In image thresholding, the goal is to separate objects from the background clearly. The key metric is accuracy of pixel classification: how many pixels are correctly labeled as foreground or background. This is important because a good thresholding method should minimize mistakes in pixel labeling to produce a clean binary image.
For adaptive and Otsu thresholding, metrics like precision and recall on foreground pixels help understand if the method captures the object well without including too much background noise.