**2.4 Compression and matching**

452 Advances in Wavelet Theory and Their Applications in Engineering, Physics and Technology

property of wavelets that makes this possible is that translations of an image result in phase changes for the wavelet coefficients. By measuring the phase changes it is possible to infer the motion of the image. A major obstacle in motion estimation is that the reliability of motion estimates depends on image content. For example, it is easy to detect the motion of a single dot in an image, but it is much harder to detect the motion of a white piece of paper on a white background. Magarey developed a method for incorporating the varying degrees of confidence in the different estimates. In tests on synthetic sequences the optimised CDWT-based algorithm showed superior accuracy under simple perturbations such as additive noise and intensity scaling between frames. In addition, the efficiency of the CDWT structure minimises the usual disadvantage of phase-based schemes– their computational complexity. Detailed analysis showed that the number of floating point operations required is comparable to or even less than that of

Efficient texture representation is important for content based retrieval of image data(Lopez &Cumplido 2004). The idea is to compute a small set of texture-describing features for each image in a database in order to allow a search of the database for images containing a certain texture. The DT-CWT has been found to be useful for classification by number of authors.Each uses the DT-CWT in different ways to compute texture features for an entire

1. De Rivaz and Kingsbury compute features given by the logarithm of the energy in each

2. Hill, Bull, and Canagarajah compute the energies of the subbands at each scale. However, in order to produce rotationally invariant texture features, they use features based on either the Fourier transform or the auto-correlation of the 6 energies at each

3. Hatipoglu, Mitra, and Kingsbury use features of the mean and standard deviations of complex wavelet subbands. However, instead of using the DT-CWT based on a fixed tree structure, they use an adaptive decomposition that continues to decompose

In many signal or image processing applications, the input data is corrupted by some noise which need to be removed or at least reduced. Wavelet denoising techniques work by adjusting the wavelet coefficients of the signal in such a way that the noise is reduced while the signal is preserved (Sivakumar,2007). There are many different methods for adjusting the coefficients but the basic principle is to keep large coefficients while reducing small coefficients. This adjustment is known as thresholding the coefficients.One rationale for this approach is that often real signals can be represented by a few large wavelet coefficients, while (for standard orthogonal wavelet transforms) white noise signals are represented by white noise of the same variance in the wavelet coefficients. Therefore the reconstruction of the signal from just the large coefficients will tend to contain most of the signal energy but little of the noise energy. An alternative rationale comes from considering the signal as being piecewise stationary. For each piece the

subbands with energy greater than a given threshold (Nabil, 2009).

standard intensity-based hierarchical algorithms.

**2.2 Classification** 

subband.

scale.

**2.3 Denoising** 

image:

Compression algorithms with wavelet-based transformations were selected in competition with compression using fractal transformations. FBI's standard has similarities with the JPEG2000 standard, and especially with an extension to the JPEG2000 standard. Further decomposition of the LH-, HL- and HH-bands like this may improve compression somewhat, since the effect of the filter bank application may be thought of as an "approximative orthonormalization process". The extension to the JPEG2000 standard also opens up for this type of more general subband decompositions. In FBI's standard different wavelets can be used, with the coefficients of the corresponding filter banks signalled in the code-stream. The only constraint on the filters is that there should be no more than 32 nonzero coefficients. This is much longer than lossy compression in JPEG2000 (9 nonzero coefficients).
