DT-MRI data visualisation using the dual tree Complex Wavelet transform

In this paper a novel visualisation method for diffusion tensor MRI datasets is introduced. This is based on the use of Complex Wavelets in order to produce "stripy" textures which depict the anisotropic component of the diffusion tensors. Grey-scale pixel intensity is used to show the isotropic component. This paper also discusses enhancements of the technique for 3D visualisation. © 2004 IEEE.

A Bayesian wavelet-based multidimensional deconvolution with sub-band emphasis

This paper proposes a new algorithm for waveletbased multidimensional image deconvolution which employs subband-dependent minimization and the dual-tree complex wavelet transform in an iterative Bayesian framework. In addition, this algorithm employs a new prior instead of the popular ℓ1 norm, and is thus able to embed a learning scheme during the iteration which helps it to achieve better deconvolution results and faster convergence. © 2008 IEEE.

Image deconvolution using a Gaussian scale mixtures model to approximate the wavelet sparseness constraint

This paper proposes to use an extended Gaussian Scale Mixtures (GSM) model instead of the conventional ℓ1 norm to approximate the sparseness constraint in the wavelet domain. We combine this new constraint with subband-dependent minimization to formulate an iterative algorithm on two shift-invariant wavelet transforms, the Shannon wavelet transform and dual-tree complex wavelet transform (DTCWT). This extented GSM model introduces spatially varying information into the deconvolution process and thus enables the algorithm to achieve better results with fewer iterations in our experiments. ©2009 IEEE.

Statistical image modelling using interscale phase relationships of complex wavelet coefficients

A novel method for modelling the statistics of 2D photographic images useful in image restoration is defined. The new method is based on the Dual Tree Complex Wavelet Transform (DT-CWT) but a phase rotation is applied to the coefficients to create complex coefficients whose phase is shift-invariant at multiscale edge and ridge features. This is in addition to the magnitude shift invariance achieved by the DT-CWT. The increased correlation between coefficients adjacent in space and scale provides an improved mechanism for signal estimation. © 2006 IEEE.

Spread transform watermarking for video sources

Spread Transform (ST) is a quantization watermarking algorithm in which vectors of the wavelet coefficients of a host work are quantized, using one of two dithered quantizers, to embed hidden information bits; Loo had some success in applying such a scheme to still images. We extend ST to the video watermarking problem. Visibility considerations require that each spreading vector refer to corresponding pixels in each of several frames, that is, a multi-frame embedding approach. Use of the hierarchical complex wavelet transform (CWT) for a visual mask reduces computation and improves robustness to jitter and valumetric scaling. We present a method of recovering temporal synchronization at the detector, and give initial results demonstrating the robustness and capacity of the scheme.

Atmospheric turbulence mitigation using complex wavelet-based fusion

Restoring a scene distorted by atmospheric turbulence is a challenging problem in video surveillance. The effect, caused by random, spatially varying, perturbations, makes a model-based solution difficult and in most cases, impractical. In this paper, we propose a novel method for mitigating the effects of atmospheric distortion on observed images, particularly airborne turbulence which can severely degrade a region of interest (ROI). In order to extract accurate detail about objects behind the distorting layer, a simple and efficient frame selection method is proposed to select informative ROIs only from good-quality frames. The ROIs in each frame are then registered to further reduce offsets and distortions. We solve the space-varying distortion problem using region-level fusion based on the dual tree complex wavelet transform. Finally, contrast enhancement is applied. We further propose a learning-based metric specifically for image quality assessment in the presence of atmospheric distortion. This is capable of estimating quality in both full-and no-reference scenarios. The proposed method is shown to significantly outperform existing methods, providing enhanced situational awareness in a range of surveillance scenarios. © 1992-2012 IEEE.

Efficient registration of nonrigid 3-D bodies

We present a novel method to perform an accurate registration of 3-D nonrigid bodies by using phase-shift properties of the dual-tree complex wavelet transform (DT-CWT). Since the phases of DT-\BBCWT coefficients change approximately linearly with the amount of feature displacement in the spatial domain, motion can be estimated using the phase information from these coefficients. The motion estimation is performed iteratively: first by using coarser level complex coefficients to determine large motion components and then by employing finer level coefficients to refine the motion field. We use a parametric affine model to describe the motion, where the affine parameters are found locally by substituting into an optical flow model and by solving the resulting overdetermined set of equations. From the estimated affine parameters, the motion field between the sensed and the reference data sets can be generated, and the sensed data set then can be shifted and interpolated spatially to align with the reference data set. © 2011 IEEE.

Complex wavelets and shift invariance

Recently we have developed a new form of discrete wavelet transform, which generates complex coefficients by using a dual tree of wavelet filters to obtain their real and imaginary parts. This introduces limited redundancy (2 m:1 for m-dimensional signals) and allows the transform to provide approximate shift invariance and directionally selective filters (properties lacking in the traditional wavelet transform) while preserving the usual properties of perfect reconstruction and computational efficiency with good well-balanced frequency responses. In this paper we analyse why the new transform can be designed to be shift invariant, and describe how to estimate the accuracy of this approximation and design suitable filters to achieve this.

Robust pairwise matching of interest points with complex wavelets

We present a matching framework to find robust correspondences between image features by considering the spatial information between them. To achieve this, we define spatial constraints on the relative orientation and change in scale between pairs of features. A pairwise similarity score, which measures the similarity of features based on these spatial constraints, is considered. The pairwise similarity scores for all pairs of candidate correspondences are then accumulated in a 2-D similarity space. Robust correspondences can be found by searching for clusters in the similarity space, since actual correspondences are expected to form clusters that satisfy similar spatial constraints in this space. As it is difficult to achieve reliable and consistent estimates of scale and orientation, an additional contribution is that these parameters do not need to be determined at the interest point detection stage, which differs from conventional methods. Polar matching of dual-tree complex wavelet transform features is used, since it fits naturally into the framework with the defined spatial constraints. Our tests show that the proposed framework is capable of producing robust correspondences with higher correspondence ratios and reasonable computational efficiency, compared to other well-known algorithms. © 1992-2012 IEEE.

Flame interactions in turbulent premixed twin V-flames

Multiple flame-flame interactions in premixed combustion are investigated using direct numerical simulations of twin turbulent V-flames for a range of turbulence intensities and length scales. Interactions are identified using a novel automatic feature extraction (AFE) technique, based on data registration using the dual-tree complex wavelet transform. Information on the time, position, and type of interactions, and their influence on the flame area is extracted using AFE. Characteristic length and time scales for the interactions are identified. The effect of interactions on the flame brush is quantified through a global stretch rate, defined as the sum of flamelet stretch and interaction stretch contributions. The effects of each interaction type are discussed. It is found that the magnitude of the fluctuations in flamelet and interaction stretch are comparable, and a qualitative sensitivity to turbulence length scale is found for one interaction type. Implications for modeling are discussed. © 2013 Copyright Taylor and Francis Group, LLC.

Multiscale object features from clustered complex wavelet coefficients

This paper introduces a method by which intuitive feature entities can be created from ILP (InterLevel Product) coefficients. The ILP transform is a pyramid of decimated complex-valued coefficients at multiple scales, derived from dual-tree complex wavelets, whose phases indicate the presence of different feature types (edges and ridges). We use an Expectation-Maximization algorithm to cluster large ILP coefficients that are spatially adjacent and similar in phase. We then demonstrate the relationship that these clusters possess with respect to observable image content, and conclude with a look at potential applications of these clusters, such as rotation- and scale-invariant object recognition. © 2005 IEEE.