Kernel adaptive filter

About: Kernel adaptive filter is a research topic. Over the lifetime, 8771 publications have been published within this topic receiving 142711 citations.

A Fast Approximation of the Bilateral Filter Using a Signal Processing Approach

Abstract: The bilateral filter is a nonlinear filter that smoothes a signal while preserving strong edges. It has demonstrated great effectiveness for a variety of problems in computer vision and computer graphics, and fast versions have been proposed. Unfortunately, little is known about the accuracy of such accelerations. In this paper, we propose a new signal-processing analysis of the bilateral filter which complements the recent studies that analyzed it as a PDE or as a robust statistical estimator. The key to our analysis is to express the filter in a higher-dimensional space where the signal intensity is added to the original domain dimensions. Importantly, this signal-processing perspective allows us to develop a novel bilateral filtering acceleration using downsampling in space and intensity. This affords a principled expression of accuracy in terms of bandwidth and sampling. The bilateral filter can be expressed as linear convolutions in this augmented space followed by two simple nonlinearities. This allows us to derive criteria for downsampling the key operations and achieving important acceleration of the bilateral filter. We show that, for the same running time, our method is more accurate than previous acceleration techniques. Typically, we are able to process a 2 megapixel image using our acceleration technique in less than a second, and have the result be visually similar to the exact computation that takes several tens of minutes. The acceleration is most effective with large spatial kernels. Furthermore, this approach extends naturally to color images and cross bilateral filtering.

Approaches to adaptive filtering

Abstract: The different methods of adaptive filtering are divided into four categories: Bayesian, maximum likelihood (ML), correlation, and covariance matching. The relationship between the methods and the difficulties associated with each method are described. New algorithms for the direct estimation of the optimal gain of a Kalman filter are given.

On the origin of the bilateral filter and ways to improve it

Abstract: Additive noise removal from a given signal is an important problem in signal processing. Among the most appealing aspects of this field are the ability to refer it to a well-established theory, and the fact that the proposed algorithms in this field are efficient and practical. Adaptive methods based on anisotropic diffusion (AD), weighted least squares (WLS), and robust estimation (RE) were proposed as iterative locally adaptive machines for noise removal. Tomasi and Manduchi (see Proc. 6th Int. Conf. Computer Vision, New Delhi, India, p.839-46, 1998) proposed an alternative noniterative bilateral filter for removing noise from images. This filter was shown to give similar and possibly better results to the ones obtained by iterative approaches. However, the bilateral filter was proposed as an intuitive tool without theoretical connection to the classical approaches. We propose such a bridge, and show that the bilateral filter also emerges from the Bayesian approach, as a single iteration of some well-known iterative algorithm. Based on this observation, we also show how the bilateral filter can be improved and extended to treat more general reconstruction problems.

Wavelet filter evaluation for image compression

Abstract: Choice of filter bank in wavelet compression is a critical issue that affects image quality as well as system design. Although regularity is sometimes used in filter evaluation, its success at predicting compression performance is only partial. A more reliable evaluation can be obtained by considering an L-level synthesis/analysis system as a single-input, single-output, linear shift-variant system with a response that varies according to the input location module (2/sup L/,2/sup L/). By characterizing a filter bank according to its impulse response and step response in addition to regularity, we obtain reliable and relevant (for image coding) filter evaluation metrics. Using this approach, we have evaluated all possible reasonably short (less than 36 taps in the synthesis/analysis pair) minimum-order biorthogonal wavelet filter banks. Of this group of over 4300 candidate filter banks, we have selected and present here the filters best suited to image compression. While some of these filters have been published previously, others are new and have properties that make them attractive in system design. >

A fast approximation of the bilateral filter using a signal processing approach

Abstract: The bilateral filter is a nonlinear filter that smoothes a signal while preserving strong edges. It has demonstrated great effectiveness for a variety of problems in computer vision and computer graphics, and a fast version has been proposed. Unfortunately, little is known about the accuracy of such acceleration. In this paper, we propose a new signal-processing analysis of the bilateral filter, which complements the recent studies that analyzed it as a PDE or as a robust statistics estimator. Importantly, this signal-processing perspective allows us to develop a novel bilateral filtering acceleration using a downsampling in space and intensity. This affords a principled expression of the accuracy in terms of bandwidth and sampling. The key to our analysis is to express the filter in a higher-dimensional space where the signal intensity is added to the original domain dimensions. The bilateral filter can then be expressed as simple linear convolutions in this augmented space followed by two simple nonlinearities. This allows us to derive simple criteria for downsampling the key operations and to achieve important acceleration of the bilateral filter. We show that, for the same running time, our method is significantly more accurate than previous acceleration techniques.