Perona-Malik Anisotropic Diffusion Research Articles

Automated Regularized Deconvolution for Eliminating Extra-Column Effects in Fast High-Efficiency Separations.

With the introduction of ultrahigh efficiency columns and fast separations, the need to eliminate peak deformation contributed by the instrument must be effectively solved. Herein, we develop a robust framework to automate deconvolution and minimize its artifacts, such as negative dips, wild noise oscillations, and ringing, by combining regularized deconvolution and Perona-Malik (PM) anisotropic diffusion methods. A asymmetric generalized normal (AGN) function is proposed to model the instrumental response for the first time. With no-column data at various flow rates, the interior point optimization algorithm extracts the parameters describing instrumental distortion. The column-only chromatogram was reconstructed using the Tikhonov regularization technique with minimal instrumental distortion. For illustration, four different chromatography systems are used in fast chiral and achiral separations with 2.1 and 4.6 mm i.d. columns. Ordinary HPLC data can approach highly optimized UHPLC data. Similarly, in fast HPLC-circular dichroism (CD) detection, 8000 plates were gained for a fast chiral separation. Moment analysis of deconvolved peaks confirms correction of the center of mass, variance, skew, and kurtosis. This approach can be easily integrated and used with virtually any separation and detection system to provide enhanced analytical data.

Center pixel weight based on Wiener filter for non-local means image denoising

In non-local means (NLM) method for image denoising, the weight of the center pixel is called the center weight (CW). The CW plays an important role for the performance of NLM. This paper proposes a novel CW by studying the relation between Perona-Malik anisotropic diffusion (PMAD) and NLM. The proposed CW is called the Wiener filter center weight (WFCW) since Wiener filter is introduced in the proposed CW computation. At the same time, the relation between non-local total variation and NLM is further disclosed. Test results show that the proposed method can achieve better results and is very efficient compared with the related NLM methods.

Mimetic finite difference methods for restoration of fundus images for automatic detection of glaucoma suspects

ABSTRACT Glaucoma is one of the leading causes of irreversible blindness in people over 40 years old. Previously, it was developed acomputational tool for automatic glaucoma detection, which implements anovel method that has shown improvement in the accuracy of the detection compared to other classical methods. However, this method is sensitive to the quality of the acquired image. For this reason, automatic image restoration of the source images is needed to improve the quality of glaucoma suspect detection. We propose to use the Perona–Malik anisotropic diffusion filter as part of the pre-processing step because apart from attenuating noise and brilliance in the images, it preserves essential information such as the borders of the optic disc and the cup boundaries, which are of particular interest in this work. We solve numerically the problem in partial differential equations, which represent the Perona–Malik diffusion filter, using explicit finite mimetic differences methods, which have the advantage of preserving the continuum properties of the mathematical operators often encountered in image processing and analysis equations, ensuring better orders of convergence. By guaranteeing these mathematical properties, the original structure of the source image is maintained, improving the diagnosis of the patient.

Approach for semi-automated measurement of fiber diameter in murine and canine skeletal muscle.

Currently available software tools for automated segmentation and analysis of muscle cross-section images often perform poorly in cases of weak or non-uniform staining conditions. To address these issues, our group has developed the MyoSAT (Myofiber Segmentation and Analysis Tool) image-processing pipeline. MyoSAT combines several unconventional approaches including advanced background leveling, Perona-Malik anisotropic diffusion filtering, and Steger’s line detection algorithm to aid in pre-processing and enhancement of the muscle image. Final segmentation is based upon marker-based watershed segmentation. Validation tests using collagen V labeled murine and canine muscle tissue demonstrate that MyoSAT can determine mean muscle fiber diameter with an average accuracy of ~92.4%. The software has been tested to work on full muscle cross-sections and works well even under non-optimal staining conditions. The MyoSAT software tool has been implemented as a macro for the freely available ImageJ software platform. This new segmentation tool allows scientists to efficiently analyze large muscle cross-sections for use in research studies and diagnostics.

Sparse reconstruction of log-conductivity in current density impedance tomography.

A new non-linear optimization approach is proposed for the sparse reconstruction of log-conductivities in current density impedance imaging. This framework comprises of minimizing an objective functional involving a least squares fit of the interior electric field data corresponding to two boundary voltage measurements, where the conductivity and the electric potential are related through an elliptic PDE arising in electrical impedance tomography. Further, the objective functional consists of a L 1 regularization term that promotes sparsity patterns in the conductivity and a Perona-Malik anisotropic diffusion term that enhances the edges to facilitate high contrast and resolution. This framework is motivated by a similar recent approach to solve an inverse problem in acousto-electric tomography. Several numerical experiments and comparison with an existing method demonstrate the effectiveness of the proposed method for superior image reconstructions of a wide-variety of log-conductivity patterns.

Robust and effective automatic parameter choice for medical image filtering.

ABSTRACTThe analysis of medical image data currently requires the interpretation of a trained and experienced user. The technological advances in imaging machinery and the understanding of disease onset, as well as medical planning, all favour the need for ever more automatic and robust methods for evaluating the health state of a subject. Here, we concentrate on methods for processing medical image data, as currently provided by existing imaging technologies, in particular the effectiveness of automatic image filtering in order to remove noise and improve the sharpness of distinct objects. The filtering approach is based on a partial differential equation, namely the Perona–Malik anisotropic diffusion equation. The approach adopted for terminating the iterative filtering procedure is based on image quality descriptors. In specific, we observe the rate of change of these to infer the transient effects of the filtering process. The entire pipeline is demonstrated to work effectively on different sets of medical image data, including MRI, CTA and CT, both in individual 2-D images in a stack, as well as treating the complete 3D volumetric dataset.

On Computing Gradient of Products in Discretized Spaces and Its Effects in PDE Image Processing

Many digital signal and image processing methods involve computing the gradient of products of functions. However, the product rule for derivatives in continuous spaces, $\partial (fg)=g\partial f + f \partial g$ , does not generally hold in discretized spaces. Hence, computing the gradient of products becomes ambiguous as the results depend on whether to treat the product $fg$ as a single function or treat $f$ and $g$ as two separate functions and use the product rule. The two alternatives lead to different results, particularly for iterative solutions of differential equations since these small differences compound. Although this ambiguity is well-known, thus far a resolution has not been proposed in the literature. In this letter, we propose a mathematically rigorous procedure that selects the better alternative in the sense of yielding approximations that are closer to the continuous space results. As an example, we discuss the Perona-Malik anisotropic diffusion equation used in image processing.

A variational framework for low-dose sinogram restoration

Pre-processing the noisy sinogram before reconstruction is an effective and efficient way to solve the low-dose X-ray Computed Tomography (CT) problem. The objective of this paper is to develop a low-dose CT image reconstruction method based on statistical sonogram smoothing approach. The proposed method is casted into a variational framework and the solution of the method is based on minimisation of energy functional. The solution of the method consists of two terms viz. data fidelity term and a regularisation term. The data fidelity term is obtained by minimising the negative log likelihood of the signal dependent Gaussian probability distribution which depicts the noise distribution in low dose X-ray CT. The second term i.e. regularisation term is a non-linear CONvolutional Virtual Electric Field Anisotropic Diffusion (CONVEF-AD) based filter which is an extension of Perona-Malik (P-M) anisotropic diffusion filter. The main task of regularisation function is to address the issue of ill-posedness of the solution for the first term. The proposed method is capable of dealing with both signal dependent and signal independent Gaussian noise i.e. mixed noise. For experimentation purpose, two different sinograms, generated from test phantom images are used. The performance of the proposed method is compared with that of existing methods. The obtained results show that the proposed method outperforms many recent approaches and is capable of removing the mixed noise in low dose X-ray CT.

A variational framework for low-dose sinogram restoration

Pre-processing the noisy sinogram before reconstruction is an effective and efficient way to solve the low-dose X-ray Computed Tomography (CT) problem. The objective of this paper is to develop a low-dose CT image reconstruction method based on statistical sonogram smoothing approach. The proposed method is casted into a variational framework and the solution of the method is based on minimisation of energy functional. The solution of the method consists of two terms viz. data fidelity term and a regularisation term. The data fidelity term is obtained by minimising the negative log likelihood of the signal dependent Gaussian probability distribution which depicts the noise distribution in low dose X-ray CT. The second term i.e. regularisation term is a non-linear CONvolutional Virtual Electric Field Anisotropic Diffusion (CONVEF-AD) based filter which is an extension of Perona-Malik (P-M) anisotropic diffusion filter. The main task of regularisation function is to address the issue of ill-posedness of the solution for the first term. The proposed method is capable of dealing with both signal dependent and signal independent Gaussian noise i.e. mixed noise. For experimentation purpose, two different sinograms, generated from test phantom images are used. The performance of the proposed method is compared with that of existing methods. The obtained results show that the proposed method outperforms many recent approaches and is capable of removing the mixed noise in low dose X-ray CT.

The Jump Set under Geometric Regularization. Part 1: Basic Technique and First-Order Denoising

Let $u \in \mbox{BV}(\Omega)$ solve the total variation denoising problem with $L^2$-squared fidelity and data $f$. Caselles et al. [Multiscale Model. Simul. 6 (2008), 879--894] have shown the containment $\mathcal{H}^{m-1}(J_u \setminus J_f)=0$ of the jump set $J_u$ of $u$ in that of $f$. Their proof unfortunately depends heavily on the co-area formula, as do many results in this area, and as such is not directly extensible to higher-order, curvature-based, and other advanced geometric regularisers, such as total generalised variation (TGV) and Euler's elastica. These have received increased attention in recent times due to their better practical regularisation properties compared to conventional total variation or wavelets. We prove analogous jump set containment properties for a general class of regularisers. We do this with novel Lipschitz transformation techniques, and do not require the co-area formula. In the present Part 1 we demonstrate the general technique on first-order regularisers, while in Part 2 we will extend it to higher-order regularisers. In particular, we concentrate in this part on TV and, as a novelty, Huber-regularised TV. We also demonstrate that the technique would apply to non-convex TV models as well as the Perona-Malik anisotropic diffusion, if these approaches were well-posed to begin with.

PDE-Based Model for Weld Defect Detection on Digital Radiographic Image

Partial differential equation (PDE)-based image processing has played a substantial role and become more popular in the recent years. In the application of weld defect detection, the PDE models can be applied for image smoothing and segmentation. In this study, anisotropic diffusion proposed by Perona Malik known as Perona Malik Anisotropic Diffusion (PMAD) model is used as a denoising process for smoothing while level set by Chan and Vese is used as detection process for segmentation. The PMAD model has been solved using Peaceman Rachford (PR) scheme in order to improve the denoising process. A set of radiographic images that contain weld defects are used as input data. The implementation of the algorithm is done using Matlab R2009a. The average error on contour-based metric and CPU times are used to evaluate the accuracy and the efficiency of the CV model and the thresholding method on the proposed denoising process. From the results, the contour detection of weld defect is improved on image after denoising process using CV model as compared with the thresholding.  In conclusion, the PDE-based model can be

Adaptive anisotropic diffusion filter for speckle noise reduction for ultrasound images

In image processing noise is possibly the most annoying problem. Ultrasound image has been used for effective diagnosis for its non-invasive, harmless, accurate and cost effectiveness. Unfortunately, ultrasound images are degraded by an intrinsic artefact called speckle. Eliminating such speckle noise is an important preprocessing task. For acquiring a better performance for denoising, an adaptive anisotropic diffusion technique for ultrasound images is presented in this paper. It is a new efficient method for denoising the image without blurring the frontiers between different regions. The proposed noise detection-oriented method is based on the differentiation of the diffusion in the direction of the gradient and the adjacent pixels of entire image. The performance of different metrics shows the proposed method exhibit better result to existing Perona-Malik anisotropic diffusion method.

A generalization of the Perona-Malik anisotropic diffusion method using restricted dissimilarity functions

AbstractThere exists a large number of techniques for content-aware smoothing. Despite its simplicity, the Perona-Malik Anisotropic Diffusion method is among the most employed ones. In this work we study this methodin detail and propose a generalization of its diffusion scheme using restricted dissimilarity functions tomeasure the intensity differences between neighbouring pixels. This generalization permits a better adap-tation of the diffusion process to the characteristics of the images.Keywords: Image processing, Anisotropic diffusion, Edge detection, Restricted dissimilarity function. 1. IntroductionNatural images usually contain a large number ofimperfections due to factors such as noise or bad il-lumination of the scene. In order to minimize theirimpact, most of the automated tasks in image pro-cessing require some kind of image preprocessing.In the specific case of edge detection, this prepro-cessing generally intends to remove small imperfec-tions or unimportant artifacts from the image, reduc-ing the number of false positives

Histogram statistics based variance controlled adaptive threshold in anisotropic diffusion for low contrast image enhancement

It is very difficult in low contrast images to distinguish between the noisy background and the regions of low gray level inter-region edges. The classical Perona–Malik anisotropic diffusion is able to smooth the defective background but cannot enhance faultless low gray level inter-region edges in such low contrast images. The proposed method provides an unsupervised machine learning process to modify the anisotropic diffusion by generating an adaptive threshold in diffusion coefficient function using statistical measures. In the proposed method, image histogram is employed to calculate the global gray level variance over the entire image and local gray level variance over the defined neighborhood of each pixel of given image. The adaptive threshold in diffusion coefficient function varies in accordance with the difference between the two variances which gives a measure of intensity contrast in that neighborhood. The experimental results from various low contrast images have shown that the proposed unsupervised machine learning approach for adaptive threshold selection in anisotropic diffusion can effectively smooth noisy background with preservation of low gradient edges.

Gradient-based Wiener filter for image denoising

In this paper, we develop a new adaptive image denoising algorithm in the presence of Gaussian noise. Because the proposed method operates in the gradient domain and is close to Wiener filter, it is named as gradient-based Wiener filter (GWF). Inspired by the Perona–Malik anisotropic diffusion (PMAD), the proposed algorithm is implemented by iterations. The parameters for the GWF are studied in full detail. At the same time, the tuning method of the gradient thresholding based on noise variance for PMAD is presented. Experimental results indicate the proposed algorithm achieves higher peak signal-to-noise ratio (PSNR) and better visual effect compared to related algorithms. On the other hand, the simulation results also show the tremendous power of the given parameter tuning method for PMAD.

Hardware-Friendly Descreening

Conventional electrophotographic printers tend to produce Moiré artifacts when used for printing images scanned from printed material such as books and magazines. We propose a novel noniterative, nonlinear, and space-variant descreening filter that removes a wide range of Moiré-causing screen frequencies in a scanned document while preserving image sharpness and edge detail. This filter is inspired by Perona-Malik's anisotropic diffusion equation. The amount of diffusion of the image intensity resulting from applying the filter is governed by an edge intensity estimate that is robust under halftone noise. More precisely, the filter extracts a spatial feature vector comprising local intensity gradients estimated from a local window in a presmoothed version of the noisy input image. Tunable nonlinear polynomial functions of this feature vector are then used to perform one iteration of a discrete diffusion controlled by the intensity gradient. The polynomial functions and feature extraction kernels are selected empirically in order to minimize computation while ensuring robust performance across a wide range of test images on a target imaging platform. The algorithm uses integer arithmetic, mostly relying on low-cost bit-wise shift and addition operations, and uses a strictly sequential architecture to provide a cost-effective and robust descreening solution in practical imaging devices including copiers and multifunction printers. We compare the performance of the proposed algorithm to other descreening solutions and demonstrate that the new algorithm improves quality over the existing methods while reducing computation.

New Riemannian techniques for directional and tensorial image data

This paper develops new geometrical filtering and edge detection algorithms for processing non-Euclidean image data. We view image data as residing on a Riemannian manifold, and we work with a representation based on the exponential map for this manifold together with the Riemannian weighted mean of image data. We show how the weighted mean can be efficiently computed using Newton's method, which converges faster than the gradient descent method described elsewhere in the literature. Based on geodesic distances and the exponential map, we extend the classical median filter and the Perona–Malik anisotropic diffusion technique to smooth non-Euclidean image data. We then propose an anisotropic Gaussian kernel for image filtering, and we also show how both the median filter and the anisotropic Gaussian filter can be combined to develop a new edge preserving filter, which is effective at removing both Gaussian noise and impulse noise. By using the intrinsic metric of the feature manifold, we also generalise Di Zenzo's structure tensor to non-Euclidean images for edge detection. We demonstrate the applications of our Riemannian filtering and edge detection algorithms both on directional and tensor-valued images.

Existence of infinitely many solutions for the one-dimensional Perona-Malik model

We establish the existence of infinitely many weak solutions for the the one-dimensional version of the well-known and widely used Perona-Malik anisotropic diffusion equation model in image processing. We establish the existence result under the homogeneous Neumann condition with smooth non-constant initial values. Our method is to convert the problem into a partial differential inclusion problem.

Astronomical image restoration using an improved anisotropic diffusion

Images secured from an astronomical telescope usually suffer from blur and from interference that scientists refer to as “noise”. Therefore, good image restoration technique has become an important tool in astronomical observation. In this paper, we propose a modified anisotropic diffusion scheme to tackle the problem of image restoration in astronomy, especially in the case of nebula images. In such images, a mass of stars may be extremely bright but also may be spread randomly in dark space, and the shape of the nebula may therefore appear obscure. To restore the original appearance of a nebula, noisy stars must be filtered out and the detailed structure of the nebula must be well enhanced. The classical Perona–Malik anisotropic diffusion model that only considers gradient information cannot filter out noisy stars from the nebula image. In this study, we propose a modified anisotropic diffusion model that incorporates both gradient and gray-level variance information to remove “sparking” stars of various sizes and brightness in a nebula image. Experimental results from a number of astronomical nebula images have shown that the proposed anisotropic diffusion scheme can effectively remove noisy stars and maintain the shape of nebula in this particular case.

Evolutionary partial differential equations for biomedical image processing

We are presenting here a model for processing space–time image sequences and applying them to 3D echo–cardiography. The non-linear evolutionary equations filter the sequence with keeping space–time coherent structures. They have been developed using ideas of regularized Perona–Malik an-isotropic diffusion and geometrical diffusion of mean curvature flow type (Malladi–Sethian), combined with Galilean invariant movie multi-scale analysis of Alvarez et al. A discretization of space–time filtering equations by means of finite volume method is discussed in detail. Computational results in processing of 3D echo–cardiographic sequences obtained by rotational acquisition technique and by real-time 3D echo volumetrics acquisition technique are presented. Quantitative error estimation is also provided.