A Spatial Thresholding Method for Image Segmentation

There has been recent interest in the segmentation of images by thresholding. We present several model based algorithms for threshold selection. We concentrate on the important two population univariate case when an image contains an object and background. However the methods are applicable to multispectral k-population images. We show how the main ideas behind two important nonspatial thresholding algorithms follow from classical discriminant analysis. We then give various new thresholding algorithms which make use of available IocaVspatial information. We consider one FLIR image and two artificial examples. A comparative study indicates that a new " alternating mean thresholding and median filtering " algorithm provides an acceptable method when the image is relatively highly contaminated. This method seems to depend less on initial values. I. INTRODUCTION We will consider the problem of image segmentation by thresh-olding. This problem and its importance were fully described recently in [l], [2], and [3]. Our main interest is with the k = 2 population case which is related to object identification. However, we shall also consider the extension to the general k-population problem. We first show that the threshold value in the segmentation algorithms of [ l ] and [2] can be deduced from the well-known statistical discriminant rule. Unlike [3], their rule is not spatial, i.e., it does not use contextual information. We give a spatial allocation rule based on the work of [4] and [ 5 ]. This is utilized to give a new thresholding algorithm. We also consider the iterated conditional modes (ICM) method [6]. Section I1 describes the nonspatial allocation rule, and shows how the allocation rules of [I] and [2] are particular cases. We summarize their iterative thresholding method in Section 111. In Section IV we give a spatial allocation rule which takes into account the spatial relationship between neighboring pixels and describe the modified iterative algorithms in Section V. In Section VI we describe ICM and its implementation. The methods are compared using synthetic images (following [3]) and one " real " FLIR (forward looking infrared) image. We conclude with a discussion of the methods in Section VIII. Our method follows naturally from a model introduced in Section 11. The method in [3] is not discussed here since it is not model orientated. Also our method applies to multispectral data, i.e., color images. In all the algorithms considered here, we do not require any prior