energyLineSegment.m

function [ sparse_line ] = energyLineSegment( img, lines, slope_lines, init_H, C1, C2 )
% given detected line segments, calculate a sparse matrix to preserving
% line struture in image
num_V = (C1+1)*(C2+1);  % number of control vertices

X_col = linspace(1,size(img,2),C2+1); % column index of cells
Y_row = linspace(1,size(img,1),C1+1); % row index of cells
x_dis = X_col(2)-X_col(1);  % the width of scale-cell
y_dis = Y_row(2)-Y_row(1);  % the height of scale-cell

Mesh_ps = zeros(4,2); Mesh_pe = zeros(4,2);
% the three indices the sparse function needs
row_sp = sum(lines(1:2:end-1,end)-1);
sp_i = zeros(16*row_sp,1); % row index
sp_j = zeros(16*row_sp,1); % column index
sp_s = zeros(16*row_sp,1); % value index
k=1;
% rotated vertical line equidistant-preserving
for i=1:2:size(lines,1)-1
    num_s = lines(i,end);  % number of sample points in this segment
    k_xy = calcSlope(init_H, slope_lines(i), [lines(i,1); lines(i+1,1)]); % line's slope after transformation
    if isinf(abs(k_xy));  nor_vec=[1,0]; else; nor_vec = [k_xy, -1];  end
    nor_vec = nor_vec./norm(nor_vec);  % normal vector of warped lines
    for j=1:num_s-1
        lps = [lines(i,j),     lines(i+1,j)];
        lpe = [lines(i,j+1),   lines(i+1,j+1)];
        pxs = min( find(lps(1)-X_col<x_dis & lps(1)-X_col>=0, 1), C2); % the x index of p's position
        pys = min( find(lps(2)-Y_row<y_dis & lps(2)-Y_row>=0, 1), C1); % the y index of p's position
        pxe = min( find(lpe(1)-X_col<x_dis & lpe(1)-X_col>=0, 1), C2); % the x index of p's position
        pye = min( find(lpe(2)-Y_row<y_dis & lpe(2)-Y_row>=0, 1), C1); % the y index of p's position
        
        nums1 = (C1+1)*(pxs-1) + pys; % index of v1*   
        nums2 = nums1 + C1+1;
        nums3 = nums2 + 1;
        nums4 = nums1 + 1;
        nume1 = (C1+1)*(pxe-1) + pye;
        nume2 = nume1 + C1+1;
        nume3 = nume2 + 1;
        nume4 = nume1 + 1;
        
        Mesh_ps(1:4,:) = [X_col(pxs), Y_row(pys);     % v1
                            X_col(pxs+1), Y_row(pys);   % v2
                            X_col(pxs+1), Y_row(pys+1); % v3
                            X_col(pxs), Y_row(pys+1)];   % v4
        Mesh_pe(1:4,:) = [X_col(pxe), Y_row(pye);     % v1
                            X_col(pxe+1), Y_row(pye);   % v2
                            X_col(pxe+1), Y_row(pye+1); % v3
                            X_col(pxe), Y_row(pye+1)];   % v4
                
        coeff_mesh_ps = meshGridAlign(Mesh_ps, lps);
        coeff_mesh_pe = meshGridAlign(Mesh_pe, lpe);
        sp_i(16*k-15:16*k) = k.*ones(1,16);
        sp_j(16*k-15:16*k) = [2*nums1-1, 2*nums2-1, 2*nums3-1, 2*nums4-1,...
                              2*nume1-1, 2*nume2-1, 2*nume3-1, 2*nume4-1,...
                              2*nums1, 2*nums2, 2*nums3, 2*nums4,...
                              2*nume1, 2*nume2, 2*nume3, 2*nume4];
        sp_s(16*k-15:16*k) = [-nor_vec(1).*coeff_mesh_ps; nor_vec(1).*coeff_mesh_pe; 
                              -nor_vec(2).*coeff_mesh_ps; nor_vec(2).*coeff_mesh_pe];
        k = k + 1;
    end
end

sparse_line = sparse(sp_i, sp_j, sp_s, row_sp, 2*num_V);

end