Is it possible numerical problem ?

I'm sorry to post long code here. But I just can't find the problem...

I tried to boost my code efficiency by removing for loop, but it came out two different results from them...

I check the first point's variable d_d, d_n, w_d, w_n in first loop. All them are the same but became different in variable sum_den

61.330229160510050 and 61.330229160510020.....That's so weired. Is it possible the numerical errors?

The input of the former one is 3D points location, neighbors for each point (num_pt*num_neighbor*3), and normal vector for each points.

for i = 1:num_pt
    p_nn(i,:,:) = p(knn(i,2:end),:);
end
function [p] = BilateralFilter(p,p_nn,normal)

min_z = min(p(:,3));
maxdepth = max(p(:,3)) - min_z;

sigma_n = 0.5;
sigma_d = 0.01 + 0.5*(p(:,3) - min_z)/maxdepth; 

p_permute = permute(p, [1 3 2]); 
n_permute = permute(normal, [1 3 2]);

d_d = sqrt(sum((p_permute - p_nn).^2,3));
d_n = abs(sum((p_nn - p_permute).*n_permute,3));

w_d = exp(-d_d.^2./2./sigma_d.^2); 
w_n = exp(-d_n.^2./2./sigma_n.^2);

residual = sum((p_nn - p_permute).*n_permute,3);
sum_num = sum(w_d.*w_n.*residaul,2);
sum_den = sum(w_d.*w_n,2);
del_p = sum_num./sum_den;
p = p + del_p.*normal;

The latter one is 3D points location, index of neighbors for each point (num_pt*num_neighbor), and normal vector for each points.

function [p] = BilateralFilter(p,knn,normal)

num_pt = size(p,1);
del_p = zeros(num_pt,1);
min_z = min(p(:,3));
maxdepth = max(p(:,3)) - min_z;

for i = 1:num_pt

    idx_nn = knn(i,2:end); 
    p_nn = p(idx_nn,:); 

    sigma_n = 0.5;
    sigma_d = 0.01 + 0.5*(p(i,3)-min_z)/maxdepth;
    d_d = abs(sqrt(sum((p(i,:)-p_nn).*(p(i,:)-p_nn),2)));
    d_n = abs(sum((p_nn-p(i,:)).*normal(i,:),2));

    w_d = exp(-d_d.^2./2./sigma_d^2);
    w_n = exp(-d_n.^2./2./sigma_n^2); 

    residual = sum((p_nn-p(i,:)).*normal(i,:),2);
    sum_num = sum(w_d.*w_n.*residaul);
    sum_den = sum(w_d.*w_n);

    del_p(i) = sum_num/sum_den;

end
p = p + del_p.*normal;

Answer 1

[Askic V]

This is called a round-off error caused by floating point arithmetic.

Please read this (it is for Python, but equally applicable):

https://pythonnumericalmethods.berkeley.edu/notebooks/chapter09.03-Roundoff-Errors.html

[AI-CHI Chang]

@Askic V Thank you for this information! However, can round-off errors cause significant differences ?( The website run 1000 times ) I ran the iterations only five times, and they all looked completely different.

[Askic V]

Please check whther this might be helpful:

https://www.mathworks.com/help/symbolic/vpa.html?searchHighlight=vpa&s_tid=srchtitle_vpa_1