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

Understanding Collective Human Behavior in Social Media Networks Via the Dynamical Hypothesis: Applications to Radicalization and Conspiratorial Beliefs

The dynamical hypothesis has served to explore the ways in which cognitive agents can be understood dynamically and considered dynamical systems. Originally used to explain simple physical systems as a metaphor for cognition (i.e., the Watt governor) and eventually more complex animal systems (e.g., bird flocks), we argue that the dynamical hypothesis is among the most viable approaches to understanding pressing modern-day issues that arise from collective human behavior in online social networks. First, we discuss how the dynamical hypothesis is positioned to describe, predict, and explain the time-evolving nature of complex systems. Next, we adopt an interdisciplinary perspective to describe how online social networks are appropriately understood as dynamical systems. We introduce a dynamical modeling approach to reveal information about emergent properties in social media, where radicalized conspiratorial beliefs arise via coordination between user-level and community-level comments. Lastly, we contrast how the dynamical hypothesis differs from alternatives in explaining collective human behavior in social networks.

Fast Blind Quality Assessment of DIBR-Synthesized Video Based on High-High Wavelet Subband

Free-viewpoint video, as the development direction of the next-generation video technologies, uses the depth-image-based rendering (DIBR) technique for the synthesis of video sequences at viewpoints, where real captured videos are missing. As reference videos at multiple viewpoints are not available, a blind reliable real-time quality metric of the synthesized video is needed. Although no-reference quality metrics dedicated to synthesized views successfully evaluate synthesized images, they are not that effective when evaluating synthesized video due to additional temporal flicker distortion typical only for video. In this paper, a new fast no-reference quality metric of synthesized video with synthesis distortions is proposed. It is guided by the fact that the DIBR-synthesized images are characterized by increased high frequency content. The metric is designed under the assumption that the perceived quality of DIBR-synthesized video can be estimated by quantifying the selected areas in the high-high wavelet subband. The threshold is used to select the most important distortion sensitive regions. The proposed No-Reference Morphological Wavelet with Threshold (NR_MWT) metric is computationally extremely efficient, comparable to PSNR, as the morphological wavelet transformation uses very short filters and only integer arithmetic. It is completely blind, without using machine learning techniques. Tested on the publicly available dataset of synthesized video sequences characterized by synthesis distortions, the metric achieves better performances and higher computational efficiency than the state-of-the-art metrics dedicated to DIBR-synthesized images and videos.

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.

Prediction of total volatile basic nitrogen contents using wavelet features from visible/near-infrared hyperspectral images of prawn (Metapenaeus ensis)

A visible/near-infrared hyperspectral imaging (HSI) system (400-1000 nm) coupled with wavelet analysis was used to determine the total volatile basic nitrogen (TVB-N) contents of prawns during cold storage. Spectral information was denoised by conducting wavelet analysis and uninformative variable elimination (UVE) algorithm, and then three wavelet features (energy, entropy and modulus maxima) were extracted. Quantitative models were established between the wavelet features and the reference TVB-N contents by using three regression algorithms. As a result, the LS-SVM model with modulus maxima features was considered as the best model for determining the TVB-N contents of prawns, with an excellent RP(2) of 0.9547, RMSEP=0.7213 mg N/100g and RPD=4.799. Finally, an image processing algorithm was developed for generating a TVB-N distribution map. This study demonstrated the possibility of applying the HSI imaging system in combination with wavelet analysis to the monitoring of TVB-N values in prawns.

Enhanced disease characterization through multi network functional normalization in fMRI

Conventionally, structural topology is used for spatial normalization during the pre-processing of fMRI. The co-existence of multiple intrinsic networks which can be detected in the resting brain are well-studied. Also, these networks exhibit temporal and spatial modulation during cognitive task vs. rest which shows the existence of common spatial excitation patterns between these identified networks. Previous work (Khullar et al., 2011) has shown that structural and functional data may not have direct one-to-one correspondence and functional activation patterns in a well-defined structural region can vary across subjects even for a well-defined functional task. The results of this study and the existence of the neural activity patterns in multiple networks motivates us to investigate multiple resting-state networks as a single fusion template for functional normalization for multi groups of subjects. We extend the previous approach (Khullar et al., 2011) by co-registering multi group of subjects (healthy control and schizophrenia patients) and by utilizing multiple resting-state networks (instead of just one) as a single fusion template for functional normalization. In this paper we describe the initial steps toward using multiple resting-state networks as a single fusion template for functional normalization. A simple wavelet-based image fusion approach is presented in order to evaluate the feasibility of combining multiple functional networks. Our results showed improvements in both the significance of group statistics (healthy control and schizophrenia patients) and the spatial extent of activation when a multiple resting-state network applied as a single fusion template for functional normalization after the conventional structural normalization. Also, our results provided evidence that the improvement in significance of group statistics lead to better accuracy results for classification of healthy controls and schizophrenia patients.

Fractal analysis of laplacian pyramidal filters applied to segmentation of soil images

The laplacian pyramid is a well-known technique for image processing in which local operators of many scales, but identical shape, serve as the basis functions. The required properties to the pyramidal filter produce a family of filters, which is unipara metrical in the case of the classical problem, when the length of the filter is 5. We pay attention to gaussian and fractal behaviour of these basis functions (or filters), and we determine the gaussian and fractal ranges in the case of single parameter a. These fractal filters loose less energy in every step of the laplacian pyramid, and we apply this property to get threshold values for segmenting soil images, and then evaluate their porosity. Also, we evaluate our results by comparing them with the Otsu algorithm threshold values, and conclude that our algorithm produce reliable test results.

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.

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.

Adaptive nonseparable wavelet transform via lifting and its application to content-based image retrieval

We present in this paper a novel way to adapt a multidimensional wavelet filter bank, based on the nonseparable lifting scheme framework, to any specific problem. It allows the design of filter banks with a desired number of degrees of freedom, while controlling the number of vanishing moments of the primal wavelet ((~)N moments) and of the dual wavelet ( N moments). The prediction and update filters, in the lifting scheme based filter banks, are defined as Neville filters of order (~)N and N, respectively. However, in order to introduce some degrees of freedom in the design, these filters are not defined as the simplest Neville filters. The proposed method is convenient: the same algorithm is used whatever the dimensionality of the signal, and whatever the lattice used. The method is applied to content-based image retrieval (CBIR): an image signature is derived from this new adaptive nonseparable wavelet transform. The method is evaluated on four image databases and compared to a similar CBIR system, based on an adaptive separable wavelet transform. The mean precision at five of the nonseparable wavelet based system is notably higher on three out of the four databases, and comparable on the other one. The proposed method also compares favorably with the dual-tree complex wavelet transform, an overcomplete nonseparable wavelet transform.

Image coding using dual-tree discrete wavelet transform

In this paper, we explore the application of 2-D dual-tree discrete wavelet transform (DDWT), which is a directional and redundant transform, for image coding. Three methods for sparsifying DDWT coefficients, i.e., matching pursuit, basis pursuit, and noise shaping, are compared. We found that noise shaping achieves the best nonlinear approximation efficiency with the lowest computational complexity. The interscale, intersubband, and intrasubband dependency among the DDWT coefficients are analyzed. Three subband coding methods, i.e., SPIHT, EBCOT, and TCE, are evaluated for coding DDWT coefficients. Experimental results show that TCE has the best performance. In spite of the redundancy of the transform, our DDWT _ TCE scheme outperforms JPEG2000 up to 0.70 dB at low bit rates and is comparable to JPEG2000 at high bit rates. The DDWT _TCE scheme also outperforms two other image coders that are based on directional filter banks. To further improve coding efficiency, we extend the DDWT to an anisotropic dual-tree discrete wavelet packets (ADDWP), which incorporates adaptive and anisotropic decomposition into DDWT. The ADDWP subbands are coded with TCE coder. Experimental results show that ADDWP _ TCE provides up to 1.47 dB improvement over the DDWT _TCE scheme, outperforming JPEG2000 up to 2.00 dB. Reconstructed images of our coding schemes are visually more appealing compared with DWT-based coding schemes thanks to the directionality of wavelets.

Theoretical foundations of spatially-variant mathematical morphology part I: binary images

We develop a general theory of spatially-variant (SV) mathematical morphology for binary images in the Euclidean space. The basic SV morphological operators (i.e., SV erosion, SV dilation, SV opening and SV closing) are defined. We demonstrate the ubiquity of SV morphological operators by providing a SV kernel representation of increasing operators. The latter representation is a generalization of Matheron's representation theorem of increasing and translation-invariant operators. The SV kernel representation is redundant, in the sense that a smaller subset of the SV kernel is sufficient for the representation of increasing operators. We provide sufficient conditions for the existence of the minimal basis representation in terms of upper-semi-continuity in the hit-or-miss topology. The latter minimal basis representation is a generalization of Maragos' minimal basis representation for increasing and translation-invariant operators. Moreover, we investigate the upper-semi-continuity property of the basic SV morphological operators. Several examples are used to demonstrate that the theory of spatially-variant mathematical morphology provides a general framework for the unification of various morphological schemes based on spatiallyvariant geometrical structuring elements (e.g., circular, affine and motion morphology). Simulation results illustrate the theory of the proposed spatially-variant morphological framework and show its potential power in various image processing applications.

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.

Multi-resolution image fusion technique and its application to forensic science

Image fusion is a process of combining two or more images into an image. It can extract features from source images, and provide more information than one image can. Multi-resolution analysis plays an important role in image processing, it provides a technique to decompose an image and extract information from coarse to fine scales. In some practical forensic examinations (such as the cartridge image check), we cannot obtain all information from just one image; on the contrary, we need information from images with difference light sources (or light ways). In this paper, we apply an image fusion method based on multi-resolution analysis to forensic science. Synthetic and real images (such as images from closed-up photography and flash photography) are used to show the capability of the multi-resolution image fusion technique.

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.

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

Interest in multiresolution techniques for signal processing and analysis is increasing steadily. An important instance of such a technique is the so-called pyramid decomposition scheme. This paper presents a general theory for constructing linear as well as nonlinear pyramid decomposition schemes for signal analysis and synthesis. The proposed theory is based on the following ingredients: 1) the pyramid consists of a (finite or infinite) number of levels such that the information content decreases toward higher levels and 2) each step toward a higher level is implemented by an (information-reducing) analysis operator, whereas each step toward a lower level is implemented by an (information-preserving) synthesis operator. One basic assumption is necessary: synthesis followed by analysis yields the identity operator, meaning that no information is lost by these two consecutive steps. Several examples of pyramid decomposition schemes are shown to be instances of the proposed theory: a particular class of linear pyramids, morphological skeleton decompositions, the morphological Haar pyramid, median pyramids, etc. Furthermore, the paper makes a distinction between single-scale and multiscale decomposition schemes, i.e., schemes without or with sample reduction. Finally, the proposed theory provides the foundation of a general approach to constructing nonlinear wavelet decomposition schemes and filter banks.