Algorithm 1. MATLAB pseudocode to calculate the rigid transformation between two 3D scanning systems from a pair of 3D checkerboard captures.

Pc2   %point cloud from capture of 3Dcb from system 2 pc1_ref %point cloud from system 1 (reference coordinate system) function Checkerboards3d_estimateT(pc2, pc1_ref)  % remove background  pc2_noBackground = abs(pc2-distEstimation) <= eps  pc1_noBackground = abs(pc1_ref-distEstimation) <= eps  for pc = pc2_noBackground, pc1_noBackground do   % fit plane, do PCA to transform from 3D into 2D   planeModel = pcfitplane(pc)   [pcaPlane,coeff,mu] = pca(planeModel)   % create regular binary grid   for [x,y] = min(pcaPlane):resolution:max(pcaPlane)    point_nn = findNearestNeighbors(pcaPlane, [x,y], 1)    if abs(point_nn-[x,y])>resolution     zGrid(x,y) = 1    end if   end for   % detect connected components (holes)   CC = bwconncomp(zGrid)   % calculate median coordinates of holes, sort them and   % use inverse PCA to transform back into 3D   Median_cc = median(CC)   holeMedians = sort(Median_cc)   holeMedians3D = holeMedians * transpose(coeff) + mu  end for  % estimate the geometric transformation between hole medians from both checkerboards  tFormEst = estimateGeometricTransform3D(holeMedians3D_2, holeMedians3D_1,’rigid’)  return tFormEst end function