Multiscale Geometric Analysis Research Articles

The multiscale directional bilateral filter and its application to multisensor image fusion

In this paper, a novel multiscale geometrical analysis called the multiscale directional bilateral filter (MDBF) which introduces the nonsubsampled directional filter bank into the multiscale bilateral filter is proposed. Through combining the characteristic of preserving edge of the bilateral filter with the ability of capturing directional information of the directional filter bank, the MDBF can better represent the intrinsic geometrical structure of images. The MDBF, which is a multiscale, multidirectional and shift-invariant image decomposition scheme, is used to fuse multisensor images in this paper. The source images are first decomposed into the directional detail subbands and the approximation subbands via the MDBF. Then, the directional detail subbands and the approximation subbands are fused according to the given fusion rule, respectively. Finally, the inverse MDBF is applied to the fused subbands to obtain the fused image. Experimental results over visible and infrared images and medical images demonstrate the superiority of our method compared with conventional methods in terms of visual inspection and objective measures.

MEDICAL IMAGE FUSION BASED ON RIPPLET TRANSFORM TYPE-I

The motivation behind fusing multimodality, multi- resolution images is to create a single image with improved interpretability. In this paper, we propose a novel multimodality Medical Image Fusion (MIF) method, based on Ripplet Transform Type-I (RT) for spatially registered, multi-sensor, multi-resolution medical images. RT is a new Multi-scale Geometric Analysis (MGA) tool, capable of resolving two dimensional (2D) singularities and representing image edges more e-ciently. The source medical images are flrst transformed by discrete RT (DRT). Difierent fusion rules are applied to the difierent subbands of the transformed images. Then inverse DRT (IDRT) is applied to the fused coe-cients to get the fused image. The performance of the proposed scheme is evaluated by various quantitative measures like Mutual Information (MI), Spatial Frequency (SF), and Entropy (EN) etc. Visual and quantitative analysis shows, that the proposed technique performs better compared to fusion scheme based on Contourlet Transform (CNT).

Crack surface extraction of industrial CT volume data using FPIT and planelet

As an advanced nondestructive testing (NDT) technology, industrial computed tomography (ICT) has been widely applied to diversified areas. In modern industry, ICT is especially useful for analyzing inner defects of complex and close work pieces. The common defects of work pieces include gas cavities, slag inclusions, cracks and shrinking cavities. Only cracks are often caused by fatigue usage. Precisely extracting a crack is important to estimate the remaining secure service time of the work piece. This paper presents a crack surface extraction method of ICT volume data based on finite plane integral transform (FPIT) and planelet. FPIT and planelet, as new methods of multiscale geometric analysis (MGA), have distinct discrimination for different plane singularities. Within the paper, firstly the definitions of FPIT and planelet are introduced. Secondly, after analyzing the components and relationship of planelet at monoscale, a fast performance of planelet transform is designed. Thirdly, the steps of the proposed crack surface extraction method are described. In numeric experiment, compared with the method of 3D facet model, C-V model and 3D wavelet respectively, the proposed method can extract the crack surface full and continuously, which,is robust to noise.

32Still Image Compression Algorithm Based on Directional Filter Banks

Hybrid wavelet and directional filter banks (HWD) is an effective multi-scale geometrical analysis method. Compared to wavelet transform, it can better capture the directional information of images. But the ringing artifact, which is caused by the coefficient quantization in transform domain, is the biggest drawback of image compression algorithms in HWD domain. In this paper, by researching on the relationship between directional decomposition and ringing artifact, an improved decomposition approach of HWD(IHWD) is proposed to reduce the ringing artifact. In addition, the IHWD algorithm and directional weighting model is applied into the JPEG2000 coding framework, and a new still image compression algorithm IJPEG2000 is proposed. The experimental results show that IJPEG2000 has better performance than JPEG2000 whether on objective evaluation method or on subjective visual feeling.

A novel algorithm of image fusion using shearlets

As a novel MGA (Multiscale Geometric Analysis) tool, shearlets are equipped with a rich mathematical structure similar to wavelets, which are associated to a multi-resolution analysis. Recently, shearlets have been used in image denoising, sparse image representation and edge detection. In this paper, as shearlet transform has the features of directionality, localization, anisotropy and multiscale, it is introduced into image fusion to obtain a fused image. The image could be decomposed by shearlet transform in any scale and any direction, and the detail information can be caught easily. Several different experiments are adopted to demonstrate that the fusion results based on shearlet transform contain more detail and smaller distortion information than any other methods does.

Multi-scale geometric analysis of Lagrangian structures in isotropic turbulence

We report the multi-scale geometric analysis of Lagrangian structures in forced isotropic turbulence and also with a frozen turbulent field. A particle backward-tracking method, which is stable and topology preserving, was applied to obtain the Lagrangian scalar field φ governed by the pure advection equation in the Eulerian form ∂tφ + u · ∇φ = 0. The temporal evolution of Lagrangian structures was first obtained by extracting iso-surfaces of φ with resolution 10243 at different times, from t = 0 to t = Te, where Te is the eddy turnover time. The surface area growth rate of the Lagrangian structure was quantified and the formation of stretched and rolled-up structures was observed in straining regions and stretched vortex tubes, respectively. The multi-scale geometric analysis of Bermejo-Moreno & Pullin (J. Fluid Mech., vol. 603, 2008, p. 101) has been applied to the evolution of φ to extract structures at different length scales and to characterize their non-local geometry in a space of reduced geometrical parameters. In this multi-scale sense, we observe, for the evolving turbulent velocity field, an evolutionary breakdown of initially large-scale Lagrangian structures that first distort and then either themselves are broken down or stretched laterally into sheets. Moreover, after a finite time, this progression appears to be insensible to the form of the initially smooth Lagrangian field. In comparison with the statistical geometry of instantaneous passive scalar and enstrophy fields in turbulence obtained by Bermejo-Moreno & Pullin (2008) and Bermejo-Moreno et al. (J. Fluid Mech., vol. 620, 2009, p. 121), Lagrangian structures tend to exhibit more prevalent sheet-like shapes at intermediate and small scales. For the frozen flow, the Lagrangian field appears to be attracted onto a stream-surface field and it develops less complex multi-scale geometry than found for the turbulent velocity field. In the latter case, there appears to be a tendency for the Lagrangian field to move towards a vortex-surface field of the evolving turbulent flow but this is mitigated by cumulative viscous effects.

STUDY ON THE ENHANCEMENT AND DENOISING OF MAMMOGRAMS

A new algorithm for mammograms enhancement and denoising based on multiscale geometric analysis(MGA) was proposed.Firstly,mammograms were decomposed into different scales and directional subbands by using nonsubsampled contourlet transform(NSCT).After modeling the coefficients of each directional subbands and using generalized gaussian mixture model(GGMM) according to the statistical property of the transform coefficients,they were categorized into strong edges,weak edges and noise by Bayesian classifier.A nonlinear mapping function was designed to enhance and suppress the different coefficients adaptively so as to obtain a good enhancement result with significant features according to the property of every subband coefficient.Finally,the mammograms were obtained by reconstructing the original maps with the modified coefficients of NSCT.Experimental results illustrate that the proposed approach is practicable and robust.

Mammograms Enhancement and Denoising Using Generalized Gaussian Mixture Model in Nonsubsampled Contourlet Transform

In this paper, a novel algorithm for mammographic image s enhancement and denoising based on Multiscale Geometric Analysis (MGA) is proposed. Firstly mammograms are decomposed into different scales and directional subbands using Nonsubsampled Contourlet Transform (NSCT). After modeling the coefficients of each directional subbands using Generalized Gaussian Mixture Model (GGMM) according to the statistical property, they are categorized into strong edges, weak edges and noise by Bayes ian classifier. To enhance the suspicious lesion and suppress the noise, a nonlinear mapping function is designed to adjust the coefficients adaptively so as to obtain a good enhancement result with significant features. Finally, the resulted mammographic images are obtained by reconstructing with the modified coefficients using NSCT. Experimental results illustrate that the proposed approach is practicable and robustness, which outperforms the spatial filters and other methods based on wavelets in terms of mass and microcalcification denoising and enhancement.

SAR IMAGE EDGE DETECTION BASED ON IMPROVED WEDGELET TRANSFORM

For SAR images,traditional edge detection methods can hardly extract edges since it is very difficult to balance the noise suppression and the integrity of edges and the veracity of edge position at the same time. However,Wedgelet,which is a multiscale geometric analysis tool,has an advantage of catching linear features. Aiming at further reducing speckle noise in SAR images,a modified cost function of Wedgelet transform was proposed. Besides,proper transform scales were selected in order to highly improve the transform speed without affecting the quality of the approximation. Based on the improved Wedgelet transform,edge detection was preformed. Experimental results show that the proposed method can suppress speckle noise in SAR images successfully and extract edges from SAR images effectively.

Image quality assessment using contourlet transform

We present a novel objective full-reference image quality assessment metric based on multiscale geometric analysis. The multichannel behavior of the human vision system is emulated by contourlet transform, a perceptual subband decomposition. Not only the contrast-masking effect but also the entropy-masking effect is considered to deal with the visual masking issue. In the error pooling stage, the frequency sensitivity of the HVS is investigated. Nonlinear and linear fusion schemes of subband distortion are compared. Extensive validation experiments are performed on two professional image databases, the LIVE database supplied by the University of Texas and the A57 database supplied by Cornell University. Compared with several state-of-the-art image quality metrics, the proposed metric demonstrates improvement on prediction accuracy and robustness.

Multiscale geometric analysis of turbulence by curvelets

In this paper, after a brief review of curvelets and their relation to classical wavelet transform, multiscale geometric analysis is systematically applied to turbulent flows in two and three dimensions. The analysis is based on the constrained minimization of a total variation functional representing the difference between the data and its representation in the curvelet space. Constrained multiscale minimization results in a minimum loss of the geometric flow features and the extraction of the coherent structures with their edges and geometry properly preserved, which is significant for turbulence modeling. The effectiveness of curvelet analysis compared to the wavelet transform is demonstrated for both two- and three-dimensional turbulent flows.

Image Quality Assessment Based on Multiscale Geometric Analysis

Reduced-reference (RR) image quality assessment (IQA) has been recognized as an effective and efficient way to predict the visual quality of distorted images. The current standard is the wavelet-domain natural image statistics model (WNISM), which applies the Kullback-Leibler divergence between the marginal distributions of wavelet coefficients of the reference and distorted images to measure the image distortion. However, WNISM fails to consider the statistical correlations of wavelet coefficients in different subbands and the visual response characteristics of the mammalian cortical simple cells. In addition, wavelet transforms are optimal greedy approximations to extract singularity structures, so they fail to explicitly extract the image geometric information, e.g., lines and curves. Finally, wavelet coefficients are dense for smooth image edge contours. In this paper, to target the aforementioned problems in IQA, we develop a novel framework for IQA to mimic the human visual system (HVS) by incorporating the merits from multiscale geometric analysis (MGA), contrast sensitivity function (CSF), and the Weber's law of just noticeable difference (JND). In the proposed framework, MGA is utilized to decompose images and then extract features to mimic the multichannel structure of HVS. Additionally, MGA offers a series of transforms including wavelet, curvelet, bandelet, contourlet, wavelet-based contourlet transform (WBCT), and hybrid wavelets and directional filter banks (HWD), and different transforms capture different types of image geometric information. CSF is applied to weight coefficients obtained by MGA to simulate the appearance of images to observers by taking into account many of the nonlinearities inherent in HVS. JND is finally introduced to produce a noticeable variation in sensory experience. Thorough empirical studies are carried out upon the LIVE database against subjective mean opinion score (MOS) and demonstrate that 1) the proposed framework has good consistency with subjective perception values and the objective assessment results can well reflect the visual quality of images, 2) different transforms in MGA under the new framework perform better than the standard WNISM and some of them even perform better than the standard full-reference IQA model, i.e., the mean structural similarity index, and 3) HWD performs best among all transforms in MGA under the framework.

Geometry of enstrophy and dissipation, grid resolution effects and proximity issues in turbulence

We perform a multi-scale non-local geometrical analysis of the structures extracted from the enstrophy and kinetic energy dissipation-rate, instantaneous fields of a numerical database of incompressible homogeneous isotropic turbulence decaying in time obtained by DNS in a periodic box. Three different resolutions are considered: 2563, 5123 and 10243 grid points, with kmax approximately 1, 2 and 4, respectively, the same initial conditions and Reλ ≈ 77. This allows a comparison of the geometry of the structures obtained for different resolutions. For the highest resolution, structures of enstrophy and dissipation evolve in a continuous distribution from blob-like and moderately stretched tube-like shapes at the large scales to highly stretched sheet-like structures at the small scales. The intermediate scales show a predominance of tube-like structures for both fields, much more pronounced for the enstrophy field. The dissipation field shows a tendency towards structures with lower curvedness than those of the enstrophy, for intermediate and small scales. The 2563 grid resolution case (kmax ≈ 1) was unable to detect the predominance of highly stretched sheet-like structures at the smaller scales in both fields. The same non-local methodology for the study of the geometry of structures, but without the multi-scale decomposition, is applied to two scalar fields used by existing local criteria for the eduction of tube- and sheet-like structures in turbulence, Q and [Aij]+, respectively, obtained from invariants of the velocity-gradient tensor and alike in the 10243 case. This adds the non-local geometrical characterization and classification to those local criteria, assessing their validity in educing particular geometries. Finally, we introduce a new methodology for the study of proximity issues among structures of different fields, based on geometrical considerations and non-local analysis, by taking into account the spatial extent of the structures. We apply it to the four fields previously studied. Tube-like structures of Q are predominantly surrounded by sheet-like structures of [Aij]+, which appear at closer distances. For the enstrophy, tube-like structures at an intermediate scale are primarily surrounded by sheets of smaller scales of the enstrophy and structures of dissipation at the same and smaller scales. A secondary contribution results from tubes of enstrophy at smaller scales appearing at farther distances. Different configurations of composite structures are presented.

Multimodality medical image fusion based on multiscale geometric analysis of contourlet transform

As a novel multiscale geometric analysis tool, contourlet has shown many advantages over the conventional image representation methods. In this paper, a new fusion algorithm for multimodal medical images based on contourlet transform is proposed. All fusion operations are performed in contourlet domain. A novel contourlet contrast measurement is developed, which is proved to be more suitable for human vision system. Other fusion rules like local energy, weighted average and selection are combined with “region” idea for coefficient selection in the lowpass and highpass subbands, which can preserve more details in source images and further improve the quality of fused image. The final fusion image is obtained by directly applying inverse contourlet transform to the fused lowpass and highpass subbands. Extensive fusion experiments have been made on three groups of multimodality CT/MR dataset, both visual and quantitative analysis show that comparing with conventional image fusion algorithms, the proposed approach can provide a more satisfactory fusion outcome.

A MODIFIED MULTIPHASE LEVEL SET EVOLUTION SCHEME FOR AERIAL IMAGE SEGMENTATION

This paper describes an innovative aerial images segmentation algorithm. The algorithm is based upon the knowledge of image multiscale geometric analysis using contourlet transform, which can extract the image's intrinsic geometrical structure efficiently. The contourlet transform is introduced to represent the most distinguished and the rotation invariant features of the image. A modified Mumford–Shah model is applied to segment the aerial image by a multifeature level set evolution. To avoid possible local minima in the level set evolution, we adjust the weighting coefficients of the multiscale features in different evolution periods, i.e. the global features have bigger weighting coefficients at the beginning stages which roughly define the shape of the contour, then bigger weighting coefficients are assigned to the detailed features for segmenting the precise shape. When the algorithm is applied to segment the aerial images with several classes, satisfied experimental results are achieved by the proposed method.

Noisy Image Segmentation by Modified Snake Model

A novel segmentation scheme for noisy image is proposed. According to the analysis of wavelet denoising method and multiscale geometric analysis techniques, an improved wavelet denoising algorithm combined with multiscale geometric analysis is presented in this paper first. Due to the isotropic nature of wavelet transform, 2D image details are not well represented in wavelet transform, which results in over smoothing. In this new denoising method, a noisy image is processed by the wavelet denoising method first, and then edges' information which has been wrongly discarded, is picked up from the residue image by multiscale geometric analysis. The final denoising image is a combination of the wavelet denoising result and the edges' information. Furthermore, incorporating prior knowledge on the contours' shape and shape similarity metric based on Fourier descriptors of snakes, a parameter-varying snake model is introduced. It addresses the problem of varying parameters during snake method. Extensive experimental results illustrate the excellent performance.

Contrast enhancement in retinal image via multi-scale geometrical analysis

We present a new multi-scale geometrical analysis method for ophthalmic image contrast enhancement based on the contourlet transform. The contourlet transform has better performance in representing edges than wavelets due to its anisotropy and directionality, and is therefore well-suited for multiscale edge enhancement. We modify the contourlet coefficients in corresponding subband and take the noise into account for more precise reconstruction and better visualization. We compare this approach with enhancement based on the curvelet transform, and the traditional Histogram Stretching (HS). Our findings are that contourlet based enhancement out-performs other enhancement methods on low contrast and dynamic range images, and can clearly identify the vessels and nerves in an ophthalmic image.

Near-Optimal Detection of Geometric Objects by Fast Multiscale Methods

We construct detectors for objects in noisy data. Examples include a detector for presence of a line segment of unknown length, position, and orientation in two-dimensional image data with additive white Gaussian noise. We focus on the following two issues. i) The optimal detection threshold-i.e., the signal strength below which no method of detection can be successful for large dataset size n. ii) The optimal computational complexity of a near-optimal detector, i.e., the complexity required to detect signals slightly exceeding the detection threshold. We describe a general approach to such problems which covers several classes of geometrically defined signals; for example, with one-dimensional data, signals having elevated mean on an interval, and, in d-dimensional data, signals with elevated mean on a rectangle, a ball, or an ellipsoid. In all these problems, we show that a naive or straightforward approach leads to detector thresholds and algorithms which are asymptotically far away from optimal. At the same time, a multiscale geometric analysis of these classes of objects allows us to derive asymptotically optimal detection thresholds and fast algorithms for near-optimal detectors.

BEAMLAB AND REPRODUCIBLE RESEARCH

In the first 'Wavelets and Statistics' conference proceedings 1, our group published 'Wavelab and Reproducible Research', in which we advocated using the internet for publication of software and data so that research results could be duplicated by others. Much has happened in the last decade that bears on the notion of reproducibility, and we will review our experience. We will also describe a new software package BEAMLAB containing routines for multiscale geometric analysis, and describe some of its capabilities. BEAMLAB makes available, in one package, all the code to reproduce all the figures in our recently published articles on beamlets, curvelets and ridgelets. The interested reader can inspect the source code to see what algorithms were used, and how parameters were set to produce the figures, and will then be able to modify the source codes to produce variations of our results. Some new examples of numerical studies based on BEAMLAB are provided here.

Digital Image-based Analysis of Morphology for Porous Materials

The porous material is one of the promising functional materials, and its macroscopic properties are strongly dependent on the microscopic morphology. To study the correlation between the microscopic heterogeneity and the macroscopic properties, a novel digital imagebased analysis methodology is proposed in this paper, which consists of high resolution X-ray CT, digital image-based modeling, multi-scale stress analysis and geometrical morphology analysis. The proposed morphology analysis enables us to predict the microscopic stress concentration for spherical porous ceramics considering the heterogeneous dispersion of spherical pores and the macroscopic loading condition. The heterogeneity can be analyzed geometrically for very huge data with approximately 58 million voxel elements quickly. The morphology analysis is helpful for the multi-scale modeling and microscopic stress evaluation. The microscopic stress distribution is also discussed in association with the random heterogeneity for ceramics with open pores and with high porosity ratios.