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Accurate extraction of the image feature directions is essential to image smoothing and other image processing tasks. We show that the gradient-based feature direction extraction method can be very erroneous. The gradient is too local, and it cannot detect oscillations. We have developed two new methods: the Hessian method, an approach using higher order differentiations, and the Gabor (1946) method, an approach using space-frequency analysis.
Carmona et al. (1998) studied this question.