We give a brief review of some of the wavelet-based techniques currently available for the analysis of arbitrary-length discrete time series. We discuss the maximal overlap discrete wavelet packet transform (MODWPT), a non-decimated version of the usual discrete wavelet packet transform, and a special case, the maximal overlap discrete wavelet transform (MODWT). Using least-asymmetric or coifle...

This portion of the notes discusses how wavelet techniques may be applied to a variety of geometric modeling tools. In particular, wavelet decompositions are shown to be useful for hierarchical control point or least squares editing. In addition, direct curve and surface manipulation methods using an underlying geometric variational principle can be solved more efficiently by using a wavelet ba...

Wavelet packets are well-known for their ability to compactly represent textures consiting of oscillatory patterns such as fingerprints or striped cloth. In this paper, we report recent work on representing both periodic and granular types of texture using adaptive wavelet basis functions. The discrimination power of a wavelet packet subband can be defined as its ability to differentiate betwee...

9 Both pixel-based scale saliency (PSS) and basis project methods focus on multiscale analysis of data content and structure. Their theoretical relations and practical combination are previously discussed. However, no models have ever been proposed for calculating scale saliency on basis-projected descriptors since then. This paper extend those ideas into mathematical models and implement them ...

The efficient representation of arbitrarily shaped image segments is an important issue in objectbased image coding. This paper describes an algorithm by which the given image segment is successively approximated using 2-D shapeindependent basis functions defined on a rectangle circumscribing the image segment. Discrete cosine and discrete wavelet basis were used in the system respectively, and...

Recent wavelet research has primarily focused on real-valued wavelet bases. However, complex wavelet bases offer a number of potential advantageous properties. For example, it has been recently suggested that the complex Daubechies wavelet can be made symmetric. However, these papers always imply that if the complex basis has a symmetry property, then it must exhibit linear phase as well. In th...

The edge detection is usually used for controlling the automation of pattern recognition in intelligent machines, traffic control and mobile devices security systems. Due to the complex of image control, the dimensions are increasing so that the single wavelet is not able to address some applications, thus, high-dimensional wavelet basis is needed. This paper introduces a construction of dual w...

Detecting and recognizing face images automatically is a difficult task due to the variability of illumination, presentation angle, face expression and other common problems of machine vision. In this paper, we represent face images as combinations of 2-D Gabor wavelet basis which are non-orthogonal. Genetic Algorithm (GA) is used to find an optimal basis derived from a combination of frequenci...

For nonstationary time series the fixed Fourier basis is no longer canonical. This article shows how the choice of analysis basis influences the detection of nonstationarities within time series. Rather than limit our basis choice to wavelet or Fourier functions we develop a new stationarity test using a (multiple) bootstrap hypothesis test based on non-decimated wavelet packets. Non-decimated ...