Image Thresholding Using the Complement Feature

A new feature (the complement feature) is proposed in an Eigen formulations for performing global image thresholding. The goal is to find an intensity or gray-level value below which is the background while above it is the foreground (object). Each pixel in the image is represented by a (2D) unit vector where the x-component is the normalized (to [0,1] or [-1,1]) intensity of the pixel, while the y-component is its complement (e.g., Euclidian L₂-Norm). The correlation matrix can then constructed to find the cross-correlation, Eigen vectors (axes of inertia) and Eigen values (description of respective sizes). Several implementations for each of the three previously mentioned categories are proposed to perform image thresholding. Interestingly, some of the proposed implementations do not require exhaustive search and a direct solution can be obtained. The results are promising on a wide range of images as demonstrated by comparison with the well-known Otsu method.