor's signal expansion on a non-orthogonal lattice can be related to the expansion on an orthogonal lattice (restricting ourselves, of course, to only those Sampling points that are part of the non-orthogonal sub-lattice), and all the techniques that have been derived for Rectangular Sampling can be used, albeit in a slightly modified form.
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Gabor's signal expansion and the Gabor transform on a non-separable time-frequency lattice
Journal of The Franklin Institute-engineering and Applied Mathematics, 2000Co-Authors: A.j. Van Leest, Mj Martin BastiaansAbstract:Abstract Gabor's signal expansion and the Gabor transform are formulated on a general, non-separable time–frequency lattice instead of on the traditional Rectangular lattice. The representation of the general lattice is based on the Rectangular lattice via a shear operation, which corresponds to a description of the general lattice by means of a lattice generator matrix that has the Hermite normal form. The shear operation on the lattice is associated with simple operations on the signal, on the synthesis and the analysis window, and on Gabor's expansion coefficients; these operations consist of multiplications by quadratic phase terms. Following this procedure, the well-known bi-orthogonality condition for the window functions in the Rectangular Sampling geometry, can be directly translated to the general case. In the same way, a modified Zak transform can be defined for the non-separable case, with the help of which Gabor's signal expansion and the Gabor transform can be brought into product forms that are identical to the ones that are well known for the Rectangular Sampling geometry.
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ISSPA - Gabor's signal expansion and a modified Zak transform for a quincunx-type Sampling geometry
ISSPA '99. Proceedings of the Fifth International Symposium on Signal Processing and its Applications (IEEE Cat. No.99EX359), 1999Co-Authors: Mj Martin Bastiaans, A.j. Van LeestAbstract:Gabor's (1946) signal expansion and the Gabor transform are formulated on a quincunx lattice instead of on the traditional Rectangular lattice; the representation of the quincunx lattice is based on the Rectangular lattice via either a shear operation or a rotation operation. A modified Zak (1972) transformation is defined with the help of which Gabor's signal expansion and the Gabor transform can be brought into product forms that are identical to the ones that are well known for the Rectangular Sampling geometry. The shear operation on the lattice is associated with an operation on the synthesis and the analysis window, consisting of a multiplication by a quadratic-phase function. Following this procedure, the well-known biorthogonality condition for the window functions in the Rectangular Sampling geometry can be directly translated to the quincunx case.
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Gabor's signal expansion and the Gabor transform for a general, non-separable Sampling geometry
1999Co-Authors: Mj Martin Bastiaans, Van Aj Arno LeestAbstract:Recently a new Sampling lattice - the quincunx lattice - has been introduced [1] as a Sampling geometry in the Gabor scheme, which geometry is different from the traditional Rectangular Sampling geometry. The quincunx lattice is just one example of the general class of non-separable time-frequency lattices. In this paper we will show how results that hold for Rectangular Sampling (see, for instance, [2,3]) can be transformed to the general, non-separable case. Gabor's signal expansion and the Gabor transform are formulated on a general, non-separable time-frequency lattice instead of on the traditional Rectangular lattice. The representation of the general lattice is based on the Rectangular lattice via a shear operation, which corresponds to a description of the general lattice by means of a lattice generator matrix that has the Hermite normal form. The shear operation on the lattice is associated with simple operations on the signal, on the synthesis and the analysis window, and on Gabor's expansion coefficients; these operations consist of multiplications by quadratic phase terms. Following this procedure, the well-known biorthogonality condition for the window functions in the Rectangular Sampling geometry, can be directly translated to the general case. In the same way, a modified Zak transform can be defined for the non-separable case, with the help of which Gabor's signal expansion and the Gabor transform can be brought into product forms that are identical to the ones that are well known for the Rectangular Sampling geometry. [1] P. Prinz, "Calculating the dual Gabor window for general Sampling sets," IEEE Trans. Signal Processing, 44 (1996) 2078-2082. [2] M.J. Bastiaans, "Gabor's signal expansion and its relation to Sampling of the sliding-window spectrum," in Advanced Topics in Shannon Sampling and Interpolation Theory, R.J. Marks II, Ed., Springer, New York (1993) 1-35. [3] H.G. Feichtinger and T. Strohmer, Eds., Gabor Analysis and Algorithms: Theory and Applications. Berlin: Birkhauser (1998).
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Gabor's signal expansion and a modified Zak transform for a quincunx-type Sampling geometry
ISSPA '99. Proceedings of the Fifth International Symposium on Signal Processing and its Applications (IEEE Cat. No.99EX359), 1999Co-Authors: Mj Martin Bastiaans, A.j. Van LeestAbstract:Gabor's (1946) signal expansion and the Gabor transform are formulated on a quincunx lattice instead of on the traditional Rectangular lattice; the representation of the quincunx lattice is based on the Rectangular lattice via either a shear operation or a rotation operation. A modified Zak (1972) transformation is defined with the help of which Gabor's signal expansion and the Gabor transform can be brought into product forms that are identical to the ones that are well known for the Rectangular Sampling geometry. The shear operation on the lattice is associated with an operation on the synthesis and the analysis window, consisting of a multiplication by a quadratic-phase function. Following this procedure, the well-known biorthogonality condition for the window functions in the Rectangular Sampling geometry can be directly translated to the quincunx case.
Cha Zhang - One of the best experts on this subject based on the ideXlab platform.
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On Sampling of image-based rendering data
2020Co-Authors: Cha Zhang, Tsuhan ChenAbstract:Image-based rendering (IBR) generates novel views from images instead of 3D models. It can be considered as a process of Sampling the light rays in the space and interpolating the ones in novel views. The Sampling of IBR is a high-dimensional Sampling problem, and is very challenging. This thesis focuses on answering two questions related to IBR Sampling, namely how many images are needed for IBR, and if such number is limited, where should we capture them. There are three major contributions in this dissertation. First, we give a complete analysis on uniform Sampling of IBR data. By introducing the surface plenoptic function, we are able to analyze the Fourier spectrum of non-Lambertian and occluded scenes. Given the spectrum, we also apply the generalized Sampling theorem on the IBR data, which results in better rendering quality than Rectangular Sampling for complex scenes. Such uniform Sampling analysis provides general guidelines on how the images in IBR should be taken. For instance, it shows that non-Lambertian and occluded scenes often require higher Sampling rate. Second, we propose a very general Sampling framework named freeform Sampling. Freeform Sampling has three categories: incremental Sampling, decremental Sampling and rearranged Sampling. When the to-be-reconstructed function values are unknown, freeform Sampling becomes active Sampling. Algorithms of active Sampling are developed for image-based rendering and show better results than the traditional uniform Sampling approach. Third, we present a self-reconfigurable camera array that we developed, which features a very efficient algorithm for real-time rendering and the ability of automatically reconfiguring the cameras to improve the rendering quality. Both are based on active Sampling. Our camera array is able to render dynamic scenes interactively at high quality. To our best knowledge, it is the first camera array in literature that can reconfigure the camera positions automatically.
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On generalized Sampling for image-based rendering data
2003 IEEE International Conference on Acoustics Speech and Signal Processing 2003. Proceedings. (ICASSP '03)., 2003Co-Authors: Cha Zhang, Tsuhan ChenAbstract:We apply generalized Sampling to image-based rendering (IBR) data, more specifically, the lightfield. We show that, in theory, the lowest Sampling rate of a lightfield when we use generalized Sampling can be as low as half of that when we use Rectangular Sampling. However, in practice, Rectangular Sampling has several advantages over generalized Sampling. We analyze the pros and cons for each Sampling approach, and explain why, in practice, Rectangular Sampling is still preferable.
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Spectral analysis for Sampling image-based rendering data
IEEE Transactions on Circuits and Systems for Video Technology, 2003Co-Authors: Cha Zhang, Tsuhan ChenAbstract:Image-based rendering (IBR) has become a very active research area in recent years. The spectral analysis problem for IBR has not been completely solved. In this paper, we present a new method to parameterize the problem, which is applicable for general-purpose IBR spectral analysis. We notice that any plenoptic function is generated by light ray emitted/reflected/refracted from the object surface. We introduce the surface plenoptic function (SPF), which represents the light rays starting from the object surface. Given that radiance along a light ray does not change unless the light ray is blocked, SPF reduces the dimension of the original plenoptic function to 6D. We are then able to map or transform the SPF to IBR representations captured along any camera trajectory. Assuming some properties on the SPF, we can analyze the properties of IBR for generic scenes such as scenes with Lambertian or non-Lambertian surfaces and scenes with or without occlusions, and for different Sampling strategies such as lightfield/concentric mosaic. We find that in most cases, even though the SPF may be band-limited, the frequency spectrum of IBR is not band-limited. We show that non-Lambertian reflections, depth variations and occlusions can all broaden the spectrum, with the latter two being more significant. SPF is defined for scenes with known geometry. When the geometry is unknown, spectral analysis is still possible. We show that with the "truncating windows" analysis and some conclusions obtained with SPF, the spectrum expansion caused by non-Lambertian reflections and occlusions can be quantatively estimated, even when the scene geometry is not explicitly known. Given the spectrum of IBR, we also study how to sample IBR data more efficiently. Our analysis is based on the generalized periodic Sampling theory with arbitrary geometry. We show that the Sampling efficiency can be up to twice of that when we use Rectangular Sampling. The advantages and disadvantages of generalized periodic Sampling for IBR are also discussed.
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Light Field Sampling
Light Field Sampling, 1Co-Authors: Cha Zhang, Tsuhan ChenAbstract:Light field is one of the most representative image-based rendering techniques that generate novel virtual views from images instead of 3D models. The light field capture and rendering process can be considered as a procedure of Sampling the light rays in the space and interpolating those in novel views. As a result, light field can be studied as a high-dimensional signal Sampling problem, which has attracted a lot of research interest and become a convergence point between computer graphics and signal processing, and even computer vision. This lecture focuses on answering two questions regarding light field Sampling, namely how many images are needed for a light field, and if such number is limited, where we should capture them. The book can be divided into three parts. First, we give a complete analysis on uniform Sampling of IBR data. By introducing the surface plenoptic function, we are able to analyze the Fourier spectrum of non-Lambertian and occluded scenes. Given the spectrum, we also apply the generalized Sampling theorem on the IBR data, which results in better rendering quality than Rectangular Sampling for complex scenes. Such uniform Sampling analysis provides general guidelines on how the images in IBR should be taken. For instance, it shows that non-Lambertian and occluded scenes often require a higher Sampling rate. Next, we describe a very general Sampling framework named freeform Sampling. Freeform Sampling handles three kinds of problems: sample reduction, minimum Sampling rate to meet an error requirement, and minimization of reconstruction error given a fixed number of samples. When the to-be-reconstructed function values are unknown, freeform Sampling becomes active Sampling. Algorithms of active Sampling are developed for light field and show better results than the traditional uniform Sampling approach. Third, we present a self-reconfigurable camera array that we developed, which features a very efficient algorithm for real-time rendering and the ability of automatically reconfiguring the cameras to improve the rendering quality. Both are based on active Sampling. Our camera array is able to render dynamic scenes interactively at high quality. To the best of our knowledge, it is the first camera array that can reconfigure the camera positions automatically.
