2D phase-independent local features for texture segmentation

For many image processing tasks, the wavelet transform is used to represent an image by oriented spatial-frequency (scale-space) channels in which some properties of the image are better represented than in image space. The spatial behaviour in each channel, and the relationships between the channels are critically important for subsequent processing. In this paper, a 2D local energy and phase representation of a wavelet transform is presented. Based on this representation, we note that in general a wavelet transform is coupled with the phase component of the analysing wavelet associated with that scale and orientation. Consequently, commonly used features, such as squaring, and half- or full-wave rectification of a wavelet transform also depend on this phase component which not only causes unnecessary spatial variation of features at each scale but also makes it more difficult to associate features meaningfully across scales. Instead, the 2D local energy of a wavelet transform is proposed as a local feature for image texture segmentation. The advantages of using this local energy feature are that the feature is not only immune to spatial variations caused by the phase component of the analysing wavelet but can be related from one scale to another. The success of the approach is demonstrated by experimental results for both real Infrared Line Scan (IRLS) aerial images and Brodatz images.