Smoothing images via the Beltrami flow in Hilbert space
نویسندگان
چکیده
The Beltrami flow is an effective tool for smoothing images in many computer vision tasks. However, a deep problem that is how to set the right embedding space is not solved in the Beltrami framework. In this paper, we attempt to find a suitable embedding space by a nonlinear map. First, the image space is mapped into a high-dimensional feature space whose dimension may be infinite. Then the Beltrami flow in the new space (Hilbert space) is introduced. It is found that directly dealing with the Beltrami flow in Hilbert space is impractical due to the unknown mapping function. Fortunately, using the well-known kernel methods, one can deal with the Beltrami flow in Hilbert space by applying dot products in the feature space. As a result, the Beltrami flow is performed in the kernel function space. We refer to this flow as the kernel Beltrami flow. Further, we extend the kernel Beltrami flow to deal with color images. Finally, we show the effectiveness of the proposed method on many types of the images including gray and color images.
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