Geodesic Bending Invariants with Landmarks¶
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This tour explores the use of farthest point sampling to compute bending invariant with classical MDS (strain minimization).
addpath('toolbox_signal')
addpath('toolbox_general')
addpath('toolbox_graph')
addpath('solutions/shapes_3_bendinginv_landmarks')
Farthest Points Landmarks Seeding¶
For large mesh, computing all the pairwise distances is intractable. It is possible to speed up the computation by restricting the computation to a small subset of landmarks.
This seeding strategy was used for surface remeshing in:
Geodesic Remeshing Using Front Propagation, Gabriel Peyr and Laurent Cohen, International Journal on Computer Vision, Vol. 69(1), p.145-156, Aug. 2006.
Load a mesh.
name = 'elephant-50kv';
options.name = name;
[vertex,faces] = read_mesh(name);
nverts = size(vertex,2);
Display it.
clf;
plot_mesh(vertex,faces, options);
Compute a sparse set of landmarks to speed up the geodesic computations. The landmarks are computed using farthest point sampling.
First landmarks, at random.
landmarks = 23057;
Dland = [];
Perform Fast Marching to compute the geodesic distance, and record it.
[Dland(:,end+1),S,Q] = perform_fast_marching_mesh(vertex, faces, landmarks(end));
Select farthest point. Here, |min(Dland,[],2)| is the distance to the set of seed points.
[tmp,landmarks(end+1)] = max( min(Dland,[],2) );
Update distance function.
[Dland(:,end+1),S,Q] = perform_fast_marching_mesh(vertex, faces, landmarks(end));
Display distances.
clf;
options.start_points = landmarks;
plot_fast_marching_mesh(vertex,faces, min(Dland,[],2) , [], options);