Multiscale Geometric Analysis Research Articles

Medical Image Fusion Based on Feature Extraction and Sparse Representation.

As a novel multiscale geometric analysis tool, sparse representation has shown many advantages over the conventional image representation methods. However, the standard sparse representation does not take intrinsic structure and its time complexity into consideration. In this paper, a new fusion mechanism for multimodal medical images based on sparse representation and decision map is proposed to deal with these problems simultaneously. Three decision maps are designed including structure information map (SM) and energy information map (EM) as well as structure and energy map (SEM) to make the results reserve more energy and edge information. SM contains the local structure feature captured by the Laplacian of a Gaussian (LOG) and EM contains the energy and energy distribution feature detected by the mean square deviation. The decision map is added to the normal sparse representation based method to improve the speed of the algorithm. Proposed approach also improves the quality of the fused results by enhancing the contrast and reserving more structure and energy information from the source images. The experiment results of 36 groups of CT/MR, MR-T1/MR-T2, and CT/PET images demonstrate that the method based on SR and SEM outperforms five state-of-the-art methods.

Remote sensing image processing based on multi-scale geometric transformation algorithm

Remote sensing image plays an irreplaceable role in the defense and civilian sides. Because there are big differences between its image-forming mechanism and visible light image, it is particularly important to study the processing algorithm for the characteristic of this type of graphics. Although the multi-scale geometric analysis algorithm has a good time-frequency characteristics itself and can well solve some multidimensional signal processing problems of the corresponding directions, there are still many shortcomings of the multi-scale geometric transformation generated by theory need to be improved. Some multiscale geometric transformations don’t have shift invariance nature and analytical nature, the direction selectivity are poor and so on, and for the characteristics of remote sensing image, different types of multi-scale geometric transformation has different processing effect. The study is mainly based on the multi-scale geometric transformation which is commonly used, and its main application areas are remote sensing image processing. The paper regards the multi-scale geometric transformation as main line, and carries out a deep and systematic study on denoising technology in SAR image of the key technology in remote sensing image processing. And the experimental results are analyzed to verify the effectiveness of the technology.

Multi-scale curvature tensor analysis of machined surfaces

Abstract This paper demonstrates the use of multi-scale curvature analysis, an areal new surface characterization technique for better understanding topographies, for analyzing surfaces created by conventional machining and grinding. Curvature, like slope and area, changes with scale of observation, or calculation, on irregular surfaces, therefore it can be used for multi-scale geometric analysis. Curvatures on a surface should be indicative of topographically dependent behavior of a surface and curvatures are, in turn, influenced by the processing and use of the surface. Curvatures have not been well characterized previously. Curvature has been used for calculations in contact mechanics and for the evaluation of cutting edges. In the current work two parts were machined and then one of them was ground. The surface topographies were measured with a scanning laser confocal microscope. Plots of curvatures as a function of position and scale are presented, and the means and standard deviations of principal curvatures are plotted as a function of scale. Statistical analyses show the relations between curvature and these two manufacturing processes at multiple scales.

Multimodal Sensor Medical Image Fusion Based on Type-2 Fuzzy Logic in NSCT Domain

Multimodal medical image fusion plays a vital role in different clinical imaging sensor applications. This paper presents a novel multimodal medical image fusion method that adopts a multiscale geometric analysis of the nonsubsampled contourlet transform (NSCT) with type-2 fuzzy logic techniques. First, the NSCT was performed on preregistered source images to obtain their high- and low-frequency subbands. Next, an effective type-2 fuzzy logic-based fused rule is proposed for fusion of the high-frequency subbands. In the presented fusion approach, the local type-2 fuzzy entropy is introduced to automatically select high-frequency coefficients. However, for the low-frequency subbands, they were fused by a local energy algorithm based on the corresponding image’s local features. Finally, the fused image was constructed by the inverse NSCT with all composite subbands. Both subjective and objective evaluations showed better contrast, accuracy, and versatility in the proposed approach compared with state-of-the-art methods. Besides, an effective color medical image fusion scheme is also given in this paper that can inhibit color distortion to a large extent and produce an improved visual effect.

A novel surface defect inspection algorithm for magnetic tile

In this paper, we propose a defect extraction method for magnetic tile images based on the shearlet transform. The shearlet transform is a method of multi-scale geometric analysis. Compared with similar methods, the shearlet transform offers higher directional sensitivity and this is useful to accurately extract geometric characteristics from data. In general, a magnetic tile image captured by CCD camera mainly consists of target area, background. Our strategy for extracting the surface defects of magnetic tile comprises two steps: image preprocessing and defect extraction. Both steps are critical. After preprocessing the image, we extract the target area. Due to the low contrast in the magnetic tile image, we apply the discrete shearlet transform to enhance the contrast between the defect area and the normal area. Next, we apply a threshold method to generate a binary image. To validate our algorithm, we compare our experimental results with Otsu method, the curvelet transform and the nonsubsampled contourlet transform. Results show that our algorithm outperforms the other methods considered and can very effectively extract defects.

Evolutionary geometry of Lagrangian structures in a transitional boundary layer

We report a geometric study of Lagrangian structures in a weakly compressible, spatially evolving transitional boundary layer at the Mach number 0.7. The Lagrangian structures in the transition process are extracted from the Lagrangian scalar field by a sliding window filter at a sequence of reference times. The multi-scale and multi-directional geometric analysis is applied to characterize the geometry of spatially evolving Lagrangian structures, including the averaged inclination and sweep angles at different scales ranging from one half of the boundary layer thickness to several viscous length scales. Here, the inclination angle is on the plane of the streamwise and wall-normal directions, and the sweep angle is on the plane of the streamwise and spanwise directions. In general, the averaged inclination angle is increased and the sweep angle is decreased with the reference time. The variation of the angles for large-scale structures is smaller than that for small-scale structures. Before the transition, the averaged inclination and sweep angles are only slightly altered for all the scales. As the transition occurs, averaged inclination angles increase and sweep angles decrease rapidly for small-scale structures. In the late transitional stage, the averaged inclination angle of small-scale structures with 30 viscous length scales is approximately 42°, and the averaged sweep angle in the logarithm law region is approximately 30°. Additionally, the geometry of Lagrangian structures in transitional boundary layer flow is compared with that in the fully developed turbulent channel flow.

A Change Detection Method of Multi-temporal SAR Images Based on Contourlet Transform

Synthetic aperture radar (SAR) imaging is very sensitive to direction, so the information that SAR images contain is often not completely same from different directions. The information obtained from multi-directions must be more abundant and more accurate than that of from a single direction in a SAR image. The Contourlet transform is a multi-scale geometric analysis theory, holding many advantages for signal processing, such as multi-resolution, multi-direction and anisotropy; therefore, it is in favor of extracting different direction information for SAR images. According to the directional sensitivity of SAR imaging and the characteristics of multi-scale and multi direction to the Contourlet transform, this paper proposed a new SAR image change detection method based on Contourlet transform, called CTCD algorithm. Using the multi-direction characteristic of Contourlet transform, the CTCD method can get more accurate changed information for multi-temporal SAR images. The practical SAR image data is employed to test the CTCD algorithm and results show that the CTCD algorithm is a feasible change detection algorithm for multi-temporal SAR images, and it can obtain more abundant and more accurate information than the direct difference change detection (DDCD) algorithm.

Change detection of remote sensing images by multi-scale geometric analysis and KICA

Change detection of remote sensing images by multi-scale geometric analysis and KICA

Surface Defect Recognition for Metals Based on Feature Fusion of Shearlets and Wavelets

Surface defects of metals are often with complexity and diversity. Wavelet transform is effective to detect singularities, it is applicable for recognition of point defects. As a relatively new method of multiscale geometric analysis(MGA), shearlet transform has good performance of directivity and optimal approximation, and it is applicable for recognition of defects with determined directions. A new recognition method of surface defects for metals is proposed, and it is based on feature fusion of shearlet transform and wavelet transform. Images of metals are decomposed into multiple directional sub-bands with shearlet transform and wavelet transform respectively. Then, means and variances of all sub-bands are computed and combined as a high dimensional feature vector. kernel locality preserving projection(KLPP) is applied to the high dimensional feature vector to remove redundant information between features. A low dimensional feature vector is generated and input to support vector machine(SVM) for classification of defects. Tested with samples captured from production lines of three typical metals, including high temperature slabs, medium and heavy plates and aluminium strips. Results show that classification rates of testing sets for high temperature slabs, medium and heavy plates and aluminium strips are 93.95%, 98.27% and 92.5% respectively. It is verified that the proposed method is a general algorithm of defect recognition for different types of metals.

A NOTE ON DAS'S PCA IN ONLINE PHASES

PCA was effective and helpful in developing a classification system. However, it was inappropriate to perform two independent PCA models on ground truth images and query image, which was described in Figure 1 in reference “Brain MR image classification using multiscale geometric analysis of ripplet,” Progress In Electromagnetics Research, Vol. 137, 1–17, 2013. In this note, we analyze the reason and revise Figure 1. In an interesting and useful paper [1] in the journal Progress In Electromagnetics Research, Das, Chowdhury, and Kundu proposed an automatic and accurate technique for classifying normal and abnormal magnetic resonance (MR) images of human brain. They used Ripplet transform Type-I (RT) to extract features, then the decomposed low frequency subband (LFS) was sent to principal component analysis (PCA) for feature reduction, and least square support vector machine (LS-SVM) for classification. The proposed system consisted of two phases: an offline phase and an online phase. The results over k-fold cross validation were excellent and superior to existing methods. However, they did not clearly describe the implementation of PCA in the online phase. Hence, this note is to remind readers some key issues of PCA in offline and online phases. Figure 1. Flowchart of Das’s MR image classification [1]. Received 21 January 2015, Accepted 17 February 2015, Scheduled 23 February 2015 * Corresponding author: Yudong Zhang (zhangyudong@njnu.edu.cn). 1 School of Computer Science and Technology, Nanjing Normal University, Nanjing, Jiangsu 210023, China. 2 Department of Applied Physics, Stanford University, Stanford, CA 94305, USA.

SAR Image Despeckling Using Scale Mixtures of Gaussians in the Nonsubsampled Contourlet Domain

The edge and contour details in SAR images are important for subsequent processing tasks. The multiscale geometric analysis method — Nonsubsampled contourlet transform (NSCT) is able to capture the geometric information of SAR images effectively. Describing the aggregation behavior of the neighborhoods coefficients, the scale mixtures of Gaussians model has exhibited favorable performances. A novel SAR image despeckling method is presented by constructing the scale mixtures of Gaussians model of NSCT. This method models the SAR images using the multiscale and multidirection information in NSCT domain. The dependency relationship of NSCT neighborhoods coefficients are also taken into consideration in our model. The speckle noise coefficients are shrinkaged by statistical prior estimation based on SAR image model constructed. Experimental results demonstrate that our method is advantageous at directional information preservation and the speckle restraint.

Sparse-filtering in directional lifting wavelet transform domain based Bayesian compressive sensing

Compressive sensing (CS) has been proposed for images that are sparse under a certain transform domain. However, many natural images are not strictly sparse in the transform domain, causing a tail-folding effect that degrades the performance of the CS reconstruction. To decrease such effect, a sparse-filtering (SF) in Directional Lifting Wavelet Transform (DLWT) domain based Bayesian compressive sensing (BCS) algorithm (DLWT-SF-TSW-BCS) is proposed. At the encoder, DLWT, an efficient multi-scale geometrical analysis (MGA) tool, is used to produce the sparse representation for natural images. Then sparse-filtering is adopted to cut off the small DLWT coefficients before random measurement. At the decoder, the interscale tree-structure redundancy in DLWT domain is further exploited in Bayesian reconstruction. Experimental results show that the proposed DLWT-SF-TSW-BCS algorithm significantly outperforms other state-of-the-art CS reconstruction algorithms, for example, peak signal to noise ratio (PSNR) gain up to 10.00 dB over the tree structured wavelet compressive sensing (TSW-CS).

Research on the Multi-Focus Image Fusion Method Based on the Second-Generation Curvelet Transformation

The optical imaging system has the limitation in scope, which is difficult to make all the objects in the same scene clear. To this issue, a multi-scale geometric analysis method – the second-generation Curvelet transform is applied into the fusion of multi-focus image. After the adjustment of the coefficients which are received by the Curvelet transform of more multi-focus image, the result image is gained by the inverse Curvelet transform. Experiments show that this method can have better fusion effect and significantly increase the space quality of multi-focus image.

A graph-based relevance feedback mechanism in content-based image retrieval

Content-Based Image Retrieval (CBIR) is an important problem in the domain of digital data management. There is indeed a growing availability of images, but unfortunately the traditional metadata-based search systems are unable to properly exploit their visual information content. In this article we introduce a novel CBIR scheme that abstracts each image in the database in terms of statistical features computed using the Multi-scale Geometric Analysis (MGA) of Non-subsampled Contourlet Transform (NSCT). Noise resilience is one of the main advantages of this feature representation. To improve the retrieval performance and reduce the semantic gap, our system incorporates a Relevance Feedback (RF) mechanism that uses a graph-theoretic approach to rank the images in accordance with the user’s feedback. First, a graph of images is constructed with edges reflecting the similarity of pairs of images with respect to the proposed feature representation. Then, images are ranked at each feedback round in terms of the probability that a random walk on this graph reaches an image tagged as relevant by the user before hitting a non-relevant one. Experimental analyses on three different databases show the effectiveness of our algorithm compared to state-of-the-art approaches in particular when the images are corrupted with different types of noise.

A Novel Image Fusion Method Using Non-Subsampled Shearlet Transform

As a novel MGA (Multiscale Geometric Analysis) tool, shearlet is equipped with a rich mathematical structure similar to wavelet. In this paper, a novel image fusion method using Non-subsampled Shearlet Transform is proposed. First, the source images are decomposed into low-pass and high-pass subbands using NSST. Second, the high-pass subbands coefficients of the images are fused according to the average gradient. Third, the low-pass subbands coefficients of the images are fused by the weighted regional entropy. Finally, the image is reconstructed by the inverse non-subsampled shearlet transform. In the method, two sets of source images and five objective parameters are used to test the algorithm. The experimental results show that the proposed method is better than the conventional DWT-based and NSCT-based methods.

Speckle reduction in optical coherence tomography images based on wave atoms.

Optical coherence tomography (OCT) is an emerging noninvasive imaging technique, which is based on low-coherence interferometry. OCT images suffer from speckle noise, which reduces image contrast. A shrinkage filter based on wave atoms transform is proposed for speckle reduction in OCT images. Wave atoms transform is a new multiscale geometric analysis tool that offers sparser expansion and better representation for images containing oscillatory patterns and textures than other traditional transforms, such as wavelet and curvelet transforms. Cycle spinning-based technology is introduced to avoid visual artifacts, such as Gibbs-like phenomenon, and to develop a translation invariant wave atoms denoising scheme. The speckle suppression degree in the denoised images is controlled by an adjustable parameter that determines the threshold in the wave atoms domain. The experimental results show that the proposed method can effectively remove the speckle noise and improve the OCT image quality. The signal-to-noise ratio, contrast-to-noise ratio, average equivalent number of looks, and cross-correlation (XCOR) values are obtained, and the results are also compared with the wavelet and curvelet thresholding techniques.

Fast Algorithm for Nonsubsampled Contourlet Transform

The multiscale geometric analysis (MGA) has been recognized as an effective strategy for image processing. As one of the discrete tools of MGA, the nonsubsampled contourlet transform (NSCT) has been widely used for image denoising, image fusion, image enhancement, feature extraction and so on. However, the processing performance is limited due to its high redundancy, and leading to an intensive computational efficiency. Therefore, its fast algorithm is desired in practice. In this paper, we adopt an optimized directional filter bank (DFB) and embed it into the NSCT to significantly accelerate the computational speed while keeping slight loss of the reconstructed performance. Experimental results show that the reconstructed image quality can satisfy the human visual system. Moreover, the improved NSCT has a speed about several times than that of the traditional one. Experimental results on image denoising also validate the feasibility and efficiency of the proposed method.

On the Splitting Algorithm Based on Multi-target Model for Image Segmentation

Against to the different regions of membership functions indicated image in the traditional image segmentation variational model, resulting segmentation is not clear, de-noising effect is not obvious problems, this paper proposes multi-target model for image segmentation and the splitting algorithm. The model uses a sparse regularization method to maintain the boundaries of segmented regions, to overcome the disadvantages of segmentation fuzzy boundaries resulting from total variation regularization. The algorithm uses the multi-scale geometric analysis tool to maintain the geometry of image, which multi-scale geometric transformations can be flexibly selected according to actual problems. Experimental results show that: the proposed model and the algorithm are feasible and effective.

An Image Fusion Method Based on NSCT and Dual-channel PCNN Model

NSCT is one of useful multiscale geometric analysis tools, which takes full advantage of geometric regularity of image intrinsic structures. The dual-channel PCNN is a simplified PCNN model, which can process multiple images by a single PCNN. This saves time in the process of image fusion and cuts down computational complexity. In this paper, we present a new image fusion scheme based on NSCT and dual-channel PCNN. Firstly, the fusion rules of subband coefficients of NSCT are discussed. For the fusion rule of low frequency coefficients, the maximum selection rule (MSR) is used. Then, for the fusion rule of high frequency coefficients, spatial frequency (SF) of each high frequency subband is considered as the gradient features of images to motivate dual-channel PCNN networks and generate pulse of neurons. At last, fused image is obtained by using the inverse NSCT transform. In order to show that the proposed method can deal with image fusion, we used two pairs of images as our experimental subjects. The proposed method is compared with other five methods. The performance of various methods is mathematically evaluated by using four image quality evaluation criteria. Experimental comparisons conducted on different fusion methods prove the effectiveness of the proposed fusion method

On Curvelet based Multi-scale Analysis of Higher Dimensional Solitons

In shallow water theory, completely integrable nonlinear partial differential equations arise at various levels of approximations/simulations. Such equations possess traveling wave solutions, called solitons, which themselves are self-phase-modulated signals. Wavelets are traditionally applied in signal processing but it has limitations to deal effectively with geometric features with line and surface singularities. Due to its poor orientation selectivity, wavelet can only capture limited directional information in signal processing. A multi-resolution geometric analysis, named curvelet transform overcomes the drawbacks of the conventional wavelet transform. Such a geometric characterization provides better understanding of cascade mechanism and dissipation range dynamics. In the present work, a multi-scale geometric analysis with curvelets as basis functions is proposed for analyzing higher dimensional lump-like solitons- that arise in the evolution of lump solutions for the Zakharov-Kuznetsov equation and the surface electromigration equation. Moreover, the application of curvelet thresholding technique for de-noising the contaminated signals is presented.