Estimating local multiple orientations

In the last decades, orientation estimation has often been investigated for instance in the domain of still image analysis for feature extraction [5] or in the context of video stream processing for motion analysis [10] [20] [27]. Applications of orientation estimation vary, for example, from the enhancement of ancient engravings to the analysis of fingerprint images or seismic data [8]. Orientation relates to the direction of the apparent structures in the observed area. At a given location in an image, orientation depends on the size of the observation window, which corresponds to the scale of analysis. Statistical techniques applied to orientation vectors (as for instance PCA [8], Rao's algorithm [5][22] or the tensor-based framework proposed by Knutsson [14]) allow to compute orientations at a large scale from orientations at a local scale. Given the capabilities of such techniques, we focus specifically on local orientation estimation. Local orientation estimation is often based on the computation of local derivatives [6][7][8] [17][22], assuming that orientation is orthogonal to the gradient vector. Nevertheless, gradient based approaches rely on the unicity of orientation at a given point and are not suitable if several orientations occur at a given location. As an illustration, the texture in Fig. 1.a shows two components with different orientations, one at 20° the other one at 60°. The spatial period of both components is 10 pixels. A structure tensor with a computing support size of 55 pixels estimates the main orientation of the texture at approximately 32° (Fig. 1.b). Indeed, this Fig.1