Pattern Recognition 41 (2008) 2337 – 2346 www.elsevier.com/locate/pr Unimodal thresholding for edge detection R. Medina-Carnicer ∗ , F.J. Madrid-Cuevas , 1 Department of Computing and Numerical Analysis, Córdoba University, 14071 Córdoba, Spain Received 19 January 2007; received in revised form 14 November 2007; accepted 16 December 2007 Abstract In this paper a novel non-parametric method is proposed for unimodal thresholding in an edge detection context. The proposed method assigns a point in a ROC (receiver operating characteristic) space to each possible threshold without the need of a reference binary image. The optimal point and the required corresponding threshold is then determined in the ROC graph. The Berkeley Segmentation Dataset has been used to evaluate the performance of the proposed method, which is compared with another two recent proposals and Otsu method.  2007 Elsevier Ltd. All rights reserved. Keywords: Unimodal thresholding; Edge detection 1. Introduction Edge detection is a topic of continuing interest because it is a key issue in image processing, computer vision and pattern recognition. Edge detection is a well-established area and there are many edge detectors proposed in the literature [1]. A variety of algorithms exist for edge characterisation and detection, such as the statistical methods [2], the difference methods [3], curve fitting [4], and multi-resolution analysis [5]. A great number of edge detectors base their strategy on: (1) calculating a characteristic image (in many cases the charac- teristic is an approximation of an image gradient module) and (2) thresholding the characteristic image to find the edge map [6–8]. In this paper the term “gradient image” is used to denote the characteristic image obtained by an edge detector. The thresholding of a gradient image is not a trivial ques- tion. Many thresholding approaches based on histograms have been described applied to segment images. These techniques [9,10] can usually be classified as non-parametric or paramet- ric methods. When these techniques are applied to unimodal ∗ Corresponding author. Tel.: +34 957 21 83 46; fax: +34 957 21 86 30. E-mail address: rmedina@uco.es (R. Medina-Carnicer). 1 This work has been developed with the support of the Research Project called “DPI2006-02608” and financed by Science and Technology Ministry of Spain and FEDER. 0031-3203/$30.00  2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.patcog.2007.12.007 histograms, they are unstable [11] because they cannot deal with similar sizes in the different classes and because these classes cannot be modelled properly. The non-stability of these meth- ods appear when in complex images pixels exists with small gradient values and they are edge points. In general, these meth- ods determine a number of edge points that can be insufficient for some applications [12,13]. Fig. 1(a) shows a gradient image obtained for the image found in Ref. [20] (image number 108005). This gradient image was obtained by smoothing the original image using a Gaussian kernel with  = 0.6 and derivating using the first difference operator. Fig. 1(e) shows the gradient image obtained for =2.4 using the same procedure described above. Figs. 1(b) and (f) show the binary edge maps obtained by the Otsu method [14] when acting on the gradient images of Figs. 1(a) and (e). The histogram of a gradient image is a typical unimodal histogram. An alternative to this problem therefore consists of using unimodal histogram thresholding techniques. Unimodal histogram thresholding is a problem that has been widely studied in the specific literature using different ap- proaches. Unimodal thresholding is a tool that it can also be useful for region segmentation. For example, in Ref. [15] the optimal threshold for region segmentation is determined of the points lying on its continuous boundary. Then, this method needs of a previous threshold obtained on the gradient image (an unimodal histogram) for the determination of the points on boundary.