The paper discusses the theory behind the dual-tree transform, shows how complex wavelets with good properties can be designed, and illustrates a range of applications in signal and image processing The authors use the complex number symbol C in CWT to avoid confusion with the often-used acronym CWT for the (different) continuous wavelet transform The four fundamentals, intertwined shortcomings of wavelet transform and some solutions are also discussed Several methods for filter design are described for dual-tree CWT that demonstrates with relatively short filters, an effective invertible approximately analytic wavelet transform can indeed be implemented using the dual-tree approach

/pdf/the-dual-tree-complex-wavelet-transform-4kfm5jwrrq.pdf

The dual-tree complex wavelet transform

A scheme is developed for classifying the types of motion perceived by a humanlike robot. It is assumed that the robot receives visual images of the scene using a perspective system model. Equations, theorems, concepts, clues, etc., relating the objects, their positions, and their motion to their images on the focal plane are presented. >

http://ieeexplore.ieee.org/iel2/815/3148/00100651.pdf

Robot vision

/pdf/philosophical-transactions-of-the-royal-society-4zs1ii7889.pdf

Philosophical Transactions of the Royal Society

Advances in Neural Information Processing Systems 25

Intelligent vehicles and advanced driver assistance systems (ADAS) need to have proper awareness of the traffic context, as well as the driver status since ADAS share the vehicle control authorities with the human driver. This paper provides an overview of the ego-vehicle driver intention inference (DII), which mainly focuses on the lane change intention on highways. First, a human intention mechanism is discussed in the beginning to gain an overall understanding of the driver intention. Next, the ego-vehicle driver intention is classified into different categories based on various criteria. A complete DII system can be separated into different modules, which consist of traffic context awareness, driver states monitoring, and the vehicle dynamic measurement module. The relationship between these modules and the corresponding impacts on the DII are analyzed. Then, the lane change intention inference system is reviewed from the perspective of input signals, algorithms, and evaluation. Finally, future concerns and emerging trends in this area are highlighted.

/pdf/driver-lane-change-intention-inference-for-intelligent-4wcx2tetfv.pdf

Driver Lane Change Intention Inference for Intelligent Vehicles: Framework, Survey, and Challenges

It is well known that a Hilbert transform pair of wavelet bases improves the lack of translation invariance of the discrete wavelet transform. However, its shapes and improvement are limited by the difficulty in applying the Hilbert transform pair to a discrete signal. In this paper, novel Hilbert transform pairs of wavelet bases, which are based on a Meyer wavelet and have a wide range of shapes, are proposed to create perfect translation invariance, and their calculation method is designed to apply these wavelet bases to any discrete signal. Therefore, perfect translation invariance is achieved with a wide range of shapes of the Hilbert transform pairs of wavelet bases.

Perfect translation invariance with a wide range of shapes of hilbert transform pairs of wavelet bases

The useful theorems for achieving perfect translation invariance have already been proved, and based on these theorems, dual-tree complex discrete wavelet transforms with perfect translation invariance have been proposed. However, due to the complication of frequency divisions with wavelet packets, it is difficult to design complex wavelet packet transforms with perfect translation invariance. In this paper, based on the aforementioned theorems, novel complex wavelet packet transforms are designed to achieve perfect translation invariance. These complex wavelet packet transforms are based on the Meyer wavelet, which has the important characteristic of possessing a wide range of shapes. In this paper, two types of complex wavelet packet transforms are designed with the optimized Meyer wavelet. One of them is based on a single Meyer wavelet and the other is based on a number of different shapes of the Meyer wavelets to create good localization of wavelet packets.

The design of complex wavelet packet transforms based on perfect translation invariance theorems

In our first report, we have proposed a complex type wavelet, the Real-Imaginary Spline Wavelet (RI-Spline wavelet) for the continuous wavelet transform and demonstrated the advantages of our approach. In this study, we develop our RI-Spline wavelet for the Discrete Wavelet Transform (DWT) that uses a fast algorithm based on Multi-resolution analysis. The DWT has a translation variance problem, so it can not catch features of the signals exactly although it has been widely used in signal analysis. In order to overcome this translation variance problem, we first develop a Complex Discrete Wavelet Transform (CDWT) using the RI-Spline wavelet and propose the Coherent Dual-Tree algorithm for the RI-Spline wavelet without increasing the computational cost very much. Then we apply this translation invariant CDWT to translation invariant de-noising. Experimental results show that our method, when applied to ECG data and music data, can obtain better de-noising results than conventional Wavelet Shrinkage.

Nonstationary signal analysis using the RI-Spline wavelet

Nonstationary signal analysis using the RI-Spline wavelet: Second report: Complex discrete wavelet transform and its application

In this study, a novel direction selection method using the two-dimensional complex discrete wavelet transform (2D-CDWT) is proposed. In order to achieve arbitrary direction selection, the directional filters are first designed. Calculation procedure of directional selection can be shown as follows: (1) The 16 sub-images are generally generated from the original image by the 2D-CDWT without a down-sampling process and the 12 sub-images that correspond to the high-frequency components are selected. (2) The 12 sub-images are filtered by using the designed directional filter. (3) The down-sampling process is carried out and the resulting images are obtained. Furthermore, this method is applied to the surface analysis of a wafer, and it is confirmed that our method is effective in detecting irregular direction components.

Zhong Zhang

Papers

Perfect translation invariance with a wide range of shapes of hilbert transform pairs of wavelet bases

The design of complex wavelet packet transforms based on perfect translation invariance theorems

Nonstationary signal analysis using the RI-Spline wavelet

Nonstationary signal analysis using the RI-Spline wavelet: Second report: Complex discrete wavelet transform and its application

Directional selection of two-dimensional complex discrete wavelet transform and its application to image processing