Accurate detection of edge orientation for color and multi-spectral imagery

The frequency domain properties of an image are used for precise detection of edge orientation in color and multi-spectral imagery. The orientation estimation is established as a minimization problem, formulated as a tensor method, and simplified by solving its dual in terms of spatial partial derivatives of the image. First, the spectral density distribution around each pixel is obtained. The edge orientation is determined by fitting a straight line to this distribution. A matching error is devised in tensor form, and minimized by rotating the frequency domain principal axes. The orientation is computed from the spatial derivatives by transposing frequency domain operations to the spatial domain. The estimated edge orientations and magnitudes for different bands are converted to vectors and summed in the vector domain. A comparison of this method with the widely used estimators shows that the adapted tensor method improves the estimation precision even in the presence of extreme noise.