Corner Detection Using Fuzzy Principles

Introduction

The human visual system has a highly developed capability for detecting many classes of patterns including visually significant arrangements of image elements. From the psychovisual aspect, points representing high curvature are one of the dominant classes of patterns that play an important role in almost all real life image analysis applications (Lowe, 1985; Loupias & Sebe, 2000; Fischler & Wolf, 1994). These points encode a significant amount of shape information. Corners are generally formed at the junction of different edge segments which may be the meeting (or crossing) of two edges. Cornerness of an edge segment depends solely on the curvature formed at the meeting point of two line segments. Corner detection is one of the fundamental tasks in computer vision and it can be regarded as a special type of feature segmentation. Extracted corners can be used for measurement and/or recognition purposes. A large number of algorithms already exist in the literature. In particular, corner detection on gray level images can be classified into two main approaches. In the first approach, the gray level image is first converted into its binary version for extraction of boundaries using some thresholding technique. After a successful extraction of boundaries, the corners or the high curvature points are detected using directional codes or other polygonal approximation techniques (Freeman & Davis, 1977). In the second approach, the gray level image is taken directly as an input for corner detection. In this chapter, the discussion is restricted to the second approach only. Most of the general-purpose detectors based on gray level, use either a topology-based or an auto-correlation- based approach and most recently machine learning strategies (Rosten et al., 2010). Topology based corner detectors, mainly use gradients and surface curvature to define the measure of cornerness. Points are marked as corners, if the value of cornerness exceeds some predefined threshold condition. Alternatively a measure of curvature can be obtained using auto-correlation (Kitchen &Rosenfeld, 1982; Zheng et al., 1999; Rattarangsi & Chin, 1999; Teh & Chin, 1989; Rosenfeld & Johnston, 1973).

There exits several classical corner detection algorithms for estimating corner points. Such detectors are based on a local structure matrix which consists on the first partial derivatives of the intensity function. An clear example is the Harris feature point detector (Harris & Stephens, 1988), which is based on a comparison: the measure of the corner strength - which is defined by the method and is based on a local structure matrix - is compared to an appropriately chosen concrete threshold. Another well known corner detector is the SUSAN (Smallest Univalue Segment Assimilating Nucleus) detector which is based on brightness comparison (Smith & Brady, 1997). It does not depend on image derivatives. The SUSAN area will reach a minimum while the nucleus lies on a corner point. The effectiveness of the above mentioned algorithms is acceptable. Recent studies such as (Zou et al., 2008) demonstrate that the Harris corner detector performs better for several circumstances in comparison to the SUSAN algorithm.