Otsuspunkt

Otsuspunkt, often referred to as Otsu's threshold in English, is the intensity value in a grayscale image that best separates foreground from background according to Otsu's method. The method selects a threshold by maximizing the between-class variance of pixel intensities, which is equivalent to minimizing the within-class variance.

Origin and naming: The technique is named after Nobuyuki Otsu, who introduced the method in 1979 for automatic image thresholding. In German-language texts, the threshold value is sometimes called otsuspunkt (literally “Otsu's point”).

Algorithm and calculation: For a grayscale image with intensity levels 0 to 255, the histogram is normalized to probabilities p_i. For each threshold t, compute the probabilities w0 and w1 of the two classes (below and above t), the means mu0 and mu1 of these classes, and the between-class variance sigma_b^2(t) = w0 w1 (mu0 - mu1)^2. The threshold t that maximizes sigma_b^2 is chosen as the otsuspunkt. The image can then be binarized by comparing each pixel to this threshold.

Variants and extensions: Otsu's method can be applied globally to the whole image or extended to multi-level thresholding (multilevel Otsu). It can be combined with pre-processing such as smoothing. The method assumes a bimodal histogram and may perform poorly on images with uneven illumination, noise, or overlapping class intensities.

Applications and limitations: Otsu's thresholding is widely used in document analysis, biometrics, and medical imaging for automatic binarization. It is fast, parameter-free, and unsupervised, but its performance degrades on non-bimodal histograms or highly noisy data. Reference implementations and tutorials are common in image processing literature.