Unimodal thresholding

Abstract

Most thresholding algorithms have difficulties processing images with unimodal distributions. In this paper an algorithm, based on finding a corner in the histogram plot, is proposed that is capable of performing bilevel thresholding of such images. Its effectiveness is demonstrated on synthetic data as well as a variety of real data, showing its successful application to edges, corners, difference images, optic flow, texture difference images, polygonal approximation of curves, and image segmentation.

Introduction

Over the years, many image thresholding techniques have been developed [1], [2], and considerable research continues at present [3], [4], [5]. The reason for this long term, ongoing effort is that none of the methods are capable of optimal performance under all conditions. Although techniques based on many different principles are available, they all operate under certain implicit or explicit assumptions. These assumptions effectively form restrictions on the successful operation of the thresholding algorithms. Examples of requirements for bilevel thresholding are that there should be two distinct modes in the intensity histogram, the peaks should not be too dissimilar in size, and they should be roughly Normal. Since different computer vision applications produce different types of images we can expect the success of any thresholding algorithm to vary according to how well its expected operating conditions are met.

This paper looks at the case where bilevel thresholding is desired even though the image histogram may only contain one obvious peak. Although performing thresholding might not seem appropriate in such cases there are in fact many instances when it is required. Take for example edge detection, which typically produces many low-magnitude edges corresponding to non-edges. The true edges produce a wide range of edge magnitudes that will often just create a fat tail on the non-edge peak in the edge histogram rather than generate a distinct peak of their own. Another example is change detection carried out by differencing pairs of images. In applications such as surveillance the amount of change will be extremely small if a wide field of view is imaged and only a small, distant object has moved. Thus the histogram could contain one enormous peak (no-change) and one tiny peak (change).

Such applications will cause difficulties for most existing thresholding algorithms, and there has been relatively little work in such areas [6], [7]. In contrast, we present in this paper a technique that is specifically intended to cope with essentially unimodal distributions rather than the more usual bimodal or multimodal distributions. That is, the second peak is either very small, or is submerged within the main peak. Section 3 describes the algorithm and analyses its performance on a variety of types of synthetic data. In Section 4 it is applied to thresholding a range of types of real data: edges, corners, difference images, optic flow, texture difference images, polygonal approximation of curves, and image segmentation. Both the theoretical and experimental analyses demonstrate the benefits of the new algorithm for such data.