Directional Bilateral Filters

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)

Guided mesh normal filtering

The joint bilateral filter is a variant of the standard bilateral filter, where the range kernel is evaluated using a guidance signal instead of the original signal. It has been successfully applied to various image processing problems, where it provides more flexibility than the standard bilateral filter to achieve high quality results. On the other hand, its success is heavily dependent on the guidance signal, which should ideally provide a robust estimation about the features of the output signal. Such a guidance signal is not always easy to construct. In this paper, we propose a novel mesh normal filtering framework based on the joint bilateral filter, with applications in mesh denoising. Our framework is designed as a two-stage process: first, we apply joint bilateral filtering to the face normals, using a properly constructed normal field as the guidance; afterwards, the vertex positions are updated according to the filtered face normals. We compute the guidance normal on a face using a neighboring patch with the most consistent normal orientations, which provides a reliable estimation of the true normal even with a high-level of noise. The effectiveness of our approach is validated by extensive experimental results

Bilateral Filter: Graph Spectral Interpretation and Extensions

In this paper we study the bilateral filter proposed by Tomasi and Manduchi, as a spectral domain transform defined on a weighted graph. The nodes of this graph represent the pixels in the image and a graph signal defined on the nodes represents the intensity values. Edge weights in the graph correspond to the bilateral filter coefficients and hence are data adaptive. Spectrum of a graph is defined in terms of the eigenvalues and eigenvectors of the graph Laplacian matrix. We use this spectral interpretation to generalize the bilateral filter and propose more flexible and application specific spectral designs of bilateral-like filters. We show that these spectral filters can be implemented with k-iterative bilateral filtering operations and do not require expensive diagonalization of the Laplacian matrix

Bilateral filter in image processing

The bilateral filter is a nonlinear filter that does spatial averaging without smoothing edges. It has shown to be an effective image denoising technique. It also can be applied to the blocking artifacts reduction. An important issue with the application of the bilateral filter is the selection of the filter parameters, which affect the results significantly. Another research interest of bilateral filter is acceleration of the computation speed. There are three main contributions of this thesis. The first contribution is an empirical study of the optimal bilateral filter parameter selection in image denoising. I propose an extension of the bilateral filter: multi resolution bilateral filter, where bilateral filtering is applied to the low-frequency sub-bands of a signal decomposed using a wavelet filter bank. The multi resolution bilateral filter is combined with wavelet thresholding to form a new image denoising framework, which turns out to be very effective in eliminating noise in real noisy images. The second contribution is that I present a spatially adaptive method to reduce compression artifacts. To avoid over-smoothing texture regions and to effectively eliminate blocking and ringing artifacts, in this paper, texture regions and block boundary discontinuities are first detected; these are then used to control/adapt the spatial and intensity parameters of the bilateral filter. The test results prove that the adaptive method can improve the quality of restored images significantly better than the standard bilateral filter. The third contribution is the improvement of the fast bilateral filter, in which I use a combination of multi windows to approximate the Gaussian filter more precisely

Dynamic Investigative Practice at the International Criminal Court

The Direct Weight Optimization (DWO) approach is a nonparametric estimation approach that has appeared in recent years within the field of nonlinear system identification. In previous work, all function classes for which DWO has been studied have included only continuous functions. However, in many applications it would be desirable also to be able to handle discontinuous functions. Inspired by the bilateral filter method from image processing, such an extension of the DWO framework is proposed for the smoothing problem. Examples show that the properties of the new approach regarding the handling of discontinuities are similar to the bilateral filter, while at the same time DWO offers a greater flexibility with respect to different function classes handled

Fast O(1) bilateral filtering using trigonometric range kernels

It is well-known that spatial averaging can be realized (in space or frequency domain) using algorithms whose complexity does not depend on the size or shape of the filter. These fast algorithms are generally referred to as constant-time or O(1) algorithms in the image processing literature. Along with the spatial filter, the edge-preserving bilateral filter [Tomasi1998] involves an additional range kernel. This is used to restrict the averaging to those neighborhood pixels whose intensity are similar or close to that of the pixel of interest. The range kernel operates by acting on the pixel intensities. This makes the averaging process non-linear and computationally intensive, especially when the spatial filter is large. In this paper, we show how the O(1) averaging algorithms can be leveraged for realizing the bilateral filter in constant-time, by using trigonometric range kernels. This is done by generalizing the idea in [Porikli2008] of using polynomial range kernels. The class of trigonometric kernels turns out to be sufficiently rich, allowing for the approximation of the standard Gaussian bilateral filter. The attractive feature of our approach is that, for a fixed number of terms, the quality of approximation achieved using trigonometric kernels is much superior to that obtained in [Porikli2008] using polynomials.Comment: Accepted in IEEE Transactions on Image Processing. Also see addendum: https://sites.google.com/site/kunalspage/home/Addendum.pd