We propose a bilateral filter with a locally controlled domain kernel for directional edge-preserving smoothing. Traditional bilateral filters use a range kernel, which is responsible for edge preservation, and a fixed domain kernel that performs smoothing. Our intuition is that orientation and anisotropy of image structures should be incorporated into the domain kernel while smoothing. For this purpose, we employ an oriented Gaussian domain kernel locally controlled by a structure tensor. The oriented domain kernel combined with a range kernel forms the directional bilateral filter. The two kernels assist each other in effectively suppressing the influence of the outliers while smoothing. To find the optimal parameters of the directional bilateral filter, we propose the use of Stein's unbiased risk estimate (SURE). We test the capabilities of the kernels separately as well as together, first on synthetic images, and then on real endoscopic images. The directional bilateral filter has better denoising performance than the Gaussian bilateral filter at various noise levels in terms of peak signal-to-noise ratio (PSNR).
Modifications of the bilateral filters have found widespread use in a number of image processing tasks such as denoising @cite_15 , illumination compensation @cite_2 , optical-flow estimation @cite_18 , demoaiscking @cite_4 , edge detection @cite_11 , etc.
@cite_18 @cite_4 @cite_2 @cite_15 @cite_11
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We propose to employ bilateral filters to solve the problem of edge detection. The proposed methodology presents an efficient and noise robust method for detecting edges. Classical bilateral filters smooth images without distorting edges. In this paper, we modify the bilateral filter to perform edge detection, which is the opposite of bilateral smoothing. The Gaussian domain kernel of the bilateral filter is replaced with an edge detection mask, and Gaussian range kernel is replaced with an inverted Gaussian kernel. The modified range kernel serves to emphasize dissimilar regions. The resulting approach effectively adapts the detection mask according as the pixel intensity differences. The results of the proposed algorithm are compared with those of standard edge detection masks. Comparisons of the bilateral edge detector with Canny edge detection algorithm, both after non-maximal suppression, are also provided. The results of our technique are observed to be better and noise-robust than those offered by methods employing masks alone, and are also comparable to the results from Canny edge detector, outperforming it in certain cases. Like bilateral filter (BF), cross bilateral filter (CBF) considers both gray-level similarities and geometric closeness of the neighboring pixels without smoothing edges, but it uses one image for finding the kernel and other to filter, and vice versa. In this paper, it is proposed to fuse source images by weighted average using the weights computed from the detail images that are extracted from the source images using CBF. The performance of the proposed method has been verified on several pairs of multisensor and multifocus images and compared with the existing methods visually and quantitatively. It is found that, none of the methods have shown consistence performance for all the performance metrics. But as compared to them, the proposed method has shown good performance in most of the cases. Further, the visual quality of the fused image by the proposed method is superior to other methods. Edge-preserving smoothing is widely used in image processing and bilateral filtering is one way to achieve it. Bilateral filter is a nonlinear combination of domain and range filters. Implementing the classical bilateral filter is computationally intensive, owing to the nonlinearity of the range filter. In the standard form, the domain and range filters are Gaussian functions and the performance depends on the choice of the filter parameters. Recently, a constant time implementation of the bilateral filter has been proposed based on raised-cosine approximation to the Gaussian to facilitate fast implementation of the bilateral filter. We address the problem of determining the optimal parameters for raised-cosine-based constant time implementation of the bilateral filter. To determine the optimal parameters, we propose the use of Stein's unbiased risk estimator (SURE). The fast bilateral filter accelerates the search for optimal parameters by faster optimization of the SURE cost. Experimental results show that the SURE-optimal raised-cosine-based bilateral filter has nearly the same performance as the SURE-optimal standard Gaussian bilateral filter and the Oracle mean squared error (MSE)-based optimal bilateral filter. Bilateral filter is an edge-preserving diffusion filter and is widely used for image denoising. The denoising quality is sensitive to the choice of the bilateral filter parameters. Here, we propose to use the Chi-Square Unbiased Risk Estimate (CURE) for optimizing bilateral filter parameters in squared magnitude MR images, which follow a non-central chi-square distribution with two degrees of freedom. CURE is an unbiased estimate of the Mean Squared Error (MSE) and it does not require any knowledge of the noise-free data. We derive explicit analytical expressions for CURE in the setting of bilateral filters and present experimental results that confirm the optimality of CURE.