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.

Biologically-inspired object recognition system with features from complex wavelets

In this paper, a novel cortex-inspired feed-forward hierarchical object recognition system based on complex wavelets is proposed and tested. Complex wavelets contain three key properties for object representation: shift invariance, which enables the extraction of stable local features; good directional selectivity, which simplifies the determination of image orientations; and limited redundancy, which allows for efficient signal analysis using the multi-resolution decomposition offered by complex wavelets. In this paper, we propose a complete cortex-inspired object recognition system based on complex wavelets. We find that the implementation of the HMAX model for object recognition in [1, 2] is rather over-complete and includes too much redundant information and processing. We have optimized the structure of the model to make it more efficient. Specifically, we have used the Caltech 5 standard dataset to compare with Serre's model in [2] (which employs Gabor filter bands). Results demonstrate that the complex wavelet model achieves a speed improvement of about 4 times over the Serre model and gives comparable recognition performance. © 2011 IEEE.

Monitoring offshore pipelines using forced transverse vibration: Data analysis

Vibration methods are used to identify faults, such as spanning and loss of cover, in long off-shore pipelines. A pipeline `pig', propelled by fluid flow, generates transverse vibration in the pipeline and the measured vibration amplitude reflects the nature of the support condition. Large quantities of vibration data are collected and analyzed by Fourier and wavelet methods.

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.

Multiply conditioned analyses of stratification in highly swirling methane/air flames

The effects of stratification on a series of highly swirling turbulent flames under globally lean conditions (φg=0.75) are investigated using a new high-spatial resolution multi-scalar dataset. This dataset features two key properties: high spatial resolution which approaches the 60 micron optical limit of the measurement system, and a wavelet oversampling methodology which significantly reduces the influence of noise. Furthermore, the very large number of realizations (30,000) acquired in the stratified cases permits statistically significant results to be obtained even after aggressive conditioning is applied. Data are doubly conditioned on equivalence ratio and the degree of stratification across the flame in each instantaneous realization. The influence of stoichiometry is limited by conditioning on the equivalence ratio at the location of peak CO mass fraction, which is shown to be a good surrogate for the location of peak heat release rate, while the stratification is quantified using a linear gradient in equivalence ratio across the instantaneous flame front. This advanced conditioning enables robust comparisons with the baseline lean premixed flame. Species mass fractions of both carbon monoxide and hydrogen are increased in temperature space under stratified conditions. Stratification is also shown to significantly increase thermal gradients, yet the derived three-dimensional flame surface density is shown to be relatively insensitive to stratification. Whilst the presence of instantaneous stratification broadens the curvature distribution relative to the premixed case, the degree of broadening is not significantly influenced by the range of global stratification ratios examined in this study. © 2012 The Combustion Institute.

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.

Improved bounds for subband-adaptive iterative shrinkage/thresholding algorithms.

This paper presents new methods for computing the step sizes of the subband-adaptive iterative shrinkage-thresholding algorithms proposed by Bayram & Selesnick and Vonesch & Unser. The method yields tighter wavelet-domain bounds of the system matrix, thus leading to improved convergence speeds. It is directly applicable to non-redundant wavelet bases, and we also adapt it for cases of redundant frames. It turns out that the simplest and most intuitive setting for the step sizes that ignores subband aliasing is often satisfactory in practice. We show that our methods can be used to advantage with reweighted least squares penalty functions as well as L1 penalties. We emphasize that the algorithms presented here are suitable for performing inverse filtering on very large datasets, including 3D data, since inversions are applied only to diagonal matrices and fast transforms are used to achieve all matrix-vector products.

Exploring the use of sensors to measure behavioral interactions: an experimental evaluation of using hand trajectories.

Humans appear to be sensitive to relative small changes in their surroundings. These changes are often initially perceived as irrelevant, but they can cause significant changes in behavior. However, how exactly people's behavior changes is often hard to quantify. A reliable and valid tool is needed in order to address such a question, ideally measuring an important point of interaction, such as the hand. Wearable-body-sensor systems can be used to obtain valuable, behavioral information. These systems are particularly useful for assessing functional interactions that occur between the endpoints of the upper limbs and our surroundings. A new method is explored that consists of computing hand position using a wearable sensor system and validating it against a gold standard reference measurement (optical tracking device). Initial outcomes related well to the gold standard measurements (r = 0.81) showing an acceptable average root mean square error of 0.09 meters. Subsequently, the use of this approach was further investigated by measuring differences in motor behavior, in response to a changing environment. Three subjects were asked to perform a water pouring task with three slightly different containers. Wavelet analysis was introduced to assess how motor consistency was affected by these small environmental changes. Results showed that the behavioral motor adjustments to a variable environment could be assessed by applying wavelet coherence techniques. Applying these procedures in everyday life, combined with correct research methodologies, can assist in quantifying how environmental changes can cause alterations in our motor behavior.

Sparse recovery of complex phase-encoded velocity images using iterative thresholding

In this paper we propose a new algorithm for reconstructing phase-encoded velocity images of catalytic reactors from undersampled NMR acquisitions. Previous work on this application has employed total variation and nonlinear conjugate gradients which, although promising, yields unsatisfactory, unphysical visual results. Our approach leverages prior knowledge about the piecewise-smoothness of the phase map and physical constraints imposed by the system under study. We show how iteratively regularizing the real and imaginary parts of the acquired complex image separately in a shift-invariant wavelet domain works to produce a piecewise-smooth velocity map, in general. Using appropriately defined metrics we demonstrate higher fidelity to the ground truth and physical system constraints than previous methods for this specific application. © 2013 IEEE.

基于Gabor小波的着色及纹理合成算法

着色和纹理合成是图形图像中的两类基本研究课题。前者需根据用户定义的彩色笔触信息，自动对黑白照片、电影或者漫画染上颜色；后者则需根据用户输入的样本纹理，经计算得出与样本纹理视觉上近似的结果纹理。这两类课题都有广泛的应用背景。如着色常常用于给经典的黑白电影或者照片自动上色，解决现在的染色工序中存在的需要大量人工交互的难题；而纹理合成常用于电影和电子游戏的地形地貌、织物、头发等等纹理的自动生成。 这两大类问题都需要分析纹理特征，并且依赖于分析结果的准确性。Gabor小波滤波器与人眼的视觉感受野相当吻合，用它来分析纹理得到的结果比较精确。鉴于此，本文把Gabor小波应用到了着色问题和纹理合成中。对于着色问题，本文用基于Gabor小波的特征向量重新定义邻居关系，然后用最优化方法迭代地对照片和卡通染色。相比以往的算法，本算法具有用户交互少、效果好、算法简单稳健的优点，并且算法允许用户逐步地添加色彩细节。对于纹理合成，本文用基于Gabor小波的特征向量来预计算K-Coherence候选集，提高了K-Coherence算法的准确性，从而改进了纹理合成的最终效果。 本文提出的算法是天然并行的，因而可利用GPU加速，做到实时计算。

基于Gabor小波特征确认多媒体消息数字水印版权标识

为解决基于数字水印的无线多媒体消息版权管理系统对提取后水印标识的自动识别问题,在充分考虑多媒体消息在传播中可能遭受攻击的基础上,提出一种基于Gabor小波特征的标识确认方案.该方案利用这类小波函数确定的滤波器适合局部分析和多方向多尺度分析的特点,提取与水印版权标识结构信息相关的统计量,形成特征集向量,通过特征集的距离比较,在小尺寸水印质量退化情况下,实现了对水印标识的识别.分析和实验表明,该方案能够满足无线多媒体消息版权管理的需求,并且在文中分析的情况下,设备的自动识别精度可以达到95%以上,较好地支持了对无线多媒体消息的版权管理.

一种高效的数字笔迹多维数据编码算法

提出了一种高效的数字笔迹数据编码算法IWPHSP(integer wavelet packet based hierarchical set partitioned).该算法通过引入整数小波包变换、层次性集合分裂、重要位组合编码和快速自适应算术编码等方法,无损地压缩了数字笔迹多维数据.实验证明,提出的IWPHSP算法是高效的.