Abstract: We present a new, single-pass nonlinear filter for edge-preserving smoothing and visual detail removal for N dimensional signals in computer graphics, image processing and computer vision applications. Built from two modified forms of Tomasi and Manduchi's bilateral filter, the new "trilateral" filter smoothes signals towards a sharply-bounded, piecewise-linear approximation. Unlike bilateral filters or anisotropic diffusion methods that smooth towards piecewise constant solutions, the trilateral filter provides stronger noise reduction and better outlier rejection in high-gradient regions, and it mimics the edge-limited smoothing behavior of shock-forming PDEs by region finding with a fast min-max stack. Yet the trilateral filter requires only one user-set parameter, filters an input signal in a single pass, and does not use an iterative solver as required by most PDE methods. Like the bilateral filter, the trilateral filter easily extends to N-dimensional signals, yet it also offers better performance for many visual applications including appearance-preserving contrast reduction problems for digital photography and denoising polygonal meshes.

Abstract: A novel adaptive smoothing approach is proposed for noise removal and feature preservation where two distinct measures are simultaneously adopted to detect discontinuities in an image. Inhomogeneity underlying an image is employed as a multiscale measure to detect contextual discontinuities for feature preservation and control of the smoothing speed, while local spatial gradient is used for detection of variable local discontinuities during smoothing. Unlike previous adaptive smoothing approaches, two discontinuity measures are combined in our algorithm for synergy in preserving nontrivial features, which leads to a constrained anisotropic diffusion process that inhomogeneity offers intrinsic constraints for selective smoothing. Thanks to the use of intrinsic constraints, our smoothing scheme is insensitive to termination times and the resultant images in a wide range of iterations are applicable to achieve nearly identical results for various early vision tasks. Our algorithm is formally analyzed and related to anisotropic diffusion. Comparative results indicate that our algorithm yields favorable smoothing results, and its application in extraction of hydrographic objects demonstrates its usefulness as a tool for early vision.

Abstract: A method including receiving data corresponding to an original three-dimensional (3D) reconstructed image, smoothing homogenous areas and enhancing edges of the original reconstructed image using edge enhancing diffusion (EED) to create edge-enhanced image data, and calculating a structural importance map. The structural importance map includes a measure of structural importance for each voxel of data in the original reconstructed image. Voxel intensities to be used to create a filtered image are determined according to at least one rule applied to the measure of structural importance.

Abstract: Diffusion weighted imaging has opened new diagnostic possibilities by using microscopic diffusion of water molecules as a means of image contrast. The directional dependence of diffusion has led to the development of diffusion tensor imaging, which allows us to characterize microscopic tissue geometry. The link between the measured NMR signal and the self-diffusion tensor is established by the so-called b matrices that depend on the gradient's direction, strength, and timing. However, in the calculation of b-matrix elements, the influence of imaging gradients on each element of the b matrix is often neglected. This may cause errors, which in turn leads to an incorrect extraction of diffusion coefficients. In cases where the imaging gradients are high (high spatial resolution), these errors may be substantial. Using a generic pulsed gradient spin-echo (PGSE) imaging sequence, the effects of neglecting the imaging gradients on the b-matrix calculation are demonstrated. By measuring an isotropic phantom with this sequence it can be analytically as well as experimentally shown that large deviations in single b-matrix elements are generated. These deviations are obtained by applying the diffusion weighting in the readout direction of the imaging dimension in combination with relatively large imaging gradients. The systematic errors can be avoided by a full b-matrix calculation considering all the gradients of the sequence or by generating cross-term free signals using the geometric average of two diffusion weighted images with opposite polarity. The importance of calculating the exact b matrices by the proposed methods is based on the fact that more precise diffusion parameters are obtained for extracting correct property maps, such as fractional anisotropy, volume ratio, or conductivity tensor maps. © 2005 Wiley Periodicals, Inc. Concepts Magn Reson Part A 25A: 53–66, 2005

Abstract: A Monte Carlo model capable of describing photon migration in arbitrary three-dimensional geometry with spatially varying optical properties and tissue anisotropy is presented. We use the model to explore the effects of anisotropy for optical measurements of the human head. An anisotropic diffusion equation that corresponds to our Monte Carlo model is derived, and a comparison between the Monte Carlo model and the diffusion equation solution with finite elements is given.

Abstract: For 2-dimensional B-mode ultrasound images, we propose an image enhancement algorithm based on a multi-resolution approach. In the proposed algorithm, we perform the directional filtering and noise reducing procedures from the coarse to fine resolution images that are obtained from the wavelet-transformed data. For directional filtering, the structural feature at each pixel is examined through the eigen-analysis. Then, if the pixel belongs to the edge region, we perform two-step directional filtering, namely, directional smoothing along the tangential direction of the edge to improve its continuity, and directional sharpening along the normal direction to enhance the contrast. Meanwhile, speckle noise is alleviated by reducing the wavelet coefficients corresponding to the homogeneous region. The reducing rate of the wavelet coefficients is determined by considering the frequency characteristics of speckle. Thereby, the algorithm reduces speckle noise efficiently without affecting the edge sharpness and enhances edges regardless their size. Note that the proposed speckle reduction scheme is based on the structural information rather than the statistics of the magnitude of wavelet coefficients as in the existing methods. The proposed algorithm is compared to the algorithm based on nonlinear anisotropic diffusion filtering and the one based on the wavelet shrinkage scheme. The experimental results show that the proposed algorithm considerably improves the subjective image quality without providing any noticeable artifact.

Abstract: The problem of random motion of charged particles in an external magnetic field is studied under the assumption that the Langevin sources produce anisotropic diffusion in velocity space and the friction force is dependent on the direction of particle motion. It is shown that in the case under consideration, the kinetic equation describing particle transitions in phase space is reduced to the equation with a Fokker-Planck collision term in the general form (non-isotropic friction coefficient and nonzero off-diagonal elements of the diffusion tensor in the velocity space). The solution of such an equation has been obtained and the explicit form of the transition probability is found. Using the obtained transition probability, the mean-square particle displacements in configuration and velocity space were calculated and compared with the results of numerical simulations, showing good agreement. The obtained results are used to generalize the theory of large-scale fluctuations in plasmas to the case of anisotropic diffusion across an external magnetic field. Such diffusion is expected to be observed in the case of an anisotropic k spectrum of fluctuations generating random particle motion (for example, in the case of drift-wave turbulence).

Abstract: Error diffusion is a popular halftoning algorithm that in its most widely used form, is inherently serial. As a serial algorithm, error diffusion offers limited opportunity for large-scale parallelism. In some implementations, it may also result in excessive bus traffic between the on-chip processor and the off-chip memory used to store the modified continuous-tone image and the halftone image. We introduce a new error diffusion algorithm in which the image is processed in two groups of interlaced blocks. Within each group, the blocks may be processed entirely independently. In the first group, the error diffusion proceeds along an outward spiral from the center of the block. Errors along the boundaries of blocks in the first group are diffused into neighboring blocks in the second group, within which the error diffusion spirals inward. A tone-dependent error diffusion training framework is used to eliminate artifacts associated with the spiral scan paths. We demonstrate image quality that is close to that achieved by conventional line-by-line error diffusion.

Abstract: In order to propel the analysis of medical ultrasound imagery from qualitative observation to quantitative measurement, the obstacles of distortion from speckle and from blurring due to the point spread function must be overcome. A recent partial differential equation (PDE) based enhancement technique has improved the ability to segment ultrasound images and to detect salient edges. However, this diffusion method often distorts the size of image features and may in fact efface subtle features. This paper proposes a new PDE that combines the enhancement of speckle reducing anisotropic diffusion (SRAD) with the mechanism of deconvolution. The resulting method, called deconvolutional speckle reducing anisotropic diffusion (DeSpeRADo), surpasses the edge localization ability of SRAD while yielding lower error in terms of area estimation and improved detection of fine features. A comparative study employs 100 experiments to contrast the quantification enabled by adaptive filtering, inverse filtering, diffusion and the new DeSpeRADo technique.

Abstract: Geophysical data are frequently collected with a fine sample interval along traverse lines but with a coarser sampling in the direction perpendicular to the traverses. This disparity in sampling intervals is particularly evident when magnetic data are collected simultaneously with airborne electromagnetic data. Interpolating this traverse data onto an evenly spaced 2D grid can result in aliasing artifacts. For example, narrow linear structures that trend at acute angles to the traverse lines are imaged as a thick/thin/thick feature, looking like a boudinage or string of beads. Applying the anisotropic diffusion process to the resulting grids of data removes the artifacts, but the grid values close to the traverses are altered significantly from their initial values. The altered values are therefore not faithful to the original traverse data. The anisotropic diffusion algorithm can be modified to constrain values close to the original traverses. This modification removes the aliasing artifacts and produces a data grid faithful to the original traverse data. Some small artifacts along the traverse lines in the final data grid become more evident when grids containing derivative data (such as the analytic signal) are generated from the new data grid. However, these small traverse-line artifacts can be removed with standard microleveling procedures. The constrained anisotropic diffusion process is iterative, and some experimentation is required to determine the appropriate number of iterations.

Abstract: In this paper, we combine 3D anisotropic diffusion and motion estimation for image denoising and improvement of motion estimation. We compare different continuous isotropic nonlinear and anisotropic diffusion processes, which can be found in literature, with a process especially designed for image sequence denoising for motion estimation. All of these processes initially improve motion estimation due to reduction of noise and high frequencies. But while all the well known processes rapidly destroy or hallucinate motion information, the process brought forward here shows considerably less information loss or violation even at motion boundaries. We show the superior behavior of this process. Further we compare the performance of a standard finite difference diffusion scheme with several schemes using derivative filters optimized for rotation invariance. Using the discrete scheme with least smoothing artifacts we demonstrate the denoising capabilities of this approach. We exploit the motion estimation to derive an automatic stopping criterion.

Abstract: Problems with extremely high-transport anisotropy often arise in strongly magnetized plasmas. The numerical solution of the highly anisotropic transport equations becomes quite difficult when the computational grid is not aligned with the strong transport direction, since this can cause large numerical errors. Constructing a finite-difference scheme for a strongly anisotropic diffusion equation on a misaligned grid is discussed, and quantitative assessment of the numerical error is made for a set of example problems.

Abstract: We study a time-delay regularization of the anisotropic diffusion model for image denoising of Malik and Perona, which has been proposed by Nitzberg and Shiota. In the two-dimensional case, we show the convergence of a numerical approximation and the existence of a weak solution. Finally, we show some experiments on images.

Abstract: Two-photon microscopy in combination with novel fluorescent labeling techniques enables imaging of three-dimensional neuronal morphologies in intact brain tissue In principle it is now possible to automatically reconstruct the dendritic branching patterns of neurons from 3D fluorescence image stacks In practice however, the signal-to-noise ratio can be low, in particular in the case of thin dendrites or axons imaged relatively deep in the tissue Here we present a nonlinear anisotropic diffusion filter that enhances the signal-to-noise ratio while preserving the original dimensions of the structural elements The key idea is to use structural information in the raw data -- the local moments of inertia -- to locally control the strength and direction of diffusion filtering A cylindrical dendrite, for example, is effectively smoothed only parallel to its longitudinal axis, not perpendicular to it This is demonstrated for artificial data as well as for in vivo 2-photon microscopic data from pyramidal neurons of rat neocortex In both cases noise is averaged out along the dendrites, leading to bridging of apparent gaps, while dendritic diameters are not affected The filter is a valuable general tool for smoothing cellular processes and is well suited for preparing data for subsequent image segmentation and neuron reconstruction

Abstract: We introduce robust variational segmentation techniques that are driven by an Edgeflow vector field. Variational image segmentation has been widely used during the past ten years. While there is a rich theory of these techniques in the literature, a detailed performance analysis on real natural images is needed to compare the various methods proposed. In this context, this paper makes the following contributions: (a) designing curve evolution and anisotropic diffusion methods that use Edgeflow vector fields to obtain good quality segmentation results over a large and diverse class of images, and (b) a detailed experimental evaluation of these segmentation methods. Our experiments show that Edgeflowbased anisotropic diffusion outperforms other competing methods by a significant margin.

Abstract: We evaluate a preprocessing method for image compression artifact reduction based on nonlinear diffusion filtering that we proposed earlier. The method consists of using edge-adaptive diffusion processes before the discrete cosine transform (DCT)-JPEG compression. By using a simple measure for artifact reduction, we show that considerable artifact reduction is achieved with preprocessing at the same bit rate as, and with no greater error than, the original compression. We also show that preprocessing helps to preserve the true contours for image processing applications. An automatic parameter selection for the preprocessing is also proposed, considering the edge histogram of the image and depending on the compression ratio. We test the method for visual quality with extensive subjective measurements. We show that, depending on the image content, preprocessing can significantly improve the visual quality at low bit rates.

Abstract: The problem of random motion of charged particles in an external magnetic field is studied under the assumption that the Langevin sources produce anisotropic diffusion in velocity space and the friction force is dependent on the direction of particle motion. It is shown that in the case under consideration, the kinetic equation describing particle transitions in phase space is reduced to the equation with a Fokker-Planck collision term in the general form (non-isotropic friction coefficient and nonzero off-diagonal elements of the diffusion tensor in the velocity space). The solution of such an equation has been obtained and the explicit form of the transition probability is found. Using the obtained transition probability, the mean-square particle displacements in configuration and velocity space were calculated and compared with the results of numerical simulations, showing good agreement. The obtained results are used to generalize the theory of large-scale fluctuations in plasmas to the case of anisotropic diffusion across an external magnetic field. Such diffusion is expected to be observed in the case of an anisotropic k spectrum of fluctuations generating random particle motion (for example, in the case of drift-wave turbulence).

Abstract: An anisotropic diffusion film has a high brightness, high luminance uniformity ratio and a high productivity, and is suitable essentially for a surface light source of planar display devices for liquid crystal display devices and the like, such as a direct backlight. In the anisotropic diffusion film, a stripe-shaped convex lens is formed on one surface of a substrate film. The cross-sectional shape of a plane vertical to the stripe direction satisfies the following conditions that (A-C) and the whole of light transmittance of the anisotropic diffusion film is 70% or more: A: the contour of the projecting part of the cross-sectional shape is a curved line; B: the aspect ratio of the projecting part of the cross-sectional shape is 1 or more but not more than 3; and C: the distance between the apexes of the adjacent projecting parts of the cross-sectional shape is 10 μm or more but not more than 100 μm.

Abstract: A unified, mean-field kinetic theory approach to the anisotropic translational diffusion observed in liquid crystals and in ferrofluids is proposed. In the dilute regime, unified expressions for the parallel as well as for the perpendicular diffusion coefficient in terms of orientational order parameters are found that apply for liquid crystals as well as for ferrofluids. This result explains the common origin of the anisotropic diffusion found in liquid crystals and in ferrofluids. Differences between the two liquids appear in the semi-dilute regime, where the diffusion coefficients depend on the specific interaction potentials. Explicit expressions for the diffusion coefficients are worked out also in this regime within a mean-field approximation. Comparisons with previous theoretical and experimental results are performed, showing satisfactory agreement to the present results.

Abstract: We developed an approach to the blind multichannel reconstruction of high-resolution images. This approach is based on breaking the image reconstruction problem into three consecutive steps: a blind multichannel restoration, a wavelet-based image fusion, and a maximum entropy image interpolation. The blind restoration step depends on estimating the two-dimensional (2-D) greatest common divisor (GCD) between each observation and a combinational image generated by a weighted averaging process of the available observations. The purpose of generating this combinational image is to get a new image with a higher signal-to-noise ratio and a blurring operator that is a coprime with all the blurring operators of the available observations. The 2-D GCD is then estimated between the new image and each observation, and thus the effect of noise on the estimation process is reduced. The multiple outputs of the restoration step are then applied to the image fusion step, which is based on wavelets. The objective of this step is to integrate the data obtained from each observation into a single image, which is then interpolated to give an enhanced resolution image. A maximum entropy algorithm is derived and used in interpolating the resulting image from the fusion step. Results show that the suggested blind image reconstruction approach succeeds in estimating a high-resolution image from noisy blurred observations in the case of relatively coprime unknown blurring operators. The required computation time of the suggested approach is moderate.

Abstract: A noisy image is transformed through a wavelet transform into multiple scales. The wavelet coefficients are classified at each scale into two categories corresponding to irregular coefficients, edge-related and regular coefficients. Different denoising algorithms are applied to different classes. Alternatively, a denoising technique is applied to the finest scale, and the wavelet coefficients at all scales are denoised through anisotropic diffusion.

Abstract: The paper proposes a novel tensor based diffusion filter, dedicated for filtering images composed of line like structures We propose a linear version of nonlinear diffusion partial derivative equation, previously presented in [5] Instead of considering nonlinearity in the image evolution process we are only including it at the computation of the diffusion tensor The unique tensor construction is based on an adaptive orientation estimation step and yields a significant reduction of the computational complexity The properties of the filter are analyzed both theoretically and experimentally

Abstract: Growth-rate distributions of GaAs on alternately inverted GaAs substrates have been investigated. Periodic thickness variations of GaAs grown by molecular beam epitaxy (MBE) on planarized surfaces of alternately inverted GaAs(100) substrates are caused by the anisotropic surface diffusion of Ga atoms. Simulation based on a simple diffusion-equation analysis that takes account of the anisotropic diffusion agrees quite well with the measured temperature dependence of the growth-rate distribution. We have also shown that practically flat GaAs surfaces can be attained by MBE growth at 300°C, where diffusion anisotropy is negligibly small.

Abstract: The application of non-linear anisotropic diffusion to reduce the speckle noise and enhance the structural boundaries in optical coherence tomography is presented Non-linear diffusion maximally low-pass filters those parts of the image that correspond to speckle noise, while preserving information associated with structural boundaries It is shown that this technique is efficient to enhance the quality of optical coherence tomogram, making the accurate image quantification possible