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.

Feasibility of differential geometry-based features in detection of anatomical feature points on patient surfaces in range image-guided radiation therapy

“…The template image was defined by the operator to include the anatomical landmarks on the patient's surface before the treatment. The range images were preprocessed for the extraction of the ROI by using a template matching between the amplitude and template images, and reducing temporal and spatial noise using Kalman [20,21] and bilateral filters [22][23][24], respectively. Next, a smooth surface for the ROI in the range image was reconstructed based on non-uniform rational B-splines (NURBS) mathematical modeling, and curvature features were computed on the mathematical surface.…”

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“…In our experiments, an efficient computational method of CBF procedure is used [24,26]. The computational complexity of this method is linear to the image size.…”

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Adaptive noise-reducing anisotropic diffusion filter

“…Also, it is slow when the kernel is large. Nonetheless, several solutions have been proposed to accelerate the evaluation of the bilateral filter such as [17][18][19][20][21]. Unfortunately, most of these approaches rely on approximations that are not based on firm theoretical foundations, and it is hard to evaluate their accuracy.…”