Otsu's method

In computer vision and image processing, Otsu's method, named after Nobuyuki Otsu (大津展之, Ōtsu Nobuyuki^?), is used to automatically perform clustering-based image thresholding, or, the reduction of a graylevel image to a binary image. The algorithm assumes that the image contains two classes of pixels following bi-modal histogram (foreground pixels and background pixels), it then calculates the optimum threshold separating the two classes so that their combined spread (intra-class variance) is minimal, or equivalently (because the sum of pairwise squared distances is constant), so that their inter-class variance is maximal. Consequently, Otsu's method is roughly a one-dimensional, discrete analog of Fisher's Discriminant Analysis.

The extension of the original method to multi-level thresholding is referred to as the multi Otsu method.

In Otsu's method we exhaustively search for the threshold that minimizes the intra-class variance (the variance within the class), defined as a weighted sum of variances of the two classes:

Weights $\omega _{0}$ $\omega _{0}$ and $\omega _{1}$ $\omega _{{1}}$ are the probabilities of the two classes separated by a threshold $t$ $t$ and $\sigma _{0}^{2}$ $\sigma _{0}^{2}$ and $\sigma _{1}^{2}$ $\sigma _{1}^{2}$ are variances of these two classes.

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