Huffman, Park and Skoug introduced a generalized Fourier-Feynman transform (GFFT) and a generalized convolution product (GCP) and they obtained the relationships between the GFFT and GCP for functionals in the Banach algebra S introduced by Cameron and Storvick. In this paper, we investigate various relationships among the GFFT, GCP and generalized first variation for functionals in S.
Unveiling the dense correspondence under the haze layer remains a challenging task, since the scattering effects result in less distinctive image features. Contrarily, dehazing is often confused by the airlightalbedo ambiguity which cannot be resolved independently at each pixel. In this paper, we introduce a deep convolutional neural network (CNN) that simultaneously estimates a disparity and clear image from a hazy stereo image pair. Both tasks are synergistically formulated by fusing depth information from the matching cost and haze transmission. To learn the optimal fusion of depth-related features, we present a novel encoderdecoder architecture that extends the core idea of attention mechanism to the simultaneous stereo matching and dehazing. As a result, our method estimates high-quality disparity for the stereo images in scattering media, and produces appearance images with enhanced visibility. Finally, we further propose an effec
Abstract. Cameron and Storvick introduced the concept of a sequential Fourier-Feynman transform and established the existence of this transform for functionals in a Banach algebraŜ of bounded functionals on classical Wiener space. In this paper we investigate various relationships between the sequential Fourier-Feynman transform and the convolution product for functionals which need not be bounded or continuous. Also we study the relationships involving this transform and the first variation.
In this paper, we define the conditional Fourier-Feynman transform and the conditional convolution product over Wiener paths in abstract Wiener space. Using a simple formula, we obtain conditional Feynman integrals of Fourier-Feynman transform and convolution product of cylinder type functions. For these functions, we evaluate the conditional Fourier-Feynman transforms and the conditional convolution products, and show that the conditional Fourier-Feynman transform of the conditional convolution product is a product of the conditional Fourier-Feynman transforms.
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