Nonlinear bilateral filters (BF) deliver a fine blend of computational simplicity and blur-free denoising. However, little is known about their nature, noise-suppressing properties, and optimal choices of filter parameters. Our study is meant to fill this gap-explaining the underlying mechanism of bilateral filtering and providing the methodology for optimal filter selection. Practical application to CT image denoising is discussed to illustrate our results.
The bilateral filter is a useful nonlinear filter which without smoothing edges, it does spatial averaging. In the literature, the effectiveness of this method for image denoising is shown. In this paper, an extension of this method is proposed which is based on complex wavelet transform. In fact, the bilateral filtering is applied to the low-frequency (approximation) subbands of the decomposed image using complex wavelet transform, while the thresholding approach is applied to the high frequency subbands. Using the bilateral filter in the complex wavelet domain forms a new image denoising fra…
Indian Institute of Technology, Hyderabad（印度理工学院海得拉巴分校）；Indian Institute of Science（印度科学学院）
The bilateral filter has diverse applications in image processing, computer vision, and computational photography. In particular, this non-linear filter is quite effective in denoising images corrupted with additive Gaussian noise. The filter, however, is known to perform poorly at large noise levels. Several adaptations of the filter have been proposed in the literature to address this shortcoming, but often at an added computational cost. In this paper, we report a simple yet effective modification that improves the denoising performance of the bilateral filter at almost no additional cost. …
The bilateral filter is an edge-preserving smoother that has diverse applications in image processing, computer vision, computer graphics, and computational photography. The filter uses a spatial kernel along with a range kernel to perform edge-preserving smoothing. In this paper, we consider the Gaussian bilateral filter where both the kernels are Gaussian. A direct implementation of the Gaussian bilateral filter requires $O(σ_s^2)$ operations per pixel, where $σ_s$ is the standard deviation of the spatial Gaussian. In fact, it is well-known that the direct implementation is slow in practice.…
The bilateral filter is known to be quite effective in denoising images corrupted with small dosages of additive Gaussian noise. The denoising performance of the filter, however, is known to degrade quickly with the increase in noise level. Several adaptations of the filter have been proposed in the literature to address this shortcoming, but often at a substantial computational overhead. In this paper, we report a simple pre-processing step that can substantially improve the denoising performance of the bilateral filter, at almost no additional cost. The modified filter is designed to be robu…
The bilateral filter is a versatile non-linear filter that has found diverse applications in image processing, computer vision, computer graphics, and computational photography. A widely-used form of the filter is the Gaussian bilateral filter in which both the spatial and range kernels are Gaussian. A direct implementation of this filter requires $O(σ^2)$ operations per pixel, where $σ$ is the standard deviation of the spatial Gaussian. In this paper, we propose an accurate approximation algorithm that can cut down the computational complexity to $O(1)$ per pixel for any arbitrary $σ$ (consta…
A direct implementation of the bilateral filter [1] requires O(σ_s^2) operations per pixel, where σ_s is the (effective) width of the spatial kernel. A fast implementation of the bilateral filter was recently proposed in [2] that required O(1) operations per pixel with respect to σ_s. This was done by using trigonometric functions for the range kernel of the bilateral filter, and by exploiting their so-called shiftability property. In particular, a fast implementation of the Gaussian bilateral filter was realized by approximating the Gaussian range kernel using raised cosines. Later, it was de…
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 …
In computer vision, image processing and computer graphics, image smoothing filtering is a very basic and important task and to be expected possessing good edge-preserving smoothing property. Here we address the problem that the edge-preserving ability of many popular local smoothing filters needs to be improved. In this paper, we propose the image Edge Restoring Filter (ERF) to restore the blur edge pixels in the output of local smoothing filters to be clear. The proposed filter can been implemented after many local smoothing filter (such as Box filter, Gaussian filter, Bilateral Filter, Guid…
Robert Bosch Center for Cyber Physical Systems（罗伯特·博世信息物理系统中心）；Indian Institute of Science（印度科学学院）
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 k…
In this paper, we consider a natural extension of the edge-preserving bilateral filter for vector-valued images. The direct computation of this non-linear filter is slow in practice. We demonstrate how a fast algorithm can be obtained by first approximating the Gaussian kernel of the bilateral filter using raised-cosines, and then using Monte Carlo sampling. We present simulation results on color images to demonstrate the accuracy of the algorithm and the speedup over the direct implementation.
The bilateral filter is a non-linear filter that uses a range filter along with a spatial filter to perform edge-preserving smoothing of images. A direct computation of the bilateral filter requires $O(S)$ operations per pixel, where $S$ is the size of the support of the spatial filter. In this paper, we present a fast and provably accurate algorithm for approximating the bilateral filter when the range kernel is Gaussian. In particular, for box and Gaussian spatial filters, the proposed algorithm can cut down the complexity to $O(1)$ per pixel for any arbitrary $S$. The algorithm has a simple…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Bernstein Center for Computational Neuroscience（伯恩斯坦计算神经科学中心）
Bilateral filters have wide spread use due to their edge-preserving properties. The common use case is to manually choose a parametric filter type, usually a Gaussian filter. In this paper, we will generalize the parametrization and in particular derive a gradient descent algorithm so the filter parameters can be learned from data. This derivation allows to learn high dimensional linear filters that operate in sparsely populated feature spaces. We build on the permutohedral lattice construction for efficient filtering. The ability to learn more general forms of high-dimensional filters can be …
Video interpolation increases the temporal resolution of a video sequence by synthesizing intermediate frames between two consecutive frames. We propose a novel deep-learning-based video interpolation algorithm based on bilateral motion estimation. First, we develop the bilateral motion network with the bilateral cost volume to estimate bilateral motions accurately. Then, we approximate bi-directional motions to predict a different kind of bilateral motions. We then warp the two input frames using the estimated bilateral motions. Next, we develop the dynamic filter generation network to yield …
In the classical bilateral filter, a fixed Gaussian range kernel is used along with a spatial kernel for edge-preserving smoothing. We consider a generalization of this filter, the so-called adaptive bilateral filter, where the center and width of the Gaussian range kernel is allowed to change from pixel to pixel. Though this variant was originally proposed for sharpening and noise removal, it can also be used for other applications such as artifact removal and texture filtering. Similar to the bilateral filter, the brute-force implementation of its adaptive counterpart requires intense comput…
IT Dept., Assiut University（阿西乌特大学信息技术系）；Assiut University（阿西乌特大学）；Egypt（埃及（注意：此处Egypt是国家，非机构，原数据可能有误，按要求应忽略））；IT Dept.（信息技术系（重复出现））
Image posterization is converting images with a large number of tones into synthetic images with distinct flat areas and a fewer number of tones. In this technical report, we present the implementation and results of using fuzzy logic in order to generate a posterized image in a simple and fast way. The image filter is based on fuzzy logic and bilateral filtering; where, the given image is blurred to remove small details. Then, the fuzzy logic is used to classify each pixel into one of three specific categories in order to reduce the number of colors. This filter was developed during building …
Low-resolution and signal-dependent noise distribution in positron emission tomography (PET) images makes denoising process an inevitable step prior to qualitative and quantitative image analysis tasks. Conventional PET denoising methods either over-smooth small-sized structures due to resolution limitation or make incorrect assumptions about the noise characteristics. Therefore, clinically important quantitative information may be corrupted. To address these challenges, we introduced a novel approach to remove signal-dependent noise in the PET images where the noise distribution was considere…
Nanjing University of Aeronautics and Astronautics（南京航空航天大学）；Hong Kong Metropolitan University（香港都会大学）
Bilateral filter (BF) is a fast, lightweight and effective tool for image denoising and well extended to point cloud denoising. However, it often involves continual yet manual parameter adjustment; this inconvenience discounts the efficiency and user experience to obtain satisfied denoising results. We propose LBF, an end-to-end learnable bilateral filtering network for point cloud denoising; to our knowledge, this is the first time. Unlike the conventional BF and its variants that receive the same parameters for a whole point cloud, LBF learns adaptive parameters for each point according its …
National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所模式识别国家重点实验室）
Computational complexity of the brute-force implementation of the bilateral filter (BF) depends on its filter kernel size. To achieve the constant-time BF whose complexity is irrelevant to the kernel size, many techniques have been proposed, such as 2D box filtering, dimension promotion, and shiftability property. Although each of the above techniques suffers from accuracy and efficiency problems, previous algorithm designers were used to take only one of them to assemble fast implementations due to the hardness of combining them together. Hence, no joint exploitation of these techniques has b…
Segmentation of an object from a video is a challenging task in multimedia applications. Depending on the application, automatic or interactive methods are desired; however, regardless of the application type, efficient computation of video object segmentation is crucial for time-critical applications; specifically, mobile and interactive applications require near real-time efficiencies. In this paper, we address the problem of video segmentation from the perspective of efficiency. We initially redefine the problem of video object segmentation as the propagation of MRF energies along the tempo…
In this paper, we introduce an iterative speckle filtering method for polarimetric SAR (PolSAR) images based on the bilateral filter. To locally adapt to the spatial structure of images, this filter relies on pixel similarities in both spatial and radiometric domains. To deal with polarimetric data, we study the use of similarities based on a statistical distance called Kullback-Leibler divergence as well as two geodesic distances on Riemannian manifolds. To cope with speckle, we propose to progressively refine the result thanks to an iterative scheme. Experiments are run over synthetic and ex…
Depth imaging has largely focused on sensor and intrinsics properties. However, the accuracy of acquire pixel is largely dependent on the capture. We propose a new depth estimation and approximation algorithm which takes an arbitrary 3D point cloud as input, with potentially complex geometric structures, and generates automatically a bounding box which is used to clamp the 3D distribution into a valid range. We then infer the desired compact geometric network from complex 3D geometries by using a series of adaptive joint bilateral filters. Our approach leverages these input depth in the constr…
The underwater images usually suffers from non-uniform lighting, low contrast, blur and diminished colors. In this paper, we proposed an image based preprocessing technique to enhance the quality of the underwater images. The proposed technique comprises a combination of four filters such as homomorphic filtering, wavelet denoising, bilateral filter and contrast equalization. These filters are applied sequentially on degraded underwater images. The literature survey reveals that image based preprocessing algorithms uses standard filter techniques with various combinations. For smoothing the im…
University of Coimbra（科英布拉大学）；Institute of Systems and Robotics（系统与机器人研究所）
High resolution depth-maps, obtained by upsampling sparse range data from a 3D-LIDAR, find applications in many fields ranging from sensory perception to semantic segmentation and object detection. Upsampling is often based on combining data from a monocular camera to compensate the low-resolution of a LIDAR. This paper, on the other hand, introduces a novel framework to obtain dense depth-map solely from a single LIDAR point cloud; which is a research direction that has been barely explored. The formulation behind the proposed depth-mapping process relies on local spatial interpolation, using…
The advancement in numerous generative models has a two-fold effect: a simple and easy generation of realistic synthesized images, but also an increased risk of malicious abuse of those images. Thus, it is important to develop a generalized detector for synthesized images of any GAN model or object category, including those unseen during the training phase. However, the conventional methods heavily depend on the training settings, which cause a dramatic decline in performance when tested with unknown domains. To resolve the issue and obtain a generalized detection ability, we propose Bilateral…
Friedrich-Alexander Universität Erlangen-Nürnberg (FAU)（埃尔朗根-纽伦堡弗里德里希-亚历山大大学）；Siemens Healthcare GmbH（西门子医疗有限公司）
Deep neural networks have shown great success in low dose CT denoising. However, most of these deep neural networks have several hundred thousand trainable parameters. This, combined with the inherent non-linearity of the neural network, makes the deep neural network diffcult to understand with low accountability. In this study we introduce JBFnet, a neural network for low dose CT denoising. The architecture of JBFnet implements iterative bilateral filtering. The filter functions of the Joint Bilateral Filter (JBF) are learned via shallow convolutional networks. The guidance image is estimated…
Qingdao University（青岛大学）；Ocean University of China（中国海洋大学）
Images captured underwater are often characterized by low contrast, color distortion, and noise. To address these visual degradations, we propose a novel scheme by constructing an adaptive color and contrast enhancement, and denoising (ACCE-D) framework for underwater image enhancement. In the proposed framework, Difference of Gaussian (DoG) filter and bilateral filter are respectively employed to decompose the high-frequency and low-frequency components. Benefited from this separation, we utilize soft-thresholding operation to suppress the noise in the high-frequency component. Specially, the…
Princeton University（普林斯顿大学）；École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
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 i…
Imam Abdulrahman Bin Faisal University（伊玛目阿卜杜勒拉赫曼·本·费萨尔大学）
To accurately quantify in vivo radiotracer uptake using Positron Emission Tomography (PET) is a challenging task due to low signal-to-noise ratio (SNR) and poor spatial resolution of PET camera along with the finite image sampling constraint. Furthermore, inter lesion variations of the SNR and contrast along with the variations in size of the lesion make the quantitation even more difficult. One of the ways to improve the quantitation is via post reconstruction filtering with Gaussian Filter (GF). Edge preserving Bilateral Filter (BF) and Nonlinear Diffusion Filter (NDF) are the alternatives t…
Friedrich-Alexander University Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希-亚历山大大学）；Fraunhofer Institute for Ceramic Technologies and Systems IKTS（弗劳恩霍夫陶瓷技术与系统研究所（IKTS））；Leibniz Institute for Analytical Sciences ISAS（莱布尼茨分析科学研究所（ISAS））；University Hospital Erlangen（埃尔朗根大学医院）；Institute for Nanotechnology and Correlative Microscopy e.V. INAM（纳米技术与关联显微镜协会研究所（INAM））
Computed tomography is widely used as an imaging tool to visualize three-dimensional structures with expressive bone-soft tissue contrast. However, CT resolution and radiation dose are tightly entangled, highlighting the importance of low-dose CT combined with sophisticated denoising algorithms. Most data-driven denoising techniques are based on deep neural networks and, therefore, contain hundreds of thousands of trainable parameters, making them incomprehensible and prone to prediction failures. Developing understandable and robust denoising algorithms achieving state-of-the-art performance …
Low-dose computed tomography (CT) denoising algorithms aim to enable reduced patient dose in routine CT acquisitions while maintaining high image quality. Recently, deep learning~(DL)-based methods were introduced, outperforming conventional denoising algorithms on this task due to their high model capacity. However, for the transition of DL-based denoising to clinical practice, these data-driven approaches must generalize robustly beyond the seen training data. We, therefore, propose a hybrid denoising approach consisting of a set of trainable joint bilateral filters (JBFs) combined with a co…
Friedrich-Alexander University of Erlangen-Nuremberg（埃尔朗根-纽伦堡大学）；Siemens Healthcare GmbH（西门子医疗有限公司）
Denoising of clinical CT images is an active area for deep learning research. Current clinically approved methods use iterative reconstruction methods to reduce the noise in CT images. Iterative reconstruction techniques require multiple forward and backward projections, which are time-consuming and computationally expensive. Recently, deep learning methods have been successfully used to denoise CT images. However, conventional deep learning methods suffer from the 'black box' problem. They have low accountability, which is necessary for use in clinical imaging situations. In this paper, we us…
Filter2Noise: A Framework for Interpretable and Zero-Shot Low-Dose CT Image Denoising
Pattern Recognition Lab, Friedrich-Alexander-University Erlangen-Nuremberg（模式识别实验室，弗里德里希-亚历山大大学埃尔朗根-纽伦堡）；Siemens Healthineers AG（西门子医疗影像有限公司）；Department of Radiology, State Key Laboratory of Complex Severe and Rare Diseases, Peking Union Medical College Hospital, Chinese Academy of Medical Sciences and Peking Union Medical College（放射科，复杂严重罕见疾病国家重点实验室，北京协和医院，中国医学科学院及北京协和医学院）；Theranostics and Translational Research Center, National Infrastructures for Translational Medicine, Institute of Clinical Medicine, Peking Union Medical College Hospital, Chinese Academy of Medical Sciences and Peking Union Medical College（诊疗与转化研究中心，国家转化医学基础设施，临床医学研究院，北京协和医院，中国医学科学院及北京协和医学院）
A.K.Choudhury School of Information Technology（A.K.乔杜里信息技术学院）；Institute of Radio Physics and Electronics（无线电物理与电子研究所）；University of Calcutta（加尔各答大学）
Edge preserving filters preserve the edges and its information while blurring an image. In other words they are used to smooth an image, while reducing the edge blurring effects across the edge like halos, phantom etc. They are nonlinear in nature. Examples are bilateral filter, anisotropic diffusion filter, guided filter, trilateral filter etc. Hence these family of filters are very useful in reducing the noise in an image making it very demanding in computer vision and computational photography applications like denoising, video abstraction, demosaicing, optical-flow estimation, stereo match…
During a surface acquisition process using 3D scanners, noise is inevitable and an important step in geometry processing is to remove these noise components from these surfaces (given as points-set or triangulated mesh). The noise-removal process (denoising) can be performed by filtering the surface normals first and by adjusting the vertex positions according to filtered normals afterwards. Therefore, in many available denoising algorithms, the computation of noise-free normals is a key factor. A variety of filters have been introduced for noise-removal from normals, with different focus poin…
