Need Help (explaning) Bilater Mesh Smoothing / Denoising

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Abdullah Khan
Abdullah Khan 2013-12-16
*Im trying to understand the Bilateral Mesh Denoising*
I have to carry on on MATLAB
I have checked out Many Toolkits developed by Matlab , I found one that good Enough
I can get the vertex and faces by the function
name = 'elephant-50kv';
options.name = name; % useful for displaying
[vertex,faces] = read_mesh(name);
This returns me the Vertex and faces also the following function provides me the Normals
[normal,normalf] = compute_normal(vertex,faces);
normal are the normal and normalf are the normals to faces
The algorithm im trying to implement is available at http://www.cs.tau.ac.il/~dcor/online_papers/papers/shachar03.pdf
The paper states the Algorithm
DenoisePoint(Vertex v, Normal n)
{qi} = neighborhood(v)
K = |{qi}|
sum = 0
normalizer = 0
for i := 1 to K
t = ||v−qi||
h =<n,v−qi>
wc = exp(−t^2/(2σc^2))
ws = exp(−h^2/(2σs^2))
sum += (wc ·ws)·h
normalizer += wc ·ws
end
return Vertex vˆ = v+n·(sum/normalizer)
Tired to do the above mentioned algo
But im not able to implement the algorithm
What is Sigma_c(σc)and Sigma_s(σs here , also cant understand h =<n,v−qi>
I wrote this code but not good enough
------------------------------------------------------------------------ clear clc
path(path, 'toolbox/');
path(path, 'off/');
clear options;
% load the mesh
name = 'elephant-50kv';
options.name = name; % useful for displaying
[vertex,faces] = read_mesh(name);
% display the mesh
clf;
plot_mesh(vertex, faces);
shading interp;
% Computing The normals for the given vertecies and faces
% compute normal per vertex and per face
[normal,normalf] = compute_normal(vertex,faces);
% Reading the number of vertices
[ dummy total_vertex]=size(vertex); % sixe vertices and Normalas are the same
% Now applying Bilateral filtering to the mesh
%Here we require a Vertex and its Neighbour , Going for all vertices for
%all removal
new_vertex_set=vertex;
for vertex_num=1:total_vertex
neighbours=[];
sum_a=[0 0 0]';
normalizer=[0 0 0]';
%finding the neighbours
input_vertex=vertex(:,vertex_num);
input_normal=normal(:,vertex_num);
sigma_c=0.4;
sigma_s=0.4;
% subracting from all vertices to see the neighbouring distance
difference=repmat(input_vertex,1,total_vertex)-vertex;
distance=abs(sum(difference)); % sum col wise in this version 2013
neighbours=find(distance < 2*sigma_c);
[dummy num_neighbours]=size(neighbours);
q_i=vertex(:,neighbours);
t=abs(repmat(input_vertex,1,num_neighbours)-q_i);
h=(repmat(input_vertex,1,num_neighbours)-q_i);
Wc=exp((-t.^2)./2*sigma_c^2);
Ws=exp(((-h.^2))./2*sigma_s^2);
sum_a=sum(((Wc.*Ws).*h)').';
normalizer=sum((Wc.*Ws)').';
new_vertex=(input_vertex+input_normal).*(sum_a./normalizer);
new_vertex_set(:,vertex_num)=new_vertex;
end % loop end for vertices
plot_mesh(new_vertex_set, faces);
shading interp;

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