Thus, formula (1.1), with constant, and the constraint, constitute the constant mean curvature (CMC) spacelike graph equation in.
Only within the slight curvature of the graph can we find the information available to separate the volume diffusion resistance from the surface integration resistance.
We introduce a sub-Riemannian analogue of the Bence Merriman Osher algorithm (Merriman et al., 1992 [42]) and show that it leads to weak solutions of the horizontal mean curvature flow of graphs over sub-Riemannian Carnot groups.
We conclude this section with a corollary of the proof in [18] [Lemma 3.6], a weak Harnack inequality that plays an important role in the proof of the regularity of the mean curvature flow for graphs over certain Lie groups established in [14].
However, our method is more efficient, because our method computes the curvature of the residual graph at only one point where the residual takes a maximum in each segmented arc.
The problem operatorname{div}biggl(frac{nabla v}{sqrt{1-|nabla v|^{2}}}biggr)=H x,v quad text{in } Omega arises from the study of prescribed mean curvature of a spacelike graph in the flat Minkowski space {L}^{N+1}:=bigl{ (x,t):xinmathbb{R}^{N},tinmathbb{R} bigr} endowed with the Lorentzian metric (sum_{i=1}^{N}dx_{i}^{2}-dt^{2}) [1].
Assuming that input data is a spatially connected sequence of edge points, we segment it into partial arcs by considering the ellipse fitting residuals and detect inliers by computing the curvature of the residual graph of each of the segmented arcs.
Significantly, the additional inflection point (denoting a change in curvature) in the bias graph of Figure 1F results from model B 12 b requiring a summing of two hyperbolae rather than being represented by a single one, as is B 12 a.
Most feature recognition methods use either a cluster-based decomposition or feature line extraction through solid angles or curvature values, followed by graph-based heuristics.
Next, we compute residuals of the fitted ellipse for all input points and select elliptic arcs among the segmented arcs by checking the curvatures of the residual graph.
