Nonlinear Anisotropic Diffusion Filtering Research Articles

Scale-Aware Edge-Preserving Full Waveform Inversion with Diffusion Filter for Crosshole Sensor Arrays.

Full waveform inversion (FWI) is recognized as a leading data-fitting methodology, leveraging the detailed information contained in physical waveform data to construct accurate, high-resolution velocity models essential for crosshole surveys. Despite its effectiveness, FWI is often challenged by its sensitivity to data quality and inherent nonlinearity, which can lead to instability and the inadvertent incorporation of noise and extraneous data into inversion models. To address these challenges, we introduce the scale-aware edge-preserving FWI (SAEP-FWI) technique, which integrates a cutting-edge nonlinear anisotropic hybrid diffusion (NAHD) filter within the gradient computation process. This innovative filter effectively reduces noise while simultaneously enhancing critical small-scale structures and edges, significantly improving the fidelity and convergence of the FWI inversion results. The application of SAEP-FWI across a variety of experimental and authentic crosshole datasets clearly demonstrates its effectiveness in suppressing noise and preserving key scale-aware and edge-delineating features, ultimately leading to clear inversion outcomes. Comparative analyses with other FWI methods highlight the performance of our technique, showcasing its ability to produce images of notably higher quality. This improvement offers a robust solution that enhances the accuracy of subsurface imaging.

On the use of nonlinear anisotropic diffusion filters for seismic imaging using the full waveform

Nonlinear anisotropic diffusion filters have been introduced in the field of image processing for image denoising and image restoration. They are based on the solution of partial differential equations involving a nonlinear anisotropic diffusion operator. From a mathematical point of view, these filters enjoy attractive properties, such as minimum–maximum principle, and an inherent decomposition of the images in different scales. We investigate in this study how these filters can be applied to help solving data-fitting inverse problems. We focus on seismic imaging using the full waveform, a well known nonlinear instance of such inverse problems. In this context, we show how the filters can be applied directly to the solution space, to enhance the structural coherence of the parameters representing the subsurface mechanical properties and accelerate the convergence. We also show how they can be applied to the seismic data itself. In the latter case, the method results in an original low-frequency data enhancement technique making it possible to stabilize the inversion process when started from an initial model away from the basin of attraction of the global minimizer. Numerical results on a 2D realistic synthetic full waveform inversion case study illustrate the interesting properties of both approaches.

Noise reducing performance of anisotropic diffusion filter and circular median filter in digital images

The speckle noise is one of the prominent features found in ultrasound images and it tends to degrade the quality of the image. There is a historic success in the works towards this approach particularly in the medical field related to image de-speckling. In this paper, a scale-space nonlinear anisotropic diffusion process and circular median filter is being combined with un-sharp masking to filter out the speckle noise from the ultrasound images. However, the performance evaluation and the comparison of both the filters are being done at each level of the process by comparing the various parameters of image quality measures. The nonlinear anisotropic diffusion filter has found to be performing better by two decimal point values in comparison to the circular median filter.

Nonlinear anisotropic diffusion filtering for the characterization of stochastic structured surfaces

Structured surfaces enhance the functionality of components. Well known is the influence of the surface structure on friction and wear behavior. Beyond this, structured surfaces are widely used for various purposes such as optical, biological or mechanical applications. Therefore, the characterization of structured surfaces and surface features becomes increasingly important. The functionality of a surface can either be tested directly or indirectly. Due to the correlation of geometric surface features and its functionality, an indirect and self-evident way is by measuring the surface topography. To obtain the geometric essentials of these features, they need to be separated from the raw surface data. The standard procedure of decomposing a surface topography is by the use of a Gaussian filter bank, gaining so called scale-limited surfaces. This procedure shows drawbacks when characterizing structured surfaces by introducing distortions to the feature boundaries. To overcome these limitations, this work proposes the use of an automatic nonlinear anisotropic diffusion filter as an initial step to separate the features from the residual surface topography because of its edge preserving properties. It is shown that the nonlinear anisotropic diffusion serves well the separation of the features and their geometrical characterization.

Automatic Choroidal Layer Segmentation Using Markov Random Field and Level Set Method.

The choroid is an important vascular layer that supplies oxygen and nourishment to the retina. The changes in thickness of the choroid have been hypothesized to relate to a number of retinal diseases in the pathophysiology. In this paper, an automatic method is proposed for segmenting the choroidal layer from macular images by using the level set framework. The three-dimensional nonlinear anisotropic diffusion filter is used to remove all the optical coherence tomography (OCT) imaging artifacts including the speckle noise and to enhance the contrast. The distance regularization and edge constraint terms are embedded into the level set method to avoid the irregular and small regions and keep information about the boundary between the choroid and sclera. Besides, the Markov random field method models the region term into the framework by correlating the single-pixel likelihood function with neighborhood information to compensate for the inhomogeneous texture and avoid the leakage due to the shadows cast by the blood vessels during imaging process. The effectiveness of this method is demonstrated by comparing against other segmentation methods on a dataset with manually labeled ground truth. The results show that our method can successfully and accurately estimate the posterior choroidal boundary.

FASART: An iterative reconstruction algorithm with inter-iteration adaptive NAD filter.

Electron tomography (ET) is an essential imaging technique for studying structures of large biological specimens. These structures are reconstructed from a set of projections obtained at different sample orientations by tilting the specimen. However, most of existing reconstruction methods are not appropriate when the data are extremely noisy and incomplete. A new iterative method has been proposed: adaptive simultaneous algebraic reconstruction with inter-iteration adaptive non-linear anisotropic diffusion (NAD) filter (FASART). We also adopted an adaptive parameter and discussed the step for the filter in this reconstruction method. Experimental results show that FASART can restrain the noise generated in the process of iterative reconstruction and still preserve the more details of the structure edges.

Retroperitoneal space organ segmentation from ct images based on the level set function

This article presents a method for solving a problem of segmentation of the retroperitoneal space organs from tomographic images. The method relies on the level set function. We also discuss a method of image preprocessing based on a nonlinear anisotropic diffusion filter, which operates by smoothing the image, while maintaining boundaries between the segments. A tomographic-image segmentation algorithm based on the level set function is synthesized.

Fully Automated Complementary DNA Microarray Segmentation using a Novel Fuzzy-based Algorithm.

DNA microarray is a powerful approach to study simultaneously, the expression of 1000 of genes in a single experiment. The average value of the fluorescent intensity could be calculated in a microarray experiment. The calculated intensity values are very close in amount to the levels of expression of a particular gene. However, determining the appropriate position of every spot in microarray images is a main challenge, which leads to the accurate classification of normal and abnormal (cancer) cells. In this paper, first a preprocessing approach is performed to eliminate the noise and artifacts available in microarray cells using the nonlinear anisotropic diffusion filtering method. Then, the coordinate center of each spot is positioned utilizing the mathematical morphology operations. Finally, the position of each spot is exactly determined through applying a novel hybrid model based on the principle component analysis and the spatial fuzzy c-means clustering (SFCM) algorithm. Using a Gaussian kernel in SFCM algorithm will lead to improving the quality in complementary DNA microarray segmentation. The performance of the proposed algorithm has been evaluated on the real microarray images, which is available in Stanford Microarray Databases. Results illustrate that the accuracy of microarray cells segmentation in the proposed algorithm reaches to 100% and 98% for noiseless/noisy cells, respectively.

Measuring myofiber orientations from high-frequency ultrasound images using multiscale decompositions

High-frequency ultrasound (HFU) has the ability to image both skeletal and cardiac muscles. The quantitative assessment of these myofiber orientations has a number of applications in both research and clinical examinations; however, difficulties arise due to the severe speckle noise contained in the HFU images. Thus, for the purpose of automatically measuring myofiber orientations from two-dimensional HFU images, we propose a two-step multiscale image decomposition method. It combines a nonlinear anisotropic diffusion filter and a coherence enhancing diffusion filter to extract myofibers. This method has been verified by ultrasound data from simulated phantoms, excised fiber phantoms, specimens of porcine hearts, and human skeletal muscles in vivo. The quantitative evaluations of both phantoms indicated that the myofiber measurements of our proposed method were more accurate than other methods. The myofiber orientations extracted from different layers of the porcine hearts matched the prediction of an established cardiac mode and demonstrated the feasibility of extracting cardiac myofiber orientations from HFU images ex vivo. Moreover, HFU also demonstrated the ability to measure myofiber orientations in vivo.

Improving the quality of electron tomography image volumes using pre-reconstruction filtering

Electron tomography produces highly magnified 3D image volumes useful for investigating the structure and function of cellular components. Image quality is degraded by multiple scattering events and quantum noise, which depend on the angle at which individual tilt projections are collected. We have adapted a biomedical imaging approach to improve image quality by enhancing individual tilt projections prior to volumetric reconstruction. Specifically, we have developed a family of non-linear anisotropic diffusion (NAD) filters parameterized by the tilt angle. We give a quantitative and qualitative evaluation of our pre-processing approach and the NAD filter. We show an improvement in the reconstructed volumes for tomograms generated from both plastic-embedded and cryo-stabilized samples of malaria parasite-infected erythrocytes.

Geometric nonlinear diffusion filter and its application to X-ray imaging

BackgroundDenoising with edge preservation is very important in digital x-ray imaging since it may allow us to reduce x-ray dose in human subjects without noticeable degradation of the image quality. In denoising filter design for x-ray imaging, edge preservation as well as noise reduction is of great concern not to lose detailed spatial information for accurate diagnosis. In addition to this, fast computation is also important since digital x-ray images are mostly comprised of large sized matrices.MethodsWe have developed a new denoising filter based on the nonlinear diffusion filter model. Rather than employing four directional gradients around the pixel of interest, we use geometric parameters derived from the local pixel intensity distribution in calculating the diffusion coefficients in the horizontal and vertical directions. We have tested the filter performance, including edge preservation and noise reduction, using low dose digital radiography and micro-CT images.ResultsThe proposed denoising filter shows performance similar to those of nonlinear anisotropic diffusion filters (ADFs), one Perona-Malik ADF and the other Weickert's ADF in terms of edge preservation and noise reduction. However, the computation time has been greatly reduced.ConclusionsWe expect the proposed denoising filter can be greatly used for fast noise reduction particularly in low-dose x-ray imaging.

A novel fuzzy C‐means algorithm for unsupervised heterogeneous tumor quantification in PET

Accurate and robust image segmentation was identified as one of the most challenging issues facing PET quantification in oncological imaging. This difficulty is compounded by the low spatial resolution and high noise characteristics of PET images. The fuzzy C-means (FCM) clustering algorithm was largely used in various medical image segmentation approaches. However, the algorithm is sensitive to both noise and intensity heterogeneity since it does not take into account spatial contextual information. To overcome this limitation, a new fuzzy segmentation technique adapted to typical noisy and low resolution oncological PET data is proposed. PET images smoothed using a nonlinear anisotropic diffusion filter are added as a second input to the proposed FCM algorithm to incorporate spatial information (FCM-S). In addition, a methodology was developed to integrate the a trous wavelet transform in the standard FCM algorithm (FCM-SW) to allow handling of heterogeneous lesions' uptake. The algorithm was applied to the simulated data of the NCAT phantom, incorporating heterogeneous lesions in the lung and clinical PET/CT images of 21 patients presenting with histologically proven nonsmall-cell lung cancer (NSCLC) and 7 patients presenting with laryngeal squamous cell carcinoma (LSCC) to assess its performance for segmenting tumors with arbitrary size, shape, and tracer uptake. For NSCLC patients, the maximal tumor diameters measured from the macroscopic examination of the surgical specimen served as the ground truth for comparison with the maximum diameter estimated by the segmentation technique, whereas for LSCC patients, the 3D macroscopic tumor volume was considered as the ground truth for comparison with the corresponding PET-based volume. The proposed algorithm was also compared to the classical FCM segmentation technique. There is a good correlation (R2 = 0.942) between the actual maximal diameter of primary NSCLC tumors estimated using the proposed PET segmentation procedure and those measured from the macroscopic examination, and the regression line agreed well with the line of identity (slope = 1.08) for the group analysis of the clinical data. The standard FCM algorithm seems to underestimate actual maximal diameters of the clinical data, resulting in a mean error of -4.6 mm (relative error of -10.8 +/- 23.1%) for all data sets. The mean error of maximal diameter estimation was reduced to 0.1 mm (0.9 +/- 14.4%) using the proposed FCM-SW algorithm. Likewise, the mean relative error on the estimated volume for LSCC patients was reduced from 21.7 +/- 22.0% for FCM to 8.6 +/- 28.3% using the proposed FCM-SW technique. A novel unsupervised PET image segmentation technique that allows the quantification of lesions in the presence of heterogeneity of tracer uptake was developed and evaluated. The technique is being further refined and assessed in clinical setting to delineate treatment volumes for the purpose of PET-guided radiation therapy treatment planning but could find other applications in clinical oncology such as the assessment of response to treatment.

Median-prior tomography reconstruction combined with nonlinear anisotropic diffusion filtering

Positron emission tomography (PET) is becoming increasingly important in the fields of medicine and biology. Penalized iterative algorithms based on maximum a posteriori (MAP) estimation for image reconstruction in emission tomography place conditions on which types of images are accepted as solutions. The recently introduced median root prior (MRP) favors locally monotonic images. MRP can preserve sharp edges, but a steplike streaking effect and much noise are still observed in the reconstructed image, both of which are undesirable. An MRP tomography reconstruction combined with nonlinear anisotropic diffusion interfiltering is proposed for removing noise and preserving edges. Analysis shows that the proposed algorithm is capable of producing better reconstructed images compared with those reconstructed by conventional maximum-likelihood expectation maximization (MLEM), MAP, and MRP-based algorithms in PET image reconstruction.

Delineating fluid-filled region boundaries in optical coherence tomography images of the retina

We evaluate the ability of a deformable model to yield accurate shape descriptions of fluid-filled regions associated with age-related macular degeneration. Calculation of retinal thickness and volume by the current optical coherence tomography (OCT) system includes fluid-filled regions or lesions along with actual retinal tissue. In order to quantify these lesions independently from the retinal tissue, they must be outlined. A deformable model was applied to OCT images of retinas demonstrating cystoids and subretinal fluid spaces. Several implementation issues were addressed in order to choose appropriate parameters. The use of a nonlinear anisotropic diffusion filter to suppress speckle noise while at the same time preserving the edges of the original image was explored. Once the contours of the lesions were outlined, quantitative analysis of the surface area and volume of the lesions was performed. The deformable model could accurately outline fluid-filled regions within the retina. The detection method tested proved effective in capturing the complexity of fluid-filled regions in OCT images. Deformable models combined with nonlinear anisotropic diffusion filtering show promise in the detection of retinal features of interest for diagnosis in clinical OCT images. Thus, fluid-filled region detection may significantly aid in analysis of treatments and diagnosis.

Empirical discrepancy measures for the evaluation of segmentation results

We present a new approach to magnetic resonance image segmentation with a Gradient-Vector-Flow-based snake applied to selective smoothing filtered images. The system also allows automated image segmentation in the presence of grey scale inhomogeneity, as in cardiac Magnetic Resonance imaging. Removal of such inhomogeneities is a difficult task, but we proved that using non-linear anisotropic diffusion filtering, myocardium edges are selectively preserved. The approach allowed medical data to be automatically segmented in order to track not only endocardium, which is usually a less difficult task, but also epicardium in anatomic and perfusion studies with Magnetic Resonance. The method developed proceeds in three distinct phases: (a) an anisotropic diffusion filtering tool is used to reduce grey scale inhomogeneity and to selectively preserve edges; (b) a Gradient-Vector-Flow-based snake is applied on filtered images to allow capturing a snake from a long range and to move into concave boundary regions; and (c) an automatic procedure based on a snake is used to fit both endocardium and epicardium borders in a multiphase, multislice examination. A good agreement (P<0.001) between manual and automatic data analysis, based on the mean difference±SD, was assessed in a pool of 907 cardiac function and perfusion images.

Nonlinear anisotropic diffusion filtering of three-dimensional image data from two-photon microscopy

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 3-D 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 two-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.

Automated cardiac MR image segmentation: theory and measurement evaluation

We present a new approach to magnetic resonance image segmentation with a Gradient-Vector-Flow-based snake applied to selective smoothing filtered images. The system also allows automated image segmentation in the presence of grey scale inhomogeneity, as in cardiac Magnetic Resonance imaging. Removal of such inhomogeneities is a difficult task, but we proved that using non-linear anisotropic diffusion filtering, myocardium edges are selectively preserved. The approach allowed medical data to be automatically segmented in order to track not only endocardium, which is usually a less difficult task, but also epicardium in anatomic and perfusion studies with Magnetic Resonance. The method developed proceeds in three distinct phases: (a) an anisotropic diffusion filtering tool is used to reduce grey scale inhomogeneity and to selectively preserve edges; (b) a Gradient-Vector-Flow-based snake is applied on filtered images to allow capturing a snake from a long range and to move into concave boundary regions; and (c) an automatic procedure based on a snake is used to fit both endocardium and epicardium borders in a multiphase, multislice examination. A good agreement ( P<0.001) between manual and automatic data analysis, based on the mean difference±SD, was assessed in a pool of 907 cardiac function and perfusion images.

Entropy-Controlled Artificial Anisotropic Diffusion for the Numerical Solution of Conservation Laws Based on Algorithms from Image Processing

In image processing are nonlinear anisotropic diffusion filters used to construct suitable filter algorithms for denoising, edge enhancement, and edge detection. We applied a nonlinear anisotropic diffusion operator in the context of the numerical solution of a scalar hyperbolic conservation law. It turns out that algorithms currently used in image processing are very well suited for the design of nonlinear higher-order dissipative terms. In particular we stabilize a central scheme, known for its oscillatory behavior, by the construction of a nonlinear diffusion term. This means constructing a diffusion matrix consisting of eigenvectors parallel and perpendicular to discontinuities and eigenvalues denoting the amount of dissipation depending on the local strength of the gradients. These directions are used to steer the amount of dissipation, which means suppressing diffusion across the shock front and using the perpendicular direction to enable the necessary diffusion to stabilize the underlying second-order scheme. This new approach allows a multidimensional view to the concept of artificial dissipation. We take the concept of entropy production in the vicinity of shock regions as an indicator for the steering of the diffusion matrix. In smooth regions, which obey an entropy equality instead of an entropy inequality, no information about the diffusion direction and strength is needed. So we add as a stabilizing term diffusion parallel to the characteristics, which turns out to be the Lax–Wendroff diffusion rate. In the case of unsteady regions we use the entropy production to blend between this diffusion term and an—still second-order—extra diffusion term with diffusion parallel to the gradient of the entropy production.

Nonlinear anisotropic diffusion filtering for multiscale edge enhancement

Nonlinear anisotropic diffusion filtering is a procedure based on nonlinearevolution partial differential equations which seeks to improve imagesqualitatively by removing noise while preserving details and even enhancingedges. However, well known implementations are sensitive to parameterswhich are necessarily tuned to sharpen a narrow range of edge slopes;otherwise, edges are either blurred or staircased. In this work, nonlinearanisotropic diffusion filters have been developed which sharpen edges over awide range of slope scales and which reduce noise conservatively withdissipation purely along feature boundaries. Specifically, the range ofsharpened edge slopes is widened as backward diffusion normal to level setsis balanced with forward diffusion tangent to level sets. Also, noise isreduced by selectively altering the balance toward diminishing normalbackward diffusion and particularly toward total variation filtering. Thetheoretical motivation for the proposed filters is presented together withcomputational results comparing them with other nonlinear anisotropicdiffusion filters on both synthetic images and magnetic resonance images.

Flame front tracking by laser induced fluorescence spectroscopy and advanced image analysis

This paper presents advanced image analysis methods for extracting information from high speed Planar Laser Induced Fluorescence (PLIF) data obtained from turbulent flames. The application of non-linear anisotropic diffusion filtering and of Active Contour Models (Snakes) is described to isolate flame boundaries. In a subsequent step, the detected flame boundaries are tracked in time using a frequency domain contour interpolation scheme. The implementations of the methods are described and possible applications of the techniques are discussed.