In this paper, threshold selection is considered in the continuous image rather than in digital image. We prove that, for each given object within 2D image, its optimal threshold is determined by the mean of the gray values of the points lying on its continuous boundary. Thus, we try to deduce threshold from the gray values of the boundary rather from the gray values of the given discrete sampling points (pixels or edge pixels). By the scheme, we well overcome some disadvantages existing in the threshold methods based on the histogram of edge pixels. Besides, the proposed method has the ability to well handle the image whose histogram has very unequal peaks and broad valley. 2003 Elsevier Science B.V. All rights reserved.