Fast Implementation Of Bilateral Filter With Application In Image Processing

As an effective information medium, an image is an important approach for our human to obtain and exchange effective information. Researchers have shown that seventy-five percent of surroundings information which was able to be perceptive by human was acquired through human visual system. Digital image processing originated in the nineteen twenties. In recent decades, with the growing popularity of the digital image, digital image processing is becoming one of the research focuses in computer science. And there are many branches in digital image processing, such as image restoration, image enhancement, image registration, image segmentation, edge detection, image compression, pattern recognition and so on.With the progress of science and technology, digital image acquisition equipment has become more and more popular, and a high quality image must be achieved in order to extract the important feature of object. However, some noise could be lead into an image in imaging system because of various disturbances while an image is obtained in the processing of image formation, transmission, reception and et al, Some details are often submerged in noise, which greatly make them difficult for image observation, feature information extraction and analysis of image processing. The mixed noise composed of Gaussian noise with impulse noise is a typical noise model in digital image. Noise will inhibit people’s comprehension to an image, in order to improving the degree of people’s understanding to the image. using appropriate methods to reduce noise before further image applications is a very important preprocessing step. Therefore, image denoising is one of the most important and basic research topic in the field of digital image processing at all times.The theory and the algorithm of image denoising keep continuous development, which is mainly powered by deeper comprehension of the image processing and more successful introductions of new mathematical methods, there have been many classics algorithms such as mean filtering, median filtering, Wiener filtering. These algorithms can remove noise, but at the same time they will bring a lot of loss of image detail, which can not reach people’s expectations. Edge is one of the basic characters of all image, which offers people important parameters to describe and recognize objects in the actual image processing problems. Thus, The basic goal of image denoising is to suppress and remove noise while preserving image edges and details. In reality, suppressing noise and preserving image edges is often a contradiction, the problems has not been well solved in image processing field.The bilateral filter is a nonlinear filter which smoothes an image signal for denoising while preserving edges and details. Bilateral filtering has raised to address the problem of blurring edges, and obtained a better effect in image enhancement. The bilateral filtering is proposed based on the theory of Gaussian filtering, just as its name implies, is a Gauss filter function based on spatial distribution, has had an extra one Gauss kernel function which is based on spatial distribution than Gaussian filtering, so as to ensure the preservation of edge. Not only does it take into account spatial proximity also considers the similarity of intensity. Only the neighborhood of similar intensity is averaged. Bilateral filtering have a great deal of improvement and development both in theory and applications, It has demonstrated great effectiveness for a variety of problems in computer vision and computer graphics. Since then, thanks to the ability of preserving edges, the use of bilateral filtering has grown rapidly and is now ubiquitous in image processing, applications. It has been used in various such as denoising, texture editing and relighting, tone management, demosaicking, and optical-flow estimation. The bilateral filter has several qualities such as simplification and flexibility that explain its success.The bilateral filter has proven to be very useful, Nevertheless it has a very large defect:calculating speed is too low. The bilateral filter is a spatial domain filter, Nonetheless, the bilateral filter need to be simultaneously calculated the spatial domain kernel function and range domain kernel function, and its frequency response is related to the input image, it is nonlinear so that performing convolution after an FFT, can only be achieved by a simple pointwise calculation, therefore bilateral filter is time-consuming. As the image resolution and the window width of templet increased, the process time of bilateral filter increase rapidly. Nowadays, the mainstream resolution of digital image is millions or even tens of millions of pixels,5so that operation time of the bilateral filter will be very long, it is unable to meet the needs of image real-time processing, the defect of slow calculation limits the application space of the bilateral filter. How to quickly implement the bilateral filter is important significance.In order to improve computational efficiency of the bilateral filtering, many scholars focus on research and improving about accelerating bilateral filter. More typical are:piecewise-linear bilateral filtering, separable kernel bilateral filtering, bilateral filtering based on local histogram, increment-dimensional bilateral filtering (bilateral grid filtering), constant time O(1) bilateral filtering, real-time O(1) bilateral filtering, triangle bilateral filtering. In addition to "separable kernel", the other algorithm improved bilateral filtering to linear filtering. These fast algorithms speed up bilateral filter greatly, however at the expense of filter precision and other application of image processing. For example, the filter accuracy of piecewise-linear bilateral filtering is not enough well. Bilateral filtering based on local histogram and the first algorithm of constant time O(1) bilateral filtering can not deal with color images and other multidimensional image. The running time of the second, thirdly algorithm of constant time O(1) bilateral filtering and triangle bilateral filtering significantly increased along with the gray standard deviation decreases. The denoising ability of real-time O(1) bilateral filtering is not well.The main content of this paper is to research efficient implementation of bilateral filtering. Speed up the computation speed of bilateral filtering to the same level as the linear filtering (such as Gaussian filtering), while guarantee the accuracy of bilateral filtering. Improve bilateral filtering algorithm based on analysis of inherent characteristics of bilateral filtering and draw on the experience of linear filtering, o overcome problems of large computational complexity and difficult for real-time systems. Starting from the view of signal and system, improve the bilateral filtering for linear filtering system. This paper presents two kinds of fast algorithms of bilateral filtering.The first algorithm is the improved increment-dimensional bilateral filtering algorithm. The main method of increment-dimensional bilateral filtering is that express the filter as linear convolution between gauss kernel function and image function in a higher-dimensional space where the signal intensity is added to the original domain dimensions, corresponding to multiplication in the frequency domain, inverse Fourier transform to the result, it will convert the tedious calculation to a fast Fourier transform calculation. Then downsample the three-dimensional matrix to reduce the computational data, for the sake of the effective acceleration. In this paper, aiming at the existing problem of Increment-Dimensional bilateral filter, this paper improve increment-dimensional bilateral filter from the three aspects of it. Firstly, improve the sampling mode; second, the matrix extend only in the third dimension before the Fourier transform extension or use gauss recursive for3D convolution. Instead of linear interpolation, we use reduction-dimension technique method based on inverse mapping and fill value. Experimental which five images are tested at different noise levels proved that the method improves the computational efficiency due to interpolation can be avoided. The running time of improved bilateral filter is less than half of increment-dimensional bilateral filter, while the filtering accuracy is close to the traditional bilateral filter.The second algorithm is dimensionality-reduction O(1) bilateral filtering algorithm, the computational complexity of the algorithm and the running time of it are independent of the filter size, only related to the size of the original image size. The algorithm through the linearization of the bilateral filter, the image matrix is mapped to conform to a one-dimensional array linear bilateral filtering system, then the linear operation of the array; and then the results will be reduced to the inverse mapping image matrix; finally, based on the original image information and mapping rules in pixel offset, achieve rapid implementation of the bilateral filter. The algorithm started with linearization for system of bilateral filtering and image matrix is mapped to one-dimensional array, then linearly filter the array. In a next step, the above calculation will be restored to the image matrix by inverse mapping. Finally, all pixels fill values in accordance with the information of the original information and mapping rules, to achieve the purpose of achieving important acceleration of the bilateral filter.The second algorithm is dimensionality-reduction O(1) bilateral filtering algorithm. This paper presents the algorithm using dimensionality reduction, to overcome problems of large computational complexity and difficult for real-time systems. The algorithm started with linearization for system of bilateral filtering and image matrix is mapped to one-dimensional array, then linearly filter the array. In a next step, the above calculation will be restored to the image matrix by inverse mapping. Finally, all pixels fill values in accordance with the information of the original information and mapping rules, to achieve the purpose of achieving important acceleration of the bilateral filter.The substance of dimensionality-reduction O(1) bilateral filtering is that convert the nonlinear operation among image and two Gauss kernels to linear operation among image and two Gauss kernels one after another by approximation method. First, the image signal is used to linear combination with gray similarity factor, the specific way is:according to a certain rule mapping (dimension reduction),convert the multidimensional image or signal to one-dimensional signals, implement one-dimensional linear filtering and normalization according to the intensity similarity factor, and get the filtered signals. Then, implement the filtered signals and spatial proximity factor for linear combination, the specific performance is that estimate the filtered intensity of pixel through linear interpolation among one-dimensional filtered signals formed for the neighborhood of each pixel. Approximate to the original bilateral filtering algorithm through the "dimensionality-reduction filter" and "estimation by interpolation". The experimental results show that:the method greatly reduces the time-consuming aspects of "filtering", improves the overall computational efficiency. The running time of dimensionality-reduction O(1) bilateral filtering is far less than the real time O(1) bilateral filtering which is mainstream at present, while the filtering accuracy is close to the traditional bilateral filter. Either the filtering precision or efficiency, the algorithm is much better than real time O(1) bilateral filtering.