Dual-Tree Complex Wavelet Transform Sample Clauses

Dual-Tree Complex Wavelet Transform. The dual-tree complex wavelet transform (DT-CWT) has been recently used in various signal and image processing applications [10], [11], [12] and [13]. It has desirable prop- erties such as shift invariance, directional selectivity and lack of aliasing. In the dual-tree CWT, two maximally decimated discrete wavelet transforms are executed in parallel, where the wavelet functions of two different trees form an approxi- mate Xxxxxxx transform pair [14]. Two-dimensional DT-CWT A A ified angle and R is a chosen radius. Then we can perform the α θ θ introduced vector product according to (5) as follows: is also directionally selective in six different orientations. We use DT-CWT complex coefficient magnitudes in detail sub- bands as pixel features and compute codifference descriptors. α α s = I(x, y) ⊕ (I where µ is the mean of the vector. − µ ), (9) Let WR(x, y) and WIm(x, y) denote, respectively, the real and imaginary part of the 2nd level complex wavelet coef- ficient at the position (x,y) corresponding to directional detail ∈ {± ± ± } ∈ {± ± ± } subbands at orientation θ, where θ 15o, 45o, 75o . The magnitude of the complex wavelet coefficent is then Mθ, computed for θ 15o, 45o, 75o . Hence, for each pixel in the average image Ia(x, y), six complex wavelet coef- ficient magnitudes Mθ(x, y) representing six different orien- tations of DT-CWT are extracted. These magnitudes will be utilized as features in the co-difference and covariance ma- trix computation for randomly sampled regions of the image Ia(x, y).