Nonlinear multiresolution signal decomposition schemes--part I: morphological pyramids

Fusion of Multispectral and Panchromatic Images Based on Morphological Operators

Nonlinear decomposition schemes constitute an alternative to classical approaches for facing the problem of data fusion. In this paper, we discuss the application of this methodology to a popular remote sensing application called pansharpening, which consists in the fusion of a low resolution multispectral image and a high-resolution panchromatic image. We design a complete pansharpening scheme based on the use of morphological half gradient operators and demonstrate the suitability of this algorithm through the comparison with the state-of-the-art approaches. Four data sets acquired by the Pleiades, Worldview-2, Ikonos, and Geoeye-1 satellites are employed for the performance assessment, testifying the effectiveness of the proposed approach in producing top-class images with a setting independent of the specific sensor.

Study on clear stereo image pair acquisition method for small objects with big vertical size in SLM vision system

Microscopic vision system with stereo light microscope (SLM) has been applied to surface profile measurement. If the vertical size of a small object exceeds the range of depth, its images will contain clear and fuzzy image regions. Hence, in order to obtain clear stereo images, we propose a microscopic sequence image fusion method which is suitable for SLM vision system. First, a solution to capture and align image sequence is designed, which outputs an aligning stereo images. Second, we decompose stereo image sequence by wavelet analysis theory, and obtain a series of high and low frequency coefficients with different resolutions. Then fused stereo images are output based on the high and low frequency coefficient fusion rules proposed in this article. The results show that Δw1 (Δw2 ) and ΔZ of stereo images in a sequence have linear relationship. Hence, a procedure for image alignment is necessary before image fusion. In contrast with other image fusion methods, our method can output clear fused stereo images with better performance, which is suitable for SLM vision system, and very helpful for avoiding image fuzzy caused by big vertical size of small objects.

QRS detection by lifting scheme constructing multi-resolution morphological decomposition

QRS complex detecting algorithm is core of ECG auto-diagnosis method and deeply influences cardiac cycle division for signal compression. However, ECG signals collected by noninvasive surface electrodes areusually mixed with several kinds of interference, and its waveform variation is the main reason for the hard realization of ECG processing. This paper proposes a QRS complex detecting algorithm based on multi-resolution mathematical morphological decomposition. This algorithm possesses superiorities in R peak detection of both mathematical morphological method and multi-resolution decomposition. Moreover, a lifting constructing method with Maximizationupdating operator is adopted to further improve the algorithm performance. And an efficient R peak search-back algorithm is employed to reduce the false positives (FP) and false negatives (FN). The proposed algorithm provides a good performance applying to MIT-BIH Arrhythmia Database, and achieves over 99% detection rate, sensitivity and positive predictivity, respectively, and calculation burden is low. Therefore, the proposed method is appropriate for portable medical devices in Telemedicine system.

Energy preserving QMF for image processing

Implementation of new biorthogonal filter banks (BFB) for image compression and denoising is performed, using test images with diversified characteristics. These new BFB’s are linear-phase, have odd lengths, and with a critical feature, namely, the filters preserve signal energy very well. Experimental results show that the proposed filter banks demonstrate promising performance improvement over the filter banks of those widely used in the image processing area, such as the CDF 9/7.

Multimodal medical volumetric data fusion using 3-D discrete shearlet transform and global-to-local rule

Traditional two-dimensional (2-D) fusion framework usually suffers from the loss of the between-slice information of the third dimension. For example, the fusion of three-dimensional (3-D) MRI slices must account for the information not only within the given slice but also the adjacent slices. In this paper, a fusion method is developed in 3-D shearlet space to overcome the drawback. On the other hand, the popularly used average-maximum fusion rule can capture only the local information but not any of the global information for it is implemented in a local window region. Thus, a global-to-local fusion rule is proposed. We firstly show the 3-D shearlet coefficients of the high-pass subbands are highly non-Gaussian. Then, we show this heavy-tailed phenomenon can be modeled by the generalized Gaussian density (GGD) and the global information between two subbands can be described by the Kullback-Leibler distance (KLD) of two GGDs. The finally fused global information can be selected according to the asymmetry of the KLD. Experiments on synthetic data and real data demonstrate that better fusion results can be obtained by the proposed method.

Image analysis through feature extraction by using top-hat transform-based morphological contrast operator

Image decomposition and reconstruction is an important way for image analysis. To be effective for image decomposition and reconstruction, a method using extracted features through top-hat transform-based morphological contrast operator (MCOTH) is proposed in this paper. First, the morphological contrast operator constructed using the top-hat transforms is discussed. Then, extracting the bright and dark image features in the result of MCOTH is given. Based on the extracted bright and dark image features, the original images are decomposed into multiscale complete decompositions using multiscale structuring elements. After processing the decomposed images following different application purposes, the final result image can be reconstructed from the processed decomposition images. To verify the effectiveness of the proposed image analysis method through image decomposition and reconstruction, the application of image enhancement and fusion are discussed. The experimental results show that because the proposed image decomposition and reconstruction method reasonably decomposes the original image into complete decomposition with useful image features at different scales, the useful image features could be easily used for different applications. After the useful image features are processed, the final result image could be reconstructed. Moreover, different types of images are used in the experiments of image enhancement and fusion, and the results are effective. Therefore, the proposed image decomposition and reconstruction method in this paper are effective methods for image analysis and could be widely used in different applications.

Edge-preserving image regularization based on morphological wavelets and dyadic trees

Despite the tremendous success of wavelet-based image regularization, we still lack a comprehensive understanding of the exact factor that controls edge preservation and a principled method to determine the wavelet decomposition structure for dimensions greater than 1. We address these issues from a machine learning perspective by using tree classifiers to underpin a new image regularizer that measures the complexity of an image based on the complexity of the dyadic-tree representations of its sublevel sets. By penalizing unbalanced dyadic trees less, the regularizer preserves sharp edges. The main contribution of this paper is the connection of concepts from structured dyadic-tree complexity measures, wavelet shrinkage, morphological wavelets, and smoothness regularization in Besov space into a single coherent image regularization framework. Using the new regularizer, we also provide a theoretical basis for the data-driven selection of an optimal dyadic wavelet decomposition structure. As a specific application example, we give a practical regularized image denoising algorithm that uses this regularizer and the optimal dyadic wavelet decomposition structure.

Interpolation-dependent image downsampling

Traditional methods for image downsampling commit to remove the aliasing artifacts. However, the influences on the quality of the image interpolated from the downsampled one are usually neglected. To tackle this problem, in this paper, we propose an interpolation-dependent image downsampling (IDID), where interpolation is hinged to downsampling. Given an interpolation method, the goal of IDID is to obtain a downsampled image that minimizes the sum of square errors between the input image and the one interpolated from the corresponding downsampled image. Utilizing a least squares algorithm, the solution of IDID is derived as the inverse operator of upsampling. We also devise a content-dependent IDID for the interpolation methods with varying interpolation coefficients. Numerous experimental results demonstrate the viability and efficiency of the proposed IDID.

Multiscale display processing of radiographic images acquired with a protoype flat panel detector

This paper study softcopy display algorithms of digital radiographic images acquired using a prototype flat panel detector. The processing is manipulated in two steps. Firstly, a look up table is applied to map the gray value of original image into proper visual scope. Then, the mapped image is decomposed into a serial subband images with a multiscale pyramid structure. The contrast of subband images are enhanced by using nolinear functions. Both performance and computational simplicity make our algorithms attractive.

Nonlinear diffusion in Laplacian pyramid domain for ultrasonic speckle reduction

A new speckle reduction method, i.e., Laplacian pyramid-based nonlinear diffusion (LPND), is proposed for medical ultrasound imaging. With this method, speckle is removed by nonlinear diffusion filtering of bandpass ultrasound images in Laplacian pyramid domain. For nonlinear diffusion in each pyramid layer, a gradient threshold is automatically determined by a variation of median absolute deviation (MAD) estimator. The performance of the proposed LPND method has been compared with that of other speckle reduction methods, including the recently proposed speckle reducing anisotropic diffusion (SRAD) and nonlinear coherent diffusion (NCD). In simulation and phantom studies, an average gain of 1.55 dB and 1.34 dB in contrast-to-noise ratio was obtained compared to SRAD and NCD, respectively. The visual comparison of despeckled in vivo ultrasound images from liver and carotid artery shows that the proposed LPND method could effectively preserve edges and detailed structures while thoroughly suppressing speckle. These preliminary results indicate that the proposed speckle reduction method could improve image quality and the visibility of small structures and fine details in medical ultrasound imaging.

Optimization of integer wavelet transforms based on difference correlation structures

In this paper, a novel lifting integer wavelet transform based on difference correlation structure (DCCS-LIWT) is proposed. First, we establish a relationship between the performance of a linear predictor and the difference correlations of an image. The obtained results provide a theoretical foundation for the following construction of the optimal lifting filters. Then, the optimal prediction lifting coefficients in the sense of least-square prediction error are derived. DCCS-LIWT puts heavy emphasis on image inherent dependence. A distinct feature of this method is the use of the variance-normalized autocorrelation function of the difference image to construct a linear predictor and adapt the predictor to varying image sources. The proposed scheme also allows respective calculations of the lifting filters for the horizontal and vertical orientations. Experimental evaluation shows that the proposed method produces better results than the other well-known integer transforms for the lossless image compression.

Object-based image analysis using multiscale connectivity

This paper introduces a novel approach for image analysis based on the notion of multiscale connectivity. We use the proposed approach to design several novel tools for object-based image representation and analysis which exploit the connectivity structure of images in a multiscale fashion. More specifically, we propose a nonlinear pyramidal image representation scheme, which decomposes an image at different scales by means of multiscale grain filters. These filters gradually remove connected components from an image that fail to satisfy a given criterion. We also use the concept of multiscale connectivity to design a hierarchical data partitioning tool. We employ this tool to construct another image representation scheme, based on the concept of component trees, which organizes partitions of an image in a hierarchical multiscale fashion. In addition, we propose a geometrically-oriented hierarchical clustering algorithm which generalizes the classical single-linkage algorithm. Finally, we propose two object-based multiscale image summaries, reminiscent of the well-known (morphological) pattern spectrum, which can be useful in image analysis and image understanding applications.

Multiresolution maximum intensity volume rendering by morphological adjunction pyramids

We describe a multiresolution extension to maximum intensity projection (MIP) volume rendering, allowing progressive refinement and perfect reconstruction. The method makes use of morphological adjunction pyramids. The pyramidal analysis and synthesis operators are composed of morphological 3-D erosion and dilation, combined with dyadic downsampling for analysis and dyadic upsampling for synthesis. In this case the MIP operator can be interchanged with the synthesis operator. This fact is the key to an efficient multiresolution MIP algorithm, because it allows the computation of the maxima along the line of sight on a coarse level, before applying a two-dimensional synthesis operator to perform reconstruction of the projection image to a finer level. For interpolation and resampling of volume data, which is required to deal with arbitrary view directions, morphological sampling is used, an interpolation method well adapted to the nonlinear character of MIP. The structure of the resulting multiresolution rendering algorithm is very similar to wavelet splatting, the main differences being that (i) linear summation of voxel values is replaced by maximum computation, and (ii) linear wavelet filters are replaced by nonlinear morphological filters.

l(p)-Multiresolution analysis: how to reduce ringing and sparsify the error

We propose to design the reduction operator of an image pyramid so as to minimize the approximation error in the l(p)-sense (not restricted to the usual p=2), where p can take noninteger values. The underlying image model is specified using shift-invariant basis functions, such as B-splines. The solution is well-defined and determined by an iterative optimization algorithm based on digital filtering. Its convergence is accelerated by the use of first and second order derivatives. For p close to 1, we show that the ringing is reduced and that the histogram of the detail image is sparse as compared with the standard case, where p=2.

Nonlinear multiresolution signal decomposition schemes--part II: morphological wavelets

In its original form, the wavelet transform is a linear tool. However, it has been increasingly recognized that nonlinear extensions are possible. A major impulse to the development of nonlinear wavelet transforms has been given by the introduction of the lifting scheme by Sweldens (1995, 1996, 1998). The aim of this paper, which is a sequel to a previous paper devoted exclusively to the pyramid transform, is to present an axiomatic framework encompassing most existing linear and nonlinear wavelet decompositions. Furthermore, it introduces some, thus far unknown, wavelets based on mathematical morphology, such as the morphological Haar wavelet, both in one and two dimensions. A general and flexible approach for the construction of nonlinear (morphological) wavelets is provided by the lifting scheme. This paper briefly discusses one example, the max-lifting scheme, which has the intriguing property that preserves local maxima in a signal over a range of scales, depending on how local or global these maxima are.