A novel adaptable accurate way for calculating the polar FFT and the log-polar FFT is developed in this paper, namely, Multilayer Fractional Fourier Transform ( MLFFT). MLFFT is a necessary addition to the pseudopolar...
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A novel adaptable accurate way for calculating the polar FFT and the log-polar FFT is developed in this paper, namely, Multilayer Fractional Fourier Transform ( MLFFT). MLFFT is a necessary addition to the pseudopolar FFT for the following reasons: It has lower interpolation errors in both polar and log-polar Fourier transforms, it reaches better accuracy with the nearly same computing complexity as the pseudopolar FFT, and provides a mechanism to increase the accuracy by increasing the user-defined computing level. This paper demonstrates both MLFFT itself and its advantages theoretically and experimentally. By emphasizing applications of MLFFT in image registration with rotation and scaling, our experiments suggest two major advantages of MLFFT: 1) Scaling up to 5 and arbitrary rotation angles or scaling up to 10 without rotation can be recovered by MLFFT, while, currently, the result recovered by the state-of-the-art algorithms is the maximum scaling of 4. 2) No iteration is needed to recover large rotation and scaling values of images by MLFFT;hence, it is more efficient than the pseudopolar-based FFT methods for image registration.
Recently researchers have started employing Monte Carlo-like line sample estimators in rendering, demonstrating dramatic reductions in variance (visible noise) for effects such as soft shadows, defocus blur, and parti...
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Recently researchers have started employing Monte Carlo-like line sample estimators in rendering, demonstrating dramatic reductions in variance (visible noise) for effects such as soft shadows, defocus blur, and participating media. Unfortunately, there is currently no formal theoretical framework to predict and analyze Monte Carlo variance using line and segment samples which have inherently anisotropic Fourier power spectra. In this work, we propose a theoretical formulation for lines and finite-length segment samples in the frequency domain that allows analyzing their anisotropic power spectra using previous isotropic variance and convergence tools. Our analysis shows that judiciously oriented line samples not only reduce the dimensionality but also pre-filter C-0 discontinuities, resulting in further improvement in variance and convergence rates. Our theoretical insights also explain how finite-length segment samples impact variance and convergence rates only by pre-filtering discontinuities. We further extend our analysis to consider (uncorrelated) multi-directional line (segment) sampling, showing that such schemes can increase variance compared to unidirectional sampling. We validate our theoretical results with a set of experiments including direct lighting, ambient occlusion, and volumetric caustics using points, lines, and segment samples.
This paper presents flott, a fast, low memory T-transform algorithm which can be used to compute the string complexity measure T-complexity. The algorithm uses approximately one third of the memory of its predecessor ...
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This paper presents flott, a fast, low memory T-transform algorithm which can be used to compute the string complexity measure T-complexity. The algorithm uses approximately one third of the memory of its predecessor while reducing the running time by about 20 percent. The flott implementation has the same worst-case memory requirements as state of the art suffix tree construction algorithms. A suffix tree can be used to efficiently compute the Lempel-Ziv production complexity, which is another measure of string complexity. The C-implementation of flott is available as Open Source software.
This paper describes a method for the efficient computation of the total autocorrelation for large multiple-output Boolean functions over a Shared Binary Decision Diagram (SBDD). The existing methods for computing the...
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This paper describes a method for the efficient computation of the total autocorrelation for large multiple-output Boolean functions over a Shared Binary Decision Diagram (SBDD). The existing methods for computing the total autocorrelation over decision diagrams are restricted to single output functions and in the case of multiple-output functions require repeating the procedure k times where k is the number of outputs. The proposed method permits to perform the computation in a single traversal of SBDD. In that order, compared to standard BDD packages, we modified the way of traversing sub-diagrams in SBDD and introduced an additional memory function kept in the hash table for storing results of the computation of the autocorrelation between two subdiagrarns in the SBDD. Due to that, the total amount of computations is reduced which makes the method feasible in practical applications. Experimental results over standard benchmarks confirm the efficiency of the method.
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