The authors propose two automatic threshold-selection schemes, based on functional approximation of the histogram. The first method is based on minimising the sum of square errors, and the second one is based on minimising the variance of the approximated histogram. Experimental results show that, on average, the latter scheme gives better results than the former one, at a small extra computational cost. A 'goodness' measure is proposed to measure the effectiveness of the two schemes, and to compare them against the entropy-based approach and the moment-based approach.