A Generalization of Otsu’s Method and Minimum Error Thresholding

We present Generalized Histogram Thresholding (GHT), a simple, fast, and effective technique for histogram-based image thresholding. GHT works by performing approximate maximum a posteriori estimation of a mixture of Gaussians with appropriate priors. We demonstrate that GHT subsumes three classic thresholding techniques as special cases: Otsu's method, Minimum Error Thresholding (MET), and weighted percentile thresholding. GHT thereby enables the continuous interpolation between those three algorithms, which allows thresholding accuracy to be improved significantly. GHT also provides a clarifying interpretation of the common practice of coarsening a histogram's bin width during thresholding. We show that GHT outperforms or matches the performance of all algorithms on a recent challenge for handwritten document image binarization (including deep neural networks trained to produce per-pixel binarizations), and can be implemented in a dozen lines of code or as a trivial modification to Otsu's method or MET.