OptimalO(1) Bilateral Filter with Arbitrary Spatial and Range Kernels Using Sparse Approximation

Shengdong Pan,Hangen He,Xiangjing An

doi:10.1155/2014/289517

Shengdong Pan, Hangen He + Show 1 more

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https://doi.org/10.1155/2014/289517

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Abstract

A number of acceleration schemes for speeding up the time-consuming bilateral filter have been proposed in the literature. Among these techniques, the histogram-based bilateral filter trades the flexibility for achievingO(1) computational complexity using box spatial kernel. A recent study shows that this technique can be leveraged forO(1) bilateral filter with arbitrary spatial and range kernels by linearly combining the results of multiple-box bilateral filters. However, this method requires many box bilateral filters to obtain sufficient accuracy when approximating the bilateral filter with a large spatial kernel. In this paper, we propose approximating arbitrary spatial kernel using a fixed number of boxes. It turns out that the multiple-box spatial kernel can be applied in manyO(1) acceleration schemes in addition to the histogram-based one. Experiments on the application to the histogram-based acceleration are presented in this paper. Results show that the proposed method has better accuracy in approximating the bilateral filter with Gaussian spatial kernel, compared with the previous histogram-based methods. Furthermore, the performance of the proposed histogram-based bilateral filter is robust with respect to the parameters of the filter kernel.

Highlights

The bilateral filter is proposed by Tomasi and Manduchi in [1]
We propose a method to approximate arbitrary spatial kernel with multiple boxes, which can be leveraged for the constant-time implementation of the bilateral filter with arbitrary spatial and range kernels
Having that an arbitrary spatial kernel is approximated with a preset number of boxes, we first exploit its use in the histogram-based bilateral filters, which is originally developed by Weiss in [20], later accelerated by Porikli in [21], and recently extended by Gunturk in [26]

Summary

Introduction

The bilateral filter is proposed by Tomasi and Manduchi in [1]. Before this name, it is called SUSAN filter [2]. Gunturk’s method does not produce sufficiently good approximation with only a few additional single-box bilateral filters when the spatial kernel is large. We focus our attention on approximating arbitrary spatial kernel with a fixed number of boxes. With this constraint, the MSE-based optimization becomes a wellknown sparse representation problem. In addition to the application to the histogram-based bilateral filter, the proposed method can be employed in other acceleration schemes by substituting the spatial filtering with a fixed times of box filtering. The proposed method for approximating arbitrary spatial kernel with a fixed number of boxes is deduced in detail.

Related Works

Histogram-Based Approximation Using Box Spatial

Experiments and Comparisons

Conclusions and Discussions