机载LiDAR点云滤波-SMRF简单形态学滤波（MATLAB代码）.zip

function B=inpaint_nans(A,method) % INPAINT_NANS: in-paints over nans in an array % usage: B=INPAINT_NANS(A) % default method % usage: B=INPAINT_NANS(A,method) % specify method used % % Solves approximation to one of several pdes to % interpolate and extrapolate holes in an array % % arguments (input): % A - nxm array with some NaNs to be filled in % % method - (OPTIONAL) scalar numeric flag - specifies % which approach (or physical metaphor to use % for the interpolation.) All methods are capable % of extrapolation, some are better than others. % There are also speed differences, as well as % accuracy differences for smooth surfaces. % % methods {0,1,2} use a simple plate metaphor. % method 3 uses a better plate equation, % but may be much slower and uses % more memory. % method 4 uses a spring metaphor. % method 5 is an 8 neighbor average, with no % rationale behind it compared to the % other methods. I do not recommend % its use. % % method == 0 --> (DEFAULT) see method 1, but % this method does not build as large of a % linear system in the case of only a few % NaNs in a large array. % Extrapolation behavior is linear. % % method == 1 --> simple approach, applies del^2 % over the entire array, then drops those parts % of the array which do not have any contact with % NaNs. Uses a least squares approach, but it % does not modify known values. % In the case of small arrays, this method is % quite fast as it does very little extra work. % Extrapolation behavior is linear. % % method == 2 --> uses del^2, but solving a direct % linear system of equations for nan elements. % This method will be the fastest possible for % large systems since it uses the sparsest % possible system of equations. Not a least % squares approach, so it may be least robust % to noise on the boundaries of any holes. % This method will also be least able to % interpolate accurately for smooth surfaces. % Extrapolation behavior is linear. % % method == 3 --+ See method 0, but uses del^4 for % the interpolating operator. This may result % in more accurate interpolations, at some cost % in speed. % % method == 4 --+ Uses a spring metaphor. Assumes % springs (with a nominal length of zero) % connect each node with every neighbor % (horizontally, vertically and diagonally) % Since each node tries to be like its neighbors, % extrapolation is as a constant function where % this is consistent with the neighboring nodes. % % method == 5 --+ See method 2, but use an average % of the 8 nearest neighbors to any element. % This method is NOT recommended for use. % % % arguments (output): % B - nxm array with NaNs replaced % % % Example: % [x,y] = meshgrid(0:.01:1); % z0 = exp(x+y); % znan = z0; % znan(20:50,40:70) = NaN; % znan(30:90,5:10) = NaN; % znan(70:75,40:90) = NaN; % % z = inpaint_nans(znan); % % % See also: griddata, interp1 % % Author: John D'Errico % e-mail address: woodchips@rochester.rr.com % Release: 2 % Release date: 4/15/06 % I always need to know which elements are NaN, % and what size the array is for any method [n,m]=size(A); A=A(:); nm=n*m; k=isnan(A(:)); % list the nodes which are known, and which will % be interpolated nan_list=find(k); known_list=find(~k); % how many nans overall nan_count=length(nan_list); % convert NaN indices to (r,c) form % nan_list==find(k) are the unrolled (linear) indices % (row,column) form [nr,nc]=ind2sub([n,m],nan_list); % both forms of index in one array: % column 1 == unrolled index % column 2 == row index % column 3 == column index nan_list=[nan_list,nr,nc]; % supply default method if (nargin<2) || isempty(method) method = 0; elseif ~ismember(method,0:5) error 'If supplied, method must be one of: {0,1,2,3,4,5}.' end % for different methods switch method case 0 % The same as method == 1, except only work on those % elements which are NaN, or at least touch a NaN. % horizontal and vertical neighbors only talks_to = [-1 0;0 -1;1 0;0 1]; neighbors_list=identify_neighbors(n,m,nan_list,talks_to); % list of all nodes we have identified all_list=[nan_list;neighbors_list]; % generate sparse array with second partials on row % variable for each element in either list, but only % for those nodes which have a row index > 1 or < n L = find((all_list(:,2) > 1) & (all_list(:,2) < n)); nl=length(L); if nl>0 fda=sparse(repmat(all_list(L,1),1,3), ... repmat(all_list(L,1),1,3)+repmat([-1 0 1],nl,1), ... repmat([1 -2 1],nl,1),nm,nm); else fda=spalloc(n*m,n*m,size(all_list,1)*5); end % 2nd partials on column index L = find((all_list(:,3) > 1) & (all_list(:,3) < m)); nl=length(L); if nl>0 fda=fda+sparse(repmat(all_list(L,1),1,3), ... repmat(all_list(L,1),1,3)+repmat([-n 0 n],nl,1), ... repmat([1 -2 1],nl,1),nm,nm); end % eliminate knowns rhs=-fda(:,known_list)*A(known_list); k=find(any(fda(:,nan_list(:,1)),2)); % and solve... B=A; B(nan_list(:,1))=fda(k,nan_list(:,1))\rhs(k); case 1 % least squares approach with del^2. Build system % for every array element as an unknown, and then % eliminate those which are knowns. % Build sparse matrix approximating del^2 for % every element in A. % Compute finite difference for second partials % on row variable first [i,j]=ndgrid(2:(n-1),1:m); ind=i(:)+(j(:)-1)*n; np=(n-2)*m; fda=sparse(repmat(ind,1,3),[ind-1,ind,ind+1], ... repmat([1 -2 1],np,1),n*m,n*m); % now second partials on column variable [i,j]=ndgrid(1:n,2:(m-1)); ind=i(:)+(j(:)-1)*n; np=n*(m-2); fda=fda+sparse(repmat(ind,1,3),[ind-n,ind,ind+n], ... repmat([1 -2 1],np,1),nm,nm); % eliminate knowns rhs=-fda(:,known_list)*A(known_list); k=find(any(fda(:,nan_list),2)); % and solve... B=A; B(nan_list(:,1))=fda(k,nan_list(:,1))\rhs(k); case 2 % Direct solve for del^2 BVP across holes % generate sparse array with second partials on row % variable for each nan element, only for those nodes % which have a row index > 1 or < n L = find((nan_list(:,2) > 1) & (nan_list(:,2) < n)); nl=length(L); if nl>0 fda=sparse(repmat(nan_list(L,1),1,3), ... repmat(nan_list(L,1),1,3)+repmat([-1 0 1],nl,1), ... repmat([1 -2 1],nl,1),n*m,n*m); else fda=spalloc(n*m,n*m,size(nan_list,1)*5); end % 2nd partials on column index L = find((nan_list(:,3) > 1) & (nan_list(:,3) < m)); nl=length(L); if nl>0 fda=fda+sparse(repmat(nan_list(L,1),1,3), ... repmat(nan_list(L,1),1,3)+repmat([-n 0 n],nl,1), ... repmat([1 -2 1],nl,1),n*m,n*m); end % fix boundary conditions at extreme corners % of the array in case there were nans there if ismember(1,nan_list(:,1)) fda(1,[1 2 n+1])=[-2 1 1]; end if ismember(n,nan_list(:,1)) fda(n,[n, n-1,n+n])=[-2 1 1]; end if ismember(nm-n+1,nan_list(:,1)) fda(nm-n+1,[nm-n+1,nm-n+2,nm-n])=[-2 1 1]; end if ismember(nm,nan_list(:,1)) fda(nm,[nm,nm-1,nm-n])=[-2 1 1]; end % eliminate knowns rhs=-fda(:,known_list)*A(known_list); % and solve... B=A; k=nan_list(:,1); B(k)=fda(k,k)\rhs(k); case 3 % The same as method == 0, except uses del^4 as the % interpolating operator. % del^4 template of neighbors talks_to = [-2 0;-1 -1;-1 0;-1 1;0 -2;0 -1; ... 0 1;0 2;1 -1;1 0;1 1;2 0]; neighbors_list=identify_neighbors(n,m,nan_list,talks_to); % list of all nodes we have identified all_list=[nan_list;neighbors_list]; % generate sparse array with del^4, but only % for thos