Need Help (explaning) Bilater Mesh Smoothing / Denoising

Question

Abdullah Khan 2013-12-16

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/109862-need-help-explaning-bilater-mesh-smoothing-denoising

在 MATLAB Online 中打开

*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;