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.

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.

A discrete wavelet transform approach to multiresolution complex SAR image generation

We present a signal processing approach using discrete wavelet transform (DWT) for the generation of complex synthetic aperture radar (SAR) images at an arbitrary number of dyadic scales of resolution. The method is computationally efficient and is free from significant system-imposed limitations present in traditional subaperture-based multiresolution image formation. Problems due to aliasing associated with biorthogonal decomposition of the complex signals are addressed. The lifting scheme of DWT is adapted to handle complex signal approximations and employed to further enhance the computational efficiency. Multiresolution SAR images formed by the proposed method are presented.

Separable and non-separable discrete wavelet transform based texture features and image classification of breast thermograms

Highly sensitive infrared cameras can produce high-resolution diagnostic images of the temperature and vascular changes of breasts. Wavelet transform based features are suitable in extracting the texture difference information of these images due to their scale-space decomposition. The objective of this study is to investigate the potential of extracted features in differentiating between breast lesions by comparing the two corresponding pectoral regions of two breast thermograms. The pectoral regions of breastsare important because near 50% of all breast cancer is located in this region. In this study, the pectoral region of the left breast is selected. Then the corresponding pectoral region of the right breast is identified. Texture features based on the first and the second sets of statistics are extracted from wavelet decomposed images of the pectoral regions of two breast thermograms. Principal component analysis is used to reduce dimension and an Adaboost classifier to evaluate classification performance. A number of different wavelet features are compared and it is shown that complex non-separable 2D discrete wavelet transform features perform better than their real separable counterparts.

Wavelet transform analysis of truncated fringe patterns in 3-D surface profilometry

Wavelet transform analysis of projected fringe pattern for phase recovery in 3-D shape measurement of objects is investigated. The present communication specifically outlines and evaluates the errors that creep in to the reconstructed profiles when fringe images do not satisfy periodicity. Three specific cases that give raise to non-periodicity of fringe image are simulated and leakage effects caused by each one of them are analyzed with continuous complex Morlet wavelet transform. Same images are analyzed with FFT method to make a comparison of the reconstructed profiles with both methods. Simulation results revealed a significant advantage of wavelet transform profilometry (WTP), that the distortions that arise due to leakage are confined to the locations of discontinuity and do not spread out over the entire projection as in the case of Fourier transform profilometry (FTP).

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.

Spatial covariation of Azotobacter abundance and soil properties: A case study using the wavelet transform

The soil microflora is very heterogeneous in its spatial distribution. The origins of this heterogeneity and its significance for soil function are not well understood. A problem for understanding spatial variation better is the assumption of statistical stationarity that is made in most of the statistical methods used to assess it. These assumptions are made explicit in geostatistical methods that have been increasingly used by soil biologists in recent years. Geostatistical methods are powerful, particularly for local prediction, but they require the assumption that the variability of a property of interest is spatially uniform, which is not always plausible given what is known about the complexity of the soil microflora and the soil environment. We have used the wavelet transform, a relatively new innovation in mathematical analysis, to investigate the spatial variation of abundance of Azotobacter in the soil of a typical agricultural landscape. The wavelet transform entails no assumptions of stationarity and is well suited to the analysis of variables that show intermittent or transient features at different spatial scales. In this study, we computed cross-variograms of Azotobacter abundance with the pH, water content and loss on ignition of the soil. These revealed scale-dependent covariation in all cases. The wavelet transform also showed that the correlation of Azotobacter abundance with all three soil properties depended on spatial scale, the correlation generally increased with spatial scale and was only significantly different from zero at some scales. However, the wavelet analysis also allowed us to show how the correlation changed across the landscape. For example, at one scale Azotobacter abundance was strongly correlated with pH in part of the transect, and not with soil water content, but this was reversed elsewhere on the transect. The results show how scale-dependent variation of potentially limiting environmental factors can induce a complex spatial pattern of abundance in a soil organism. The geostatistical methods that we used here make assumptions that are not consistent with the spatial changes in the covariation of these properties that our wavelet analysis has shown. This suggests that the wavelet transform is a powerful tool for future investigation of the spatial structure and function of soil biota. (c) 2006 Elsevier Ltd. All rights reserved.

Fingerprint analysis using wavelet transform with application to compression and feature extraction

The main goal of this research is to design an efficient compression al~ gorithm for fingerprint images. The wavelet transform technique is the principal tool used to reduce interpixel redundancies and to obtain a parsimonious representation for these images. A specific fixed decomposition structure is designed to be used by the wavelet packet in order to save on the computation, transmission, and storage costs. This decomposition structure is based on analysis of information packing performance of several decompositions, two-dimensional power spectral density, effect of each frequency band on the reconstructed image, and the human visual sensitivities. This fixed structure is found to provide the "most" suitable representation for fingerprints, according to the chosen criteria. Different compression techniques are used for different subbands, based on their observed statistics. The decision is based on the effect of each subband on the reconstructed image according to the mean square criteria as well as the sensitivities in human vision. To design an efficient quantization algorithm, a precise model for distribution of the wavelet coefficients is developed. The model is based on the generalized Gaussian distribution. A least squares algorithm on a nonlinear function of the distribution model shape parameter is formulated to estimate the model parameters. A noise shaping bit allocation procedure is then used to assign the bit rate among subbands. To obtain high compression ratios, vector quantization is used. In this work, the lattice vector quantization (LVQ) is chosen because of its superior performance over other types of vector quantizers. The structure of a lattice quantizer is determined by its parameters known as truncation level and scaling factor. In lattice-based compression algorithms reported in the literature the lattice structure is commonly predetermined leading to a nonoptimized quantization approach. In this research, a new technique for determining the lattice parameters is proposed. In the lattice structure design, no assumption about the lattice parameters is made and no training and multi-quantizing is required. The design is based on minimizing the quantization distortion by adapting to the statistical characteristics of the source in each subimage. 11 Abstract Abstract Since LVQ is a multidimensional generalization of uniform quantizers, it produces minimum distortion for inputs with uniform distributions. In order to take advantage of the properties of LVQ and its fast implementation, while considering the i.i.d. nonuniform distribution of wavelet coefficients, the piecewise-uniform pyramid LVQ algorithm is proposed. The proposed algorithm quantizes almost all of source vectors without the need to project these on the lattice outermost shell, while it properly maintains a small codebook size. It also resolves the wedge region problem commonly encountered with sharply distributed random sources. These represent some of the drawbacks of the algorithm proposed by Barlaud [26). The proposed algorithm handles all types of lattices, not only the cubic lattices, as opposed to the algorithms developed by Fischer [29) and Jeong [42). Furthermore, no training and multiquantizing (to determine lattice parameters) is required, as opposed to Powell's algorithm [78). For coefficients with high-frequency content, the positive-negative mean algorithm is proposed to improve the resolution of reconstructed images. For coefficients with low-frequency content, a lossless predictive compression scheme is used to preserve the quality of reconstructed images. A method to reduce bit requirements of necessary side information is also introduced. Lossless entropy coding techniques are subsequently used to remove coding redundancy. The algorithms result in high quality reconstructed images with better compression ratios than other available algorithms. To evaluate the proposed algorithms their objective and subjective performance comparisons with other available techniques are presented. The quality of the reconstructed images is important for a reliable identification. Enhancement and feature extraction on the reconstructed images are also investigated in this research. A structural-based feature extraction algorithm is proposed in which the unique properties of fingerprint textures are used to enhance the images and improve the fidelity of their characteristic features. The ridges are extracted from enhanced grey-level foreground areas based on the local ridge dominant directions. The proposed ridge extraction algorithm, properly preserves the natural shape of grey-level ridges as well as precise locations of the features, as opposed to the ridge extraction algorithm in [81). Furthermore, it is fast and operates only on foreground regions, as opposed to the adaptive floating average thresholding process in [68). Spurious features are subsequently eliminated using the proposed post-processing scheme.