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In this table, ℓ v) denotes the label of vertex v and the obtained edges and labels refer to Fig. 15, which shows the result up through (mathcal {G}_{7}), which is not the root of the tree.

Once these transformed weights are obtained, edges are added to the network in order of non-increasing weight until a stopping criterion (such as a specific number of edges) is met.

We obtain edge and circuit conditions, then propose a conjecture for the graph to be forest.

The first's modes contain higher frequencies that correspond to image transitions; based on this EMD property we will use the first's modes to obtain edge information.

Atabany et al. developed a robust scene edge enhancement algorithm that focused on efficiently blurring the original image with anisotropic smoothing to obtain edge enhancement of only the major image edge boundaries while effectively ignoring minor detail edge occurrences [14].

Differently from [1] we consider here the Sobel operator [8] for edge detection, since this is one of the most used methodologies to obtain edge information due to its simplicity and efficiency.

The methods we use to obtain edge scores are described below; many of these methods have been previously published, and software to compute these scores is freely available.

A straight forward approach would be to use a trained texture descriptor to obtain edge probabilities.

Model averaging of these was then performed to obtain edge confidence scores.

The length of forest field edges is also computed and divided by the buffer surface to obtain edge density (in km/km).

We obtain edge set E ^ by stitching node neighborhoods as prescribed by Equation (5), where we define the neighborhood of node s as N ^ (s ) = { t ∈ V ∖ { s } : u s T W T W u t ≠ 0 }.

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