Efficiently Updating Feasible Regions for Fitting Discrete Polynomial Curve

We deal with the problem of fitting a discrete polynomial curve to 2D data in the presence of outliers. Finding a maximal inlier set from given data that describes a discrete polynomial curve is equivalent with finding the feasible region corresponding to the set in the parameter space. When iteratively adding a data point to the current inlier set, how to update its feasible region is a crucial issue. This work focuses on how to track vertices of feasible regions in accordance with newly coming inliers. When a new data point is added to the current inlier set, a new vertex is obtained as the intersection point of an edge (or a face) of the feasible region for the current inlier set and a facet (or two facets) of the feasible region for the data point being added. Evaluating all possible combinations of an edge (or a face) and a facet (or two facets) is, however, computationally expensive. We propose an efficient computation in this incremental evaluation that eliminates combinations producing no vertices of the updated feasible region. This computation facilitates collecting the vertices of the updated feasible region. Experimental results demonstrate our proposed computation efficiently reduces practical running time.