function u = collage(r, s, interieur)

    r = double(r);
    s = double(s);
    
    [nb_lignes,nb_colonnes,nb_canaux] = size(r);
    nb_pixels = nb_lignes * nb_colonnes;

    e = ones(nb_pixels, 1);

    Dx = spdiags([-e e],[0 nb_lignes], nb_pixels, nb_pixels);
    Dx(end-nb_lignes+1:end,:) = 0;
    
    Dy = spdiags([-e e],[0 1],nb_pixels, nb_pixels);
    Dy(nb_lignes:nb_lignes:end,:) = 0;

    X = zeros(size(r(:,:,1)));
    X(1, :) = 1;
    X(nb_lignes, :) = 1;
    X(:, 1) = 1;
    X(:, nb_colonnes) = 1;
    indices_bord_r = find(X);

    n_bord_r = length(indices_bord_r);
    n_r = nb_pixels;

    A = Dx' * Dx + Dy' * Dy;
    A(indices_bord_r,:) = sparse(1:n_bord_r,indices_bord_r,ones(n_bord_r,1),n_bord_r,n_r);

    % Calcul de l'imagette résultat u, canal par canal :
    u = r;
    for k = 1:nb_canaux
    
        u_k = u(:,:,k);
        s_k = s(:,:,k);
        r_k = r(:,:,k);

        grad_s = [Dx * s_k(:) , Dy * s_k(:)];
        grad_r = [Dx * u_k(:) , Dy * u_k(:)];

        grad_g = grad_r;
        grad_g(interieur, :) = grad_s(interieur, :);

        b = Dx' * grad_g(:,1) + Dy' * grad_g(:,2);
        b(indices_bord_r) = r_k(indices_bord_r);
        u_k = -A \ -b;

        u_k = reshape(u_k, nb_lignes, nb_colonnes);
        u(:,:,k) = u_k;

    end