Citation Context

... u2 = arg min u∈BV (Ω) (f − u) 2 � . This minimization procedure attempts to match normals as well as grey-level values. In [29] the denoised normal �n1 was computed by using a one-harmonic map as in =-=[46]-=-: �� �n1 = arg min |�n|=1 � � |∇�n| + λ �n − ∇f � � 2 . |∇f| Unlike all the other methods discussed in this paper, this is not a convex minimization problem, and it does not produce an image u1 satisf...

Citation Context

...c formulation of the Total Variation (TV) restoration model was given in [8], Beltrami flows were proposed in [23, 34, 4], and nonlinear heat equations borrowed from harmonic theory were presented in =-=[25, 35, 43]-=-. Most of these approaches were applied in the case where the target manifold was the unit hypersphere Sn−1 . The problem of building PDEs acting on fields of orthogonal matrices was also discussed in...

Citation Context

... our algorithm. In fact, the functional for the minimization problem we solve in the second step is identical to one of the terms in the inpainting functional of [23]. Another closely related work is =-=[24]-=-. That paper deals with minimization of constrained functionals, and in particular with -harmonic maps. For a vector valued function , they proposed an elegant way of solving with Dirichlet or Neumann...

Citation Context

...lts are sufficiently accurate if the normalization is applied repeatedly between sufficiently short diffusion times [39]. More theoretically sound methods make use of the Levi-Civita connection [43], =-=[44]-=- and the metric imposed by the manifold [45], but these methods are slower than component-wise diffusion and the accuracy gain is neglectable in most cases. In addition, we want to be able to weight t...

Citation Context

...rticular flat target manifolds as the whole ���� space or as those in [37], the projection is not needed. Other authors, e.g., [8, 28], have avoided the projection step for particular cases, w=-=hile in [51]-=- the authors modify the given variational formulation, in some restricted cases, to include the projection step. 3saround. On the other hand, not all surfaces (manifolds) are originally represented in...

Citation Context

...traints there are various numerical methods introduced to accurately compute non-flat features. Some mathematical analysis on S N constraints is studied in [26], and numerical methods are explored in =-=[47]-=-. In this paper, we introduce variational colorization models which use a penalty term to deal with S 2 constraint. The penalization method simplifies the computation by avoiding the direct numerical ...

Citation Context

...Lysaker-Osher-Tai (LOT) in [11] involving a smoothing of the normal vectors ∇d0/|∇d0| in the first step, and then finding a surface to fit the smoothed normals in the second step, based on ideas from =-=[4, 2, 16]-=-. In this paper we use the same two-step approach, but we modify the first step being motivated by the observation that tangent directions to the isophote lines (lines along which the intensity is con...

Citation Context

...ence of heavy noise. Note that as in [16] the curvature-based method can include multiple directions. Various papers deal with the smoothing of normal vectors by minimizing certain energy functionals =-=[17, 18, 19, 20, 21, 22]-=- and use this information for subsequent denoising. In general these minimization procedures are much more expensive then our double direction approach. Kimmel, Sochen et al. suggested restoration tec...