Computational Geometry Algorithms and Applications by Berg etc

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It can also be expressed as a dual functional: TVε (u) = sup Ω u div v − χ∗ε (v) dx v → Cc1 (Γ, Rd ) , with χ∗ε (t) = ψ 1− ◦ 1 − |t| 2 for |t| < 1, else. This reduces the tendency towards piecewise constant solutions. However, as χε still grows as fast as | · |, discontinuities and consequently, the staircasing effect still appears. Such an observation can generally be made for first-order functionals penalizing the measure-valued gradient with linear growth at ◦. One approach to overcome these defects is to incorporate higher-order derivatives into the image model.

46] with ϕ = 100, T = 425. 0449. These results demonstrate the effectiveness of our method for direction diffusion, even in cases where the staircasing effect may cause unwanted artifacts. Fast Regularization of Matrix-Valued Images 33 Fig. 1. TV regularization of SO(n) data. Left-to-right, top-to-bottom: the initial estimated field for a 4-piece piecewise constant motion field, a concentric motion field, the denoised images for the piecewise constant field and the concentric motion field. Different colors mark different orientations of the initial/estimated dense field, black arrows signify the measured motion vectors, and blue arrows demonstrate the estimated field after sampling.

5. It can be seen that for a careful choice of the regularization parameter, total variation in the group elements is seen to significantly reduce rigid motion estimation errors. Furthermore, it allows us to discern the main rigidly moving parts in the sequence by producing a scale-space of rigid motions. Visualization is accomplished by projecting the embedded matrix 34 G. Rosman et al. Fig. 2. TV regularization of SO(n) data, based on the same data from Fig. 1, with a higher-order regularity term.

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