On Total Variation Minimization and Surface Evolution Using Parametric Maximum Flows

Abstract

In a recent paper Boykov et al. (LNCS, Vol. 3953, pp. 409-422, 2006) propose an approach for computing curve and surface evolution using a variational approach and the geo-cuts method of Boykov and Kolmogorov (International conference on computer vision, pp. [26][27][28][29][30][31][32][33] 2003). We recall in this paper how this is related to well-known approaches for mean curvature motion, introduced by Alm-

An Introduction to Total Variation for Image Analysis

“…We will not describe this approach in these notes, and refer to [23], and the references therein, for details.…”

“…Table 1 gives an overview of the algorithms and parameter settings we used in our performance evaluation. All algorithms were implemented in pure Matlab, except for the graph-cut algorithm, whose main routine was implemented in optimized C/C++ (see [23] for more details). In addition, we implemented an parallel shows the clean and noisy input images and the second row shows results for different values of the regularization parameter λ.…”

Continuous limits of discrete perimeters

“…Clearly it inherits the nonlocal and anisotropic features of the discrete perimeter. We show that the Γ-limit in the L 1 -topology is given by the anisotropic total variation 6) where u belongs to the space BV (Ω) of functions of bounded variation (see Sect. 2), Du/|Du| ∈ S N −1 denoting the Radon-Nikodym derivative of Du with respect to its total variation |Du|.…”

Segmentation with Non-linear Regional Constraints via Line-Search Cuts

“…Section 3.1 reviews standard line-search techniques [17]. Section 3.2 shows how a global linesearch for energy (2) can be approximated by minimizing a Lagrangian of (2) using efficient parametric max-flow techniques [15,16]. At each iteration, our Lagrangian uses a linear approximation of R(S) detailed in Section 3.3.…”

“…1(b). Since Lagrangian (13) has only linear and quadratic submodular terms, all solutions S(t) can be efficiently explored by parametric max-flow methods [15,16]. Our global line-search selects the best solution S * with respect to original energy E in (2); see Fig.…”