In this paper we consider the problem of finding a near-optimal policy in a continuous space, dis... more In this paper we consider the problem of finding a near-optimal policy in a continuous space, discounted Markovian Decision Problem (MDP) by employing value-function-based methods when only a single trajectory of a fixed policy is available as the input. We study a policy-iteration algorithm where the iterates are obtained via empirical risk minimization with a risk function that penalizes high magnitudes of the Bellman-residual. Our main result is a finite-sample, high-probability bound on the performance of the computed policy that depends on the mixing rate of the trajectory, the capacity of the function set as measured by a novel capacity concept (the VC-crossing dimension), the approximation power of the function set and the controllability properties of the MDP. Moreover, we prove that when a linear parameterization is used the new algorithm is equivalent to Least-Squares Policy Iteration. To the best of our knowledge this is the first theoretical result for off-policy control learning over continuous state-spaces using a single trajectory.
Stereoscopic rendering and 3D stereo displays are quickly becoming mainstream. The natural extens... more Stereoscopic rendering and 3D stereo displays are quickly becoming mainstream. The natural extension is autostereoscopic multi-view displays which, by the use of parallax barriers or lenticular lenses, can accommodate many simultaneous viewers without the need for active or passive glasses. As these displays, for the foreseeable future, will support only a rather limited number of views, there is a need for high-quality interperspective antialiasing. We present a specialized algorithm for efficient multi-view image generation from a camera line using ray tracing, which builds on previous methods for multi-dimensional adaptive sampling and reconstruction of light fields. We introduce multi-view silhouette edges to detect sharp geometrical discontinuities in the radiance function. These are used to significantly improve the quality of the reconstruction. In addition, we exploit shader coherence by computing analytical visibility between shading points and the camera line, and by sharing shading computations over the camera line.
This paper presents an algorithm for image completion based on the views of large displacement. A... more This paper presents an algorithm for image completion based on the views of large displacement. A distinct from most existing image completion methods, which exploit only the target image’s own information to complete the damaged regions, our algorithm makes full use of a large displacement view (LDV) of the same scene, which introduces enough information to resolve the original ill-posed problem. To eliminate any perspective distortion during the warping of the LDV image, we first decompose the target image and the LDV one into several corresponding planar scene regions (PSRs) and transform the candidate PSRs on the LDV image onto their correspondences on the target image. Then using the transformed PSRs, we develop a new image repairing algorithm, coupled with graph cut based image stitching, texture synthesis based image inpainting, and image fusion based hole filling, to complete the missing regions seamlessly. Finally, the ghost effect between the repaired region and its surroundings is eliminated by Poisson image blending. Our algorithm effectively preserves the structure information on the missing area of the target image and produces a repaired result comparable to its original appearance. Experiments show the effectiveness of our method.
We consider bounds on the prediction error of classification algorithms based on sample compressi... more We consider bounds on the prediction error of classification algorithms based on sample compression. We refine the notion of a compression scheme to distinguish permutation and repetition invariant and non-permutation and repetition invariant compression schemes leading to different prediction error bounds. Also, we extend known results on compression to the case of non-zero empirical risk. We provide bounds on the prediction error of classifiers returned by mistake-driven online learning algorithms by interpreting mistake bounds as bounds on the size of the respective compression scheme of the algorithm. This leads to a bound on the prediction error of perceptron solutions that depends on the margin a support vector machine would achieve on the same training sample. Furthermore, using the property of compression we derive bounds on the average prediction error of kernel classifiers in the PAC-Bayesian framework. These bounds assume a prior measure over the expansion coefficients in the data-dependent kernel expansion and bound the average prediction error uniformly over subsets of the space of expansion coefficients.
... and Expo, 2007, pp. 12–15. [18]Alin C.Popescu, and Hany Farid, “Exposing digital forgeries in... more ... and Expo, 2007, pp. 12–15. [18]Alin C.Popescu, and Hany Farid, “Exposing digital forgeries in color filter array interpolated images,” IEEE Transactions on Signal Processing, vol. 53, no. 10, pp. 3948–3959, 2005. [19] J. He, Z ...
In this paper we consider the problem of finding a near-optimal policy in a continuous space, dis... more In this paper we consider the problem of finding a near-optimal policy in a continuous space, discounted Markovian Decision Problem (MDP) by employing value-function-based methods when only a single trajectory of a fixed policy is available as the input. We study a policy-iteration algorithm where the iterates are obtained via empirical risk minimization with a risk function that penalizes high magnitudes of the Bellman-residual. Our main result is a finite-sample, high-probability bound on the performance of the computed policy that depends on the mixing rate of the trajectory, the capacity of the function set as measured by a novel capacity concept (the VC-crossing dimension), the approximation power of the function set and the controllability properties of the MDP. Moreover, we prove that when a linear parameterization is used the new algorithm is equivalent to Least-Squares Policy Iteration. To the best of our knowledge this is the first theoretical result for off-policy control learning over continuous state-spaces using a single trajectory.
Stereoscopic rendering and 3D stereo displays are quickly becoming mainstream. The natural extens... more Stereoscopic rendering and 3D stereo displays are quickly becoming mainstream. The natural extension is autostereoscopic multi-view displays which, by the use of parallax barriers or lenticular lenses, can accommodate many simultaneous viewers without the need for active or passive glasses. As these displays, for the foreseeable future, will support only a rather limited number of views, there is a need for high-quality interperspective antialiasing. We present a specialized algorithm for efficient multi-view image generation from a camera line using ray tracing, which builds on previous methods for multi-dimensional adaptive sampling and reconstruction of light fields. We introduce multi-view silhouette edges to detect sharp geometrical discontinuities in the radiance function. These are used to significantly improve the quality of the reconstruction. In addition, we exploit shader coherence by computing analytical visibility between shading points and the camera line, and by sharing shading computations over the camera line.
This paper presents an algorithm for image completion based on the views of large displacement. A... more This paper presents an algorithm for image completion based on the views of large displacement. A distinct from most existing image completion methods, which exploit only the target image’s own information to complete the damaged regions, our algorithm makes full use of a large displacement view (LDV) of the same scene, which introduces enough information to resolve the original ill-posed problem. To eliminate any perspective distortion during the warping of the LDV image, we first decompose the target image and the LDV one into several corresponding planar scene regions (PSRs) and transform the candidate PSRs on the LDV image onto their correspondences on the target image. Then using the transformed PSRs, we develop a new image repairing algorithm, coupled with graph cut based image stitching, texture synthesis based image inpainting, and image fusion based hole filling, to complete the missing regions seamlessly. Finally, the ghost effect between the repaired region and its surroundings is eliminated by Poisson image blending. Our algorithm effectively preserves the structure information on the missing area of the target image and produces a repaired result comparable to its original appearance. Experiments show the effectiveness of our method.
We consider bounds on the prediction error of classification algorithms based on sample compressi... more We consider bounds on the prediction error of classification algorithms based on sample compression. We refine the notion of a compression scheme to distinguish permutation and repetition invariant and non-permutation and repetition invariant compression schemes leading to different prediction error bounds. Also, we extend known results on compression to the case of non-zero empirical risk. We provide bounds on the prediction error of classifiers returned by mistake-driven online learning algorithms by interpreting mistake bounds as bounds on the size of the respective compression scheme of the algorithm. This leads to a bound on the prediction error of perceptron solutions that depends on the margin a support vector machine would achieve on the same training sample. Furthermore, using the property of compression we derive bounds on the average prediction error of kernel classifiers in the PAC-Bayesian framework. These bounds assume a prior measure over the expansion coefficients in the data-dependent kernel expansion and bound the average prediction error uniformly over subsets of the space of expansion coefficients.
... and Expo, 2007, pp. 12–15. [18]Alin C.Popescu, and Hany Farid, “Exposing digital forgeries in... more ... and Expo, 2007, pp. 12–15. [18]Alin C.Popescu, and Hany Farid, “Exposing digital forgeries in color filter array interpolated images,” IEEE Transactions on Signal Processing, vol. 53, no. 10, pp. 3948–3959, 2005. [19] J. He, Z ...
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