A Brief Survey of Recent Edge-Preserving Smoothing Algorithms on Digital Images
---
paper_title: Bilateral filtering for gray and color images

paper_content:

Bilateral filtering smooths images while preserving edges, by means of a nonlinear combination of nearby image values. The method is noniterative, local, and simple. It combines gray levels or colors based on both their geometric closeness and their photometric similarity, and prefers near values to distant values in both domain and range. In contrast with filters that operate on the three bands of a color image separately, a bilateral filter can enforce the perceptual metric underlying the CIE-Lab color space, and smooth colors and preserve edges in a way that is tuned to human perception. Also, in contrast with standard filtering, bilateral filtering produces no phantom colors along edges in color images, and reduces phantom colors where they appear in the original image.
---
paper_title: Real-time edge-aware image processing with the bilateral grid

paper_content:

We present a new data structure---the bilateral grid, that enables fast edge-aware image processing. By working in the bilateral grid, algorithms such as bilateral filtering, edge-aware painting, and local histogram equalization become simple manipulations that are both local and independent. We parallelize our algorithms on modern GPUs to achieve real-time frame rates on high-definition video. We demonstrate our method on a variety of applications such as image editing, transfer of photographic look, and contrast enhancement of medical images.
---
paper_title: Fast Trilateral Filtering

paper_content:

This paper compares the original implementation of the trilateral filter with two proposed speed improvements. One is using simple look-up-tables, and leads to exactly the same results as the original filter. The other technique is using a novel way of truncating the look-up-table (LUT) to a user specified required accuracy. Here, results differ from those of the original filter, but to a very minor extent. The paper shows that measured speed improvements of this second technique are in the order of several magnitudes, compared to the original or LUT trilateral filter.
---
paper_title: Scale-space and edge detection using anisotropic diffusion

paper_content:

A new definition of scale-space is suggested, and a class of algorithms used to realize a diffusion process is introduced. The diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing. It is shown that the 'no new maxima should be generated at coarse scales' property of conventional scale space is preserved. As the region boundaries in the approach remain sharp, a high-quality edge detector which successfully exploits global information is obtained. Experimental results are shown on a number of images. Parallel hardware implementations are made feasible because the algorithm involves elementary, local operations replicated over the image. >
---
paper_title: Constant time O(1) bilateral filtering

paper_content:

This paper presents three novel methods that enable bilateral filtering in constant time O(1) without sampling. Constant time means that the computation time of the filtering remains same even if the filter size becomes very large. Our first method takes advantage of the integral histograms to avoid the redundant operations for bilateral filters with box spatial and arbitrary range kernels. For bilateral filters constructed by polynomial range and arbitrary spatial filters, our second method provides a direct formulation by using linear filters of image powers without any approximation. Lastly, we show that Gaussian range and arbitrary spatial bilateral filters can be expressed by Taylor series as linear filter decompositions without any noticeable degradation of filter response. All these methods drastically decrease the computation time by cutting it down constant times (e.g. to 0.06 seconds per 1MB image) while achieving very high PSNRpsilas over 45 dB. In addition to the computational advantages, our methods are straightforward to implement.
---
paper_title: Scale-space and edge detection using anisotropic diffusion

paper_content:

A new definition of scale-space is suggested, and a class of algorithms used to realize a diffusion process is introduced. The diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing. It is shown that the 'no new maxima should be generated at coarse scales' property of conventional scale space is preserved. As the region boundaries in the approach remain sharp, a high-quality edge detector which successfully exploits global information is obtained. Experimental results are shown on a number of images. Parallel hardware implementations are made feasible because the algorithm involves elementary, local operations replicated over the image. >
---
paper_title: Bilateral filtering for gray and color images

paper_content:

Bilateral filtering smooths images while preserving edges, by means of a nonlinear combination of nearby image values. The method is noniterative, local, and simple. It combines gray levels or colors based on both their geometric closeness and their photometric similarity, and prefers near values to distant values in both domain and range. In contrast with filters that operate on the three bands of a color image separately, a bilateral filter can enforce the perceptual metric underlying the CIE-Lab color space, and smooth colors and preserve edges in a way that is tuned to human perception. Also, in contrast with standard filtering, bilateral filtering produces no phantom colors along edges in color images, and reduces phantom colors where they appear in the original image.
---
paper_title: Scale-space and edge detection using anisotropic diffusion

paper_content:

A new definition of scale-space is suggested, and a class of algorithms used to realize a diffusion process is introduced. The diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing. It is shown that the 'no new maxima should be generated at coarse scales' property of conventional scale space is preserved. As the region boundaries in the approach remain sharp, a high-quality edge detector which successfully exploits global information is obtained. Experimental results are shown on a number of images. Parallel hardware implementations are made feasible because the algorithm involves elementary, local operations replicated over the image. >
---
paper_title: Bilateral filtering for gray and color images

paper_content:

Bilateral filtering smooths images while preserving edges, by means of a nonlinear combination of nearby image values. The method is noniterative, local, and simple. It combines gray levels or colors based on both their geometric closeness and their photometric similarity, and prefers near values to distant values in both domain and range. In contrast with filters that operate on the three bands of a color image separately, a bilateral filter can enforce the perceptual metric underlying the CIE-Lab color space, and smooth colors and preserve edges in a way that is tuned to human perception. Also, in contrast with standard filtering, bilateral filtering produces no phantom colors along edges in color images, and reduces phantom colors where they appear in the original image.
---
paper_title: On the origin of the bilateral filter and ways to improve it

paper_content:

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.
---
paper_title: On the origin of the bilateral filter and ways to improve it

paper_content:

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.
---
paper_title: A Fast Approximation of the Bilateral Filter Using a Signal Processing Approach

paper_content:

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. Tlie 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 down-sampling 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.
---
paper_title: Real-time edge-aware image processing with the bilateral grid

paper_content:

We present a new data structure---the bilateral grid, that enables fast edge-aware image processing. By working in the bilateral grid, algorithms such as bilateral filtering, edge-aware painting, and local histogram equalization become simple manipulations that are both local and independent. We parallelize our algorithms on modern GPUs to achieve real-time frame rates on high-definition video. We demonstrate our method on a variety of applications such as image editing, transfer of photographic look, and contrast enhancement of medical images.
---
paper_title: Separable Bilateral Filtering for Fast Video Preprocessing

paper_content:

Bilateral filtering is an edge-preserving filtering technique that employs both geometric closeness and photometric similarity of neighboring pixels to construct its filter kernel. Multi-dimensional bilateral filtering is computationally expensive because the adaptive kernel has to be recomputed at every pixel. In this paper, we present a separable implementation of the bilateral filter. The separable implementation offers equivalent adaptive filtering capability at a fraction of execution time compared to the traditional filter. Because of this efficiency, the separable bilateral filter can be used for fast preprocessing of images and videos. Experiments show that better image quality and higher compression efficiency is achievable if the original video is preprocessed with the separable bilateral filter.
---
paper_title: Separable Bilateral Filtering for Fast Video Preprocessing

paper_content:

Bilateral filtering is an edge-preserving filtering technique that employs both geometric closeness and photometric similarity of neighboring pixels to construct its filter kernel. Multi-dimensional bilateral filtering is computationally expensive because the adaptive kernel has to be recomputed at every pixel. In this paper, we present a separable implementation of the bilateral filter. The separable implementation offers equivalent adaptive filtering capability at a fraction of execution time compared to the traditional filter. Because of this efficiency, the separable bilateral filter can be used for fast preprocessing of images and videos. Experiments show that better image quality and higher compression efficiency is achievable if the original video is preprocessed with the separable bilateral filter.
---
paper_title: Hardware software co-design of a fast bilateral filter in FPGA

paper_content:

Bilateral filters are widely used in computer vision and digital imaging applications such as denoising, video abstraction, demosaicing, optical-flow estimation etc. to name a few. Its smoothing and edge preserving characteristics suites perfectly for image and video processing applications, yet its high computational complexity makes real-time hardware implementation a challenging task. This paper provides an efficient Field Programmable Gate Array (FPGA) based implementation of an edge preserving fast bilateral filter on a hardware software co-design environment of a most recent algorithm preserving the boundaries, spikes and canyons in presence of noise. Further, the four stage parallel pipelined architecture greatly improves the speed of operation. Moreover, our separable kernel implementation of the filtering hardware increases the speed of execution by almost five times than the traditional convolution filtering, while utilizing less hardware resource.
---
paper_title: Real-time edge-aware image processing with the bilateral grid

paper_content:

We present a new data structure---the bilateral grid, that enables fast edge-aware image processing. By working in the bilateral grid, algorithms such as bilateral filtering, edge-aware painting, and local histogram equalization become simple manipulations that are both local and independent. We parallelize our algorithms on modern GPUs to achieve real-time frame rates on high-definition video. We demonstrate our method on a variety of applications such as image editing, transfer of photographic look, and contrast enhancement of medical images.
---
paper_title: Fast median and bilateral filtering

paper_content:

Median filtering is a cornerstone of modern image processing and is used extensively in smoothing and de-noising applications. The fastest commercial implementations (e.g. in Adobe® Photoshop® CS2) exhibit O(r) runtime in the radius of the filter, which limits their usefulness in realtime or resolution-independent contexts. We introduce a CPU-based, vectorizable O(log r) algorithm for median filtering, to our knowledge the most efficient yet developed. Our algorithm extends to images of any bit-depth, and can also be adapted to perform bilateral filtering. On 8-bit data our median filter outperforms Photoshop's implementation by up to a factor of fifty.
---
paper_title: Hardware software co-design of a fast bilateral filter in FPGA

paper_content:

Bilateral filters are widely used in computer vision and digital imaging applications such as denoising, video abstraction, demosaicing, optical-flow estimation etc. to name a few. Its smoothing and edge preserving characteristics suites perfectly for image and video processing applications, yet its high computational complexity makes real-time hardware implementation a challenging task. This paper provides an efficient Field Programmable Gate Array (FPGA) based implementation of an edge preserving fast bilateral filter on a hardware software co-design environment of a most recent algorithm preserving the boundaries, spikes and canyons in presence of noise. Further, the four stage parallel pipelined architecture greatly improves the speed of operation. Moreover, our separable kernel implementation of the filtering hardware increases the speed of execution by almost five times than the traditional convolution filtering, while utilizing less hardware resource.
---
paper_title: Constant time O(1) bilateral filtering

paper_content:

This paper presents three novel methods that enable bilateral filtering in constant time O(1) without sampling. Constant time means that the computation time of the filtering remains same even if the filter size becomes very large. Our first method takes advantage of the integral histograms to avoid the redundant operations for bilateral filters with box spatial and arbitrary range kernels. For bilateral filters constructed by polynomial range and arbitrary spatial filters, our second method provides a direct formulation by using linear filters of image powers without any approximation. Lastly, we show that Gaussian range and arbitrary spatial bilateral filters can be expressed by Taylor series as linear filter decompositions without any noticeable degradation of filter response. All these methods drastically decrease the computation time by cutting it down constant times (e.g. to 0.06 seconds per 1MB image) while achieving very high PSNRpsilas over 45 dB. In addition to the computational advantages, our methods are straightforward to implement.
---
paper_title: Theoretical Foundations of Anisotropic Diffusion in Image Processing

paper_content:

Theoretical Foundations of Anisotropic Diffusion in Image Processing. A frequent problem in low-level vision consists of eliminating noise and small-scale details from an image while still preserving or even enhancing the edge structure. Nonlinear anisotropic diffusion filtering may be one possibility to achieve these goals. The objective of the present paper is to review the author’s results on a scale-space interpretation of a class of diffusion filters which comprises also several nonlinear anisotropic models. It is demonstrated that these models—which use an adapted diffusion tensor instead of a scalar diffusivity—offer advantages over isotropic filters. Most of the restoration and scale-space properties carry over from the continuous to the discrete case. Applications are presented ranging from preprocessing of medical images and postprocessing of fluctuating numerical data to visualizing quality relevant features for the grading of wood surfaces and fabrics.
---
paper_title: Image processing through reaction combined with nonlinear diffusion

paper_content:

We propose a method based on nonlinear diffusion and reaction for edge detection and contrast enhancement in image processing. We prove that the mathematical model is well posed and show numerically that the processed image can be observed on the asymptotic state of its solution. We illustrate the methods on test images and show on medical images how it can help to draw contours and detect one-dimensional coherent signals.
---
paper_title: Real-time edge-aware image processing with the bilateral grid

paper_content:

We present a new data structure---the bilateral grid, that enables fast edge-aware image processing. By working in the bilateral grid, algorithms such as bilateral filtering, edge-aware painting, and local histogram equalization become simple manipulations that are both local and independent. We parallelize our algorithms on modern GPUs to achieve real-time frame rates on high-definition video. We demonstrate our method on a variety of applications such as image editing, transfer of photographic look, and contrast enhancement of medical images.
---
paper_title: Separable Bilateral Filtering for Fast Video Preprocessing

paper_content:

Bilateral filtering is an edge-preserving filtering technique that employs both geometric closeness and photometric similarity of neighboring pixels to construct its filter kernel. Multi-dimensional bilateral filtering is computationally expensive because the adaptive kernel has to be recomputed at every pixel. In this paper, we present a separable implementation of the bilateral filter. The separable implementation offers equivalent adaptive filtering capability at a fraction of execution time compared to the traditional filter. Because of this efficiency, the separable bilateral filter can be used for fast preprocessing of images and videos. Experiments show that better image quality and higher compression efficiency is achievable if the original video is preprocessed with the separable bilateral filter.
---
paper_title: Multispectral Bilateral Video Fusion

paper_content:

We present a technique for enhancing underexposed visible-spectrum video by fusing it with simultaneously captured video from sensors in nonvisible spectra, such as Short Wave IR or Near IR. Although IR sensors can accurately capture video in low-light and night-vision applications, they lack the color and relative luminances of visible-spectrum sensors. RGB sensors do capture color and correct relative luminances, but are underexposed, noisy, and lack fine features due to short video exposure times. Our enhanced fusion output is a reconstruction of the RGB input assisted by the IR data, not an incorporation of elements imaged only in IR. With a temporal noise reduction, we first remove shot noise and increase the color accuracy of the RGB footage. The IR video is then normalized to ensure cross-spectral compatibility with the visible-spectrum video using ratio images. To aid fusion, we decompose the video sources with edge-preserving filters. We introduce a multispectral version of the bilateral filter called the "dual bilateral" that robustly decomposes the RGB video. It utilizes the less-noisy IR for edge detection but also preserves strong visible-spectrum edges not in the IR. We fuse the RGB low frequencies, the IR texture details, and the dual bilateral edges into a noise-reduced video with sharp details, correct chrominances, and natural relative luminances
---
paper_title: Trilateral filtering for biomedical images

paper_content:

Filtering is a core operation in low level computer vision. It is a preliminary process in many biomedical image processing applications. Bilateral filtering has been applied to smooth biomedical images while preserving the edges. However, to avoid oversmoothing structures of sizes comparable to the image resolutions, a narrow spatial window has to be used. This leads to the necessity of performing more iterations in the filtering process. In this paper, we propose a novel filtering technique namely trilateral filter, which can achieve edge-preserving smoothing with a narrow spatial window in only a few iterations. The experimental results have shown that our novel method provides greater noise reduction than bilateral filtering and smooths biomedical images without over-smoothing ridges and shifting the edge locations, as compared to other noise reduction methods.
---
paper_title: Capture of hair geometry from multiple images

paper_content:

Hair is a major feature of digital characters. Unfortunately, it has a complex geometry which challenges standard modeling tools. Some dedicated techniques exist, but creating a realistic hairstyle still takes hours. Complementary to user-driven methods, we here propose an image-based approach to capture the geometry of hair.The novelty of this work is that we draw information from the scattering properties of the hair that are normally considered a hindrance. To do so, we analyze image sequences from a fixed camera with a moving light source. We first introduce a novel method to compute the image orientation of the hairs from their anisotropic behavior. This method is proven to subsume and extend existing work while improving accuracy. This image orientation is then raised into a 3D orientation by analyzing the light reflected by the hair fibers. This part relies on minimal assumptions that have been proven correct in previous work.Finally, we show how to use several such image sequences to reconstruct the complete hair geometry of a real person. Results are shown to illustrate the fidelity of the captured geometry to the original hair. This technique paves the way for a new approach to digital hair generation.
---
paper_title: Bilateral filter based orientation smoothing of EBSD data

paper_content:

Bilateral filter based orientation smoothing was implemented in this study to improve the angular precision of orientation maps for deposited and deformed structures of pure Cu obtained from electron backscattered diffraction (EBSD) measurements. Applying the method to the deformed and deposited structures, the accuracy of misorientation (or the limit of orientation noise) is enhanced from 0.7° to 0.25° and 0.07°, respectively. Orientation smoothing has two features: preservation of boundary structures or deformed substructures and significant reduction in orientation noise after only one pass.
---
paper_title: On the origin of the bilateral filter and ways to improve it

paper_content:

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.
---
paper_title: Flash photography enhancement via intrinsic relighting

paper_content:

We enhance photographs shot in dark environments by combining a picture taken with the available light and one taken with the flash. We preserve the ambiance of the original lighting and insert the sharpness from the flash image. We use the bilateral filter to decompose the images into detail and large scale. We reconstruct the image using the large scale of the available lighting and the detail of the flash. We detect and correct flash shadows. This combines the advantages of available illumination and flash photography.
---
paper_title: Multispectral Bilateral Video Fusion

paper_content:

We present a technique for enhancing underexposed visible-spectrum video by fusing it with simultaneously captured video from sensors in nonvisible spectra, such as Short Wave IR or Near IR. Although IR sensors can accurately capture video in low-light and night-vision applications, they lack the color and relative luminances of visible-spectrum sensors. RGB sensors do capture color and correct relative luminances, but are underexposed, noisy, and lack fine features due to short video exposure times. Our enhanced fusion output is a reconstruction of the RGB input assisted by the IR data, not an incorporation of elements imaged only in IR. With a temporal noise reduction, we first remove shot noise and increase the color accuracy of the RGB footage. The IR video is then normalized to ensure cross-spectral compatibility with the visible-spectrum video using ratio images. To aid fusion, we decompose the video sources with edge-preserving filters. We introduce a multispectral version of the bilateral filter called the "dual bilateral" that robustly decomposes the RGB video. It utilizes the less-noisy IR for edge detection but also preserves strong visible-spectrum edges not in the IR. We fuse the RGB low frequencies, the IR texture details, and the dual bilateral edges into a noise-reduced video with sharp details, correct chrominances, and natural relative luminances
---
paper_title: Multiscale shape and detail enhancement from multi-light image collections

paper_content:

We present a new image-based technique for enhancing the shape and surface details of an object. The input to our system is a small set of photographs taken from a fixed viewpoint, but under varying lighting conditions. For each image we compute a multiscale decomposition based on the bilateral filter and then reconstruct an enhanced image that combines detail information at each scale across all the input images. Our approach does not require any information about light source positions, or camera calibration, and can produce good results with 3 to 5 input images. In addition our system provides a few high-level parameters for controlling the amount of enhancement and does not require pixel-level user input. We show that the bilateral filter is a good choice for our multiscale algorithm because it avoids the halo artifacts commonly associated with the traditional Laplacian image pyramid. We also develop a new scheme for computing our multiscale bilateral decomposition that is simple to implement, fast O(N2 log N) and accurate.
---
paper_title: Image-based modeling and photo editing

paper_content:

We present an image-based modeling and editing system that takes a single photo as input. We represent a scene as a layered collection of depth images, where each pixel encodes both color and depth. Starting from an input image, we employ a suite of user-assisted techniques, based on a painting metaphor, to assign depths and extract layers. We introduce two specific editing operations. The first, a “clone brushing tool,” permits the distortion-free copying of parts of a picture, by using a parameterization optimization technique. The second, a “texture-illuminance decoupling filter,” discounts the effect of illumination on uniformly textured areas, by decoupling large- and small-scale features via bilateral filtering. Our system enables editing from different viewpoints, extracting and grouping of image-based objects, and modifying the shape, color, and illumination of these objects.
---
paper_title: Stereo Matching With Color-Weighted Correlation, Hierarchical Belief Propagation And Occlusion Handling

paper_content:

In this paper, we contrive a stereo matching algorithm with careful handling of disparity, discontinuity and occlusion. This algorithm works a worldwide matching stereo model which is based on minimization of energy. The global energy comprises two terms, firstly the data term and secondly the smoothness term. The data term is approximated by a color-weighted correlation, then refined in obstruct and low-texture areas in many applications of hierarchical loopy belief propagation algorithm. The results during the experiment are evaluated on the Middlebury data sets, showing that out algorithm is the top performer among all the algorithms listed there
---
paper_title: Spatial-Depth Super Resolution for Range Images

paper_content:

We present a new post-processing step to enhance the resolution of range images. Using one or two registered and potentially high-resolution color images as reference, we iteratively refine the input low-resolution range image, in terms of both its spatial resolution and depth precision. Evaluation using the Middlebury benchmark shows across-the-board improvement for sub-pixel accuracy. We also demonstrated its effectiveness for spatial resolution enhancement up to 100 times with a single reference image.
---
paper_title: Non-iterative, feature-preserving mesh smoothing

paper_content:

With the increasing use of geometry scanners to create 3D models, there is a rising need for fast and robust mesh smoothing to remove inevitable noise in the measurements. While most previous work has favored diffusion-based iterative techniques for feature-preserving smoothing, we propose a radically different approach, based on robust statistics and local first-order predictors of the surface. The robustness of our local estimates allows us to derive a non-iterative feature-preserving filtering technique applicable to arbitrary "triangle soups". We demonstrate its simplicity of implementation and its efficiency, which make it an excellent solution for smoothing large, noisy, and non-manifold meshes.
---
paper_title: The Mollification Method and the Numerical Solution of Ill-Posed Problems: Murio/The Mollification

paper_content:

Numerical Differentiation as an Inverse Problem Abel's Integral Equation One-Dimensional Inverse Heat Conduction Problem (IHCP) Two-Dimensional Inverse Heat Conduction Problem Applications of the Space Marching Solution of the IHCP Applications of Stable Numerical Differentiation Procedures.
---
paper_title: Real-time video abstraction

paper_content:

We present an automatic, real-time video and image abstraction framework that abstracts imagery by modifying the contrast of visually important features, namely luminance and color opponency. We reduce contrast in low-contrast regions using an approximation to anisotropic diffusion, and artificially increase contrast in higher contrast regions with difference-of-Gaussian edges. The abstraction step is extensible and allows for artistic or data-driven control. Abstracted images can optionally be stylized using soft color quantization to create cartoon-like effects with good temporal coherence. Our framework design is highly parallel, allowing for a GPU-based, real-time implementation. We evaluate the effectiveness of our abstraction framework with a user-study and find that participants are faster at naming abstracted faces of known persons compared to photographs. Participants are also better at remembering abstracted images of arbitrary scenes in a memory task.
---
paper_title: Bilateral filtering-based optical flow estimation with occlusion detection

paper_content:

Using the variational approaches to estimate optical flow between two frames, the flow discontinuities between different motion fields are usually not distinguished even when an anisotropic diffusion operator is applied. In this paper, we propose a multi-cue driven adaptive bilateral filter to regularize the flow computation, which is able to achieve the smoothly varied optical flow field with highly desirable motion discontinuities. First, we separate the traditional one-step variational updating model into a two-step filtering-based updating model. Then, employing our occlusion detector, we reformulate the energy functional of optical flow estimation by explicitly introducing an occlusion term to balance the energy loss due to the occlusion or mismatches. Furthermore, based on the two-step updating framework, a novel multi-cue driven bilateral filter is proposed to substitute the original anisotropic diffusion process, and it is able to adaptively control the diffusion process according to the occlusion detection, image intensity dissimilarity, and motion dissimilarity. After applying our approach on various video sources (movie and TV) in the presence of occlusion, motion blurring, non-rigid deformation, and weak textureness, we generate a spatial-coherent flow field between each pair of input frames and detect more accurate flow discontinuities along the motion boundaries.
---
paper_title: Bilateral filtering for gray and color images

paper_content:

Bilateral filtering smooths images while preserving edges, by means of a nonlinear combination of nearby image values. The method is noniterative, local, and simple. It combines gray levels or colors based on both their geometric closeness and their photometric similarity, and prefers near values to distant values in both domain and range. In contrast with filters that operate on the three bands of a color image separately, a bilateral filter can enforce the perceptual metric underlying the CIE-Lab color space, and smooth colors and preserve edges in a way that is tuned to human perception. Also, in contrast with standard filtering, bilateral filtering produces no phantom colors along edges in color images, and reduces phantom colors where they appear in the original image.
---
paper_title: A Fundamental Relationship between Bilateral Filtering , Adaptive Smoothing , and the Nonlinear Diffusion Equation

paper_content:

In this paper, the relationship between bilateral filtering and anisotropic diffusion is examined. The bilateral filtering approach represents a large class of nonlinear digital image filters. We first explore the connection between anisotropic diffusion and adaptive smoothing, and then the connection between adaptive smoothing and bilateral filtering. Previously, adaptive smoothing was considered to be an inconsistent approximation to the nonlinear diffusion equation. We extend adaptive smoothing to make it consistent, thus enabling a unified viewpoint that relates nonlinear digital image filters and the nonlinear diffusion equation.
---
paper_title: A Fast Approximation of the Bilateral Filter Using a Signal Processing Approach

paper_content:

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. Tlie 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 down-sampling 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.
---
paper_title: Scale-space and edge detection using anisotropic diffusion

paper_content:

A new definition of scale-space is suggested, and a class of algorithms used to realize a diffusion process is introduced. The diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing. It is shown that the 'no new maxima should be generated at coarse scales' property of conventional scale space is preserved. As the region boundaries in the approach remain sharp, a high-quality edge detector which successfully exploits global information is obtained. Experimental results are shown on a number of images. Parallel hardware implementations are made feasible because the algorithm involves elementary, local operations replicated over the image. >
---
paper_title: Trilateral filtering for biomedical images

paper_content:

Filtering is a core operation in low level computer vision. It is a preliminary process in many biomedical image processing applications. Bilateral filtering has been applied to smooth biomedical images while preserving the edges. However, to avoid oversmoothing structures of sizes comparable to the image resolutions, a narrow spatial window has to be used. This leads to the necessity of performing more iterations in the filtering process. In this paper, we propose a novel filtering technique namely trilateral filter, which can achieve edge-preserving smoothing with a narrow spatial window in only a few iterations. The experimental results have shown that our novel method provides greater noise reduction than bilateral filtering and smooths biomedical images without over-smoothing ridges and shifting the edge locations, as compared to other noise reduction methods.
---
paper_title: Fast Trilateral Filtering

paper_content:

This paper compares the original implementation of the trilateral filter with two proposed speed improvements. One is using simple look-up-tables, and leads to exactly the same results as the original filter. The other technique is using a novel way of truncating the look-up-table (LUT) to a user specified required accuracy. Here, results differ from those of the original filter, but to a very minor extent. The paper shows that measured speed improvements of this second technique are in the order of several magnitudes, compared to the original or LUT trilateral filter.
---
paper_title: Flash photography enhancement via intrinsic relighting

paper_content:

We enhance photographs shot in dark environments by combining a picture taken with the available light and one taken with the flash. We preserve the ambiance of the original lighting and insert the sharpness from the flash image. We use the bilateral filter to decompose the images into detail and large scale. We reconstruct the image using the large scale of the available lighting and the detail of the flash. We detect and correct flash shadows. This combines the advantages of available illumination and flash photography.
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paper_title: Digital photography with flash and no-flash image pairs

paper_content:

Digital photography has made it possible to quickly and easily take a pair of images of low-light environments: one with flash to capture detail and one without flash to capture ambient illumination. We present a variety of applications that analyze and combine the strengths of such flash/no-flash image pairs. Our applications include denoising and detail transfer (to merge the ambient qualities of the no-flash image with the high-frequency flash detail), white-balancing (to change the color tone of the ambient image), continuous flash (to interactively adjust flash intensity), and red-eye removal (to repair artifacts in the flash image). We demonstrate how these applications can synthesize new images that are of higher quality than either of the originals.
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paper_title: Multispectral Bilateral Video Fusion

paper_content:

We present a technique for enhancing underexposed visible-spectrum video by fusing it with simultaneously captured video from sensors in nonvisible spectra, such as Short Wave IR or Near IR. Although IR sensors can accurately capture video in low-light and night-vision applications, they lack the color and relative luminances of visible-spectrum sensors. RGB sensors do capture color and correct relative luminances, but are underexposed, noisy, and lack fine features due to short video exposure times. Our enhanced fusion output is a reconstruction of the RGB input assisted by the IR data, not an incorporation of elements imaged only in IR. With a temporal noise reduction, we first remove shot noise and increase the color accuracy of the RGB footage. The IR video is then normalized to ensure cross-spectral compatibility with the visible-spectrum video using ratio images. To aid fusion, we decompose the video sources with edge-preserving filters. We introduce a multispectral version of the bilateral filter called the "dual bilateral" that robustly decomposes the RGB video. It utilizes the less-noisy IR for edge detection but also preserves strong visible-spectrum edges not in the IR. We fuse the RGB low frequencies, the IR texture details, and the dual bilateral edges into a noise-reduced video with sharp details, correct chrominances, and natural relative luminances
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paper_title: Bilateral filtering for gray and color images

paper_content:

Bilateral filtering smooths images while preserving edges, by means of a nonlinear combination of nearby image values. The method is noniterative, local, and simple. It combines gray levels or colors based on both their geometric closeness and their photometric similarity, and prefers near values to distant values in both domain and range. In contrast with filters that operate on the three bands of a color image separately, a bilateral filter can enforce the perceptual metric underlying the CIE-Lab color space, and smooth colors and preserve edges in a way that is tuned to human perception. Also, in contrast with standard filtering, bilateral filtering produces no phantom colors along edges in color images, and reduces phantom colors where they appear in the original image.
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paper_title: A Fast Approximation of the Bilateral Filter Using a Signal Processing Approach

paper_content:

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. Tlie 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 down-sampling 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.
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paper_title: Guided Image Filtering

paper_content:

In this paper, we propose a novel explicit image filter called guided filter. Derived from a local linear model, the guided filter computes the filtering output by considering the content of a guidance image, which can be the input image itself or another different image. The guided filter can be used as an edge-preserving smoothing operator like the popular bilateral filter [1], but it has better behaviors near edges. The guided filter is also a more generic concept beyond smoothing: It can transfer the structures of the guidance image to the filtering output, enabling new filtering applications like dehazing and guided feathering. Moreover, the guided filter naturally has a fast and nonapproximate linear time algorithm, regardless of the kernel size and the intensity range. Currently, it is one of the fastest edge-preserving filters. Experiments show that the guided filter is both effective and efficient in a great variety of computer vision and computer graphics applications, including edge-aware smoothing, detail enhancement, HDR compression, image matting/feathering, dehazing, joint upsampling, etc.
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paper_title: Constant time O(1) bilateral filtering

paper_content:

This paper presents three novel methods that enable bilateral filtering in constant time O(1) without sampling. Constant time means that the computation time of the filtering remains same even if the filter size becomes very large. Our first method takes advantage of the integral histograms to avoid the redundant operations for bilateral filters with box spatial and arbitrary range kernels. For bilateral filters constructed by polynomial range and arbitrary spatial filters, our second method provides a direct formulation by using linear filters of image powers without any approximation. Lastly, we show that Gaussian range and arbitrary spatial bilateral filters can be expressed by Taylor series as linear filter decompositions without any noticeable degradation of filter response. All these methods drastically decrease the computation time by cutting it down constant times (e.g. to 0.06 seconds per 1MB image) while achieving very high PSNRpsilas over 45 dB. In addition to the computational advantages, our methods are straightforward to implement.
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Title: A Brief Survey of Recent Edge-Preserving Smoothing Algorithms on Digital Images

Section 1: Introduction
Description 1: Write an introduction to edge-preserving smoothing algorithms, explain their significance in reducing noise while preserving important image features, and give an overview of various historical methods from nonlinear diffusion to the trilateral filter.

Section 2: Edge preserving through nonlinear diffusion to trilateral filtering
Description 2: Discuss the concept of edge-preserving starting with Perona and Malik's nonlinear diffusion method aimed at reducing noise while preserving significant image content, and the developments leading to the trilateral filter.

Section 3: Motivation leading to realizing the anisotropic diffusion filter
Description 3: Explain the motivation behind anisotropic diffusion filtering, including the mathematical formulation and discussion on gradient vectors and diffusion coefficients for edge detection and preservation.

Section 4: Edge preserving diffusion through Non-Linear Gaussian filters
Description 4: Describe the non-linear Gaussian filter method proposed by Aurich and Weule, its principles, the approach to filtering, and the effect of varying parameters on smoothing results.

Section 5: Nonlinear Gaussian filtering extension to bilateral filtering
Description 5: Explain the transition from Gaussian filtering to bilateral filtering, detailing the drawbacks of Gaussian smoothing and the concept of bilateral filtering with domain and range components.

Section 6: Efficient ways to implement bilateral filtering
Description 6: Discuss different methods to implement bilateral filtering efficiently, including brute force approach, Jacobi algorithm approach, layered approach, bilateral grid approach, separable filter kernel approach, local histogram approach, and polynomial range kernels.

Section 7: Applications of edge preserving filters
Description 7: Outline various applications of edge-preserving filters, including contrast enhancement, coherence enhancement, denoising, video processing, medical imaging, orientation smoothing, contrast management, decomposition for detail enhancement, image fusion, and more.

Section 8: Connection among various edge preserving filters
Description 8: Detail the relationships and connections between various edge-preserving filters such as the Yaroslavsky filter, bilateral filter, anisotropic diffusion, local mode filtering, and robust mode filtering.

Section 9: Recent extensions/variations of bilateral filter
Description 9: Provide an overview of recent extensions and variations of the bilateral filter, including the trilateral filter, joint and dual bilateral filters, nonlocal-means, and guided filter, discussing their developments and advantages.

Section 10: Conclusions and future scope
Description 10: Summarize the key findings from the survey, discuss the current state of edge-preserving smoothing algorithms, their challenges, and potential areas for future research and improvements.