A schematic overview of the presented technique is shown in Figure 5.3. Input is given by a grayscale or color image (RGB color space is used for all examples). The algorithm runs iteratively and stops after a user-deﬁned number of iterations,
controlling the strength of the abstraction. For each iteration, adaptive ﬂowguided smoothing (Figure 5.1(a)) and sharpening (Figure 5.1(b)) are performed. Both techniques require information about the local structure, which is obtained by an eigenvalue analysis of the smoothed structure tensor and computed twice for every iteration, once before the smoothing and again before the sharpening. With every iteration, the result becomes closer to a piecewise-constant image, with large smooth or even ﬂat image regions where no distinguished orientation is deﬁned. Since having valid orientations deﬁned for these regions is important for the stability of the algorithm, the structure tensor from the previous calculation is used in this case. For the ﬁrst calculation, where no result from a previous computation is available, a relaxation of the structure tensor is performed. As a ﬁnal step, edges are smoothed by ﬂow-guided smoothing with a small ﬁlter kernel (Figure 5.1(c)). In the following sections, the diﬀerent stages of the algorithm are examined in detail.