Image Segmentation
Suppose that the dark regions in the image correspond to the background, and the bright regions to objects. Then, ?1 < ?2, and all pixels below a threshold T may be considered to be background, and all pixels above T may be considered as object pixels.The probability of erroneous classification is then
To find the optimal threshold, we may differentiate E(T) with respect to T and equate the result to zero, which leads to
Applying this result to the Gaussian PDFs gives (after taking logarithms and some simplification) the quadratic equation