Exact Fast Algorithm For Optimal Linear Separation Of 2D Distribution

The paper presents a new fast computation scheme for linear separation in two-dimensional feature space. This scheme is based on a combination of several image processing techniques: fast Hough transform, cumulative sum computation and expression of optimized criterion as a function of additive statistics. It is shown that complexity of the scheme is O(n log n) for chosen set of criteria. Two appropriate criteria are discussed, both being a 2D extension of well-known Otsu’s criterion: standard one considering covariance trace and one considering covariance second eigenvalues. Applicability of the latter criterion for the color segmentation problem is discussed.