RANSAC Multivariate Regression

Question

I am using RANSAC as my robust regression method. I found a neat toolbox here which performs RANSAC by Marco Zuliani. I saw that there are examples for a line and a plane but what if there are many independent variables as in multivariate regression. Is there anyway to modify the code to handle this?

What I tried thus far is modifying the 3D code to handle N dimensions. When I do this I get all the points as inliers and I know that probably is not correct. This is over-fitting the data. Below are the modifications I tired to make.

For test_RANSAC_plane.m I just added more rows to X

For estimate_plane.m:

function [Theta, k] = estimate_plane(X, s)
    % cardinality of the MSS
    k = size(X,1);

    if (nargin == 0) || isempty(X)
        Theta = [];
        return;
    end;

    if (nargin == 2) && ~isempty(s)
        X = X(:, s);
    end;

    % check if we have enough points
    N = size(X, 2);
    if (N < k)
        error('estimate_plane:inputError', ...
            'At least k points are required');
    end;

    A = [];
    for i=1:k
        A = [A transpose(X(i, :))];
    end
    A = [A ones(N, 1)];
    [U S V] = svd(A);
    Theta = V(:, k+1);

    return;

For error_plane.m:

function [E T_noise_squared d] = error_plane(Theta, X, sigma, P_inlier)
    % compute the squared error
    E = [];
    k = size(X,1);
    den = 0;

    if ~isempty(Theta) && ~isempty(X)
        for i=1:k
            den = den + Theta(i)^2;
        end

        sum = Theta(1)*X(1,:);
        for j=2:k
            sum = sum + Theta(j)*X(j,:);
        end
        sum = sum + Theta(j+1);
        E = (sum).^2 / den;                 
    end;

    % compute the error threshold
    if (nargout > 1)
        if (P_inlier == 0)
            T_noise_squared = sigma;
        else
            d = k;
            % compute the inverse probability
            T_noise_squared = sigma^2 * chi2inv_LUT(P_inlier, d);
        end; 
    end; 
    return;

Answer 1

I don't know about this toolbox but I have used this function in the past:

http://www.peterkovesi.com/matlabfns/Robust/ransac.m

It's not as sophisticated but works well and has no problem coping with arbitrary dimensionality