I have a point cloud made up of 37817 3D vertices (data here). For each vertex i, I compute all neighbors within 15mm (NeighborVert{i}). A sphere is fit using these neighbors through sphereFit (source code). Squared distance of each of the identified neighbor to the surface of the sphere, denoted as epsilon{i}(j), is calculated to quantify residual of each neighbor to the fitted sphere. I then sum all values within epsilon{i} across j and store the result as E(i), which measures the overall fit of the sphere for neighbors of vertex i. The above process is implemented through the MATLAB code below:

T = readtable("<path>\Vertices.xlsx", 'ReadVariableNames',false);
Vertices = table2array(T);
Vertfmt = pointCloud(Vertices);
radius = 15; 

for i = 1:size(Vertices, 1)
    [NeighborIndex{i}] = findNeighborsInRadius(Vertfmt, Vertices(i,:), radius);
    NeighborVert{i} = Vertices(NeighborIndex{i},:);
    [center(i, :), r(i)] = sphereFit(NeighborVert{i});
        for j = 1:length(NeighborIndex{i})
            epsilon{i}(j) = abs((NeighborVert{i}(j, 1) - center(i, 1))^2 + (NeighborVert{i}(j, 2) - center(i, 2))^2 + (NeighborVert{i}(j, 3) - center(i, 3))^2 - r(i)^2);
            E(i) = sum(epsilon{i}(j));
        end
end

epsilon{i} should contain multiple values because the squared distance of all neighbors of vertex i to the surface of the fitted sphere is stored. However, my result showed that each epsilon{i} contains only 1 value. How can I save all epsilon{i}(j)s within epsilon{i} during each iteration?

Besides, is my code for E(i) correctly sum across j for all epsilon{i}(j)s?

0 Answers