Generic, Model-Based Edge Estimation in the Image Surface

Similarly, crease edgels can be determined by convolving the image with the second derivative of the mask. Most of the discussions in this paper will focus on detecting the delta edgel, but they can be applied to the other two types of edgels as well.
Generic, Model-Based Edge Estimation in the Image Surface
Pei-Chun Chiang, Thomas O. Binford
Robotics Laboratory, Computer Science Department Stanford University, Stanford CA 94305
Abstract
Delta Edge
Step Edge
Crease Edge
Figure 1: The transverse pro les of the three main types of edges. are interesting, i.e. discontinuities along curves with cross sections in the form of delta, step, and crease, as shown in Fig. 1 1]. In the past, a variety of segmentation algorithms have been developed, like the Binford-Horn operator 2], the Marr-Hildreth operator 3], the Canny operator 4], the Nalwa-Binford operator 5], However, the results are not satisfactory, primarily because they don't produce extended edges with su cient quality, thus, restricting their applications. Since edge linking to form extended edges is an exponential branching process, accuracy of edgel estimation was required to cut the branching to tolerable limits. With the WangBinford operator 6] 7], high quality extended edges have been obtained. Now, the operator described here performs substantially better. There are three principal problems in previous edge detection algorithms, excluding the Wang-Binford operator. A main problem is that the shading e ect was not taken into account; that is, the intensity of an image along an edge was modeled as a constant, which is not true in the real scene. The second problem is that the estimates of orientation and position were not accurate. The inaccuracy raised severe problems in linking pixels into extended edges, and then in the follow-up processes. The third problem is that only step edges were covered in those algorithms. There are three main types of edges: delta edges, step edges, and crease edges. A signi cant amount of information in an image is lost if only step edges can be detected.
Edge detection is the process of estimating extended curve discontinuities in the image intensity surface. As a primary module in image understanding systems, its performance is critical. This paper presents a new family of algorithms for detecting edges in an image. Edges with delta, step and crease cross sections along curves are found. In the algorithm, an image is convolved at each pixel at four orientations. Then, the best least-squares estimate of an edge is made over a 2x2x2 cube determined by adjacent x, y, and ' values. Finally, the detected edge image is built by a primitive linking process. Both theoretical analyses and simulation experiments have been done; real images have been analyzed. Quantitative results indicate that the proposed detector has superior detection and localization; the standard deviations of orientation and transverse position are a factor of four better than the Wang-Binford operator at the same signal to noise ratio. It performs well even when the ratio is less than 4. In the Successor paradigm, objects are interpreted globally by Bayesian networks that express probabilities among a hierarchy of uncertain geometric hypotheses. The 3D levels in Successor include: object (physical), 3D volume, 3D surface, 3D curve, and 3D point. Quasi-invariants and invariants correspond 3D surfaces to 2D image areas, 3D curves to 2D image curves, and 3D points to 2D image points. Successor requires reasonable measurement of extended image edges and of relations among extended edges in order to build 3D interpretations. The performance of the edge detector a ects most modules in image understanding systems, like stereo, motion, and surface estimation. Until recently, the quality of measurement of extended edges extracted from images was very unsatisfactory from the standpoint of vision systems. The Wang-Binford operator provided reasonable extended edges. This algorithm provides substantial improvements in the quality of measurement of extended edges. An intensity image I (x; y) is a mathematical surface. Edges in an image correspond to intensity discontinuities in the image surface. Low-order discontinuities 1
1 Introduction
ቤተ መጻሕፍቲ ባይዱ
A new edge detector which overcomes all these problems is presented here. It provides least-squares estimates of the position, orientation, and amplitude of an edge, which are no longer sensitive to shading. In addition, it estimates three kinds of edges by using a single family of algorithms. Though the Wang-Binford operator can also estimate all three edge types reasonably well, the performance of this detector improves dramatically over Wang-Binford from both practical and statistical standpoints. Based on accurate estimates and the statistical analyses of edgels, isolated edgels are aggregated into extended edges. The linking process is still under development, but the current results look promising. In this paper, a generic edge model is introduced in Section 2, then the edge detector is developed in Section 3. The statistical analysis is discussed in Section 4. Real images are tested in Section 5. The conclusions are given in Section 6.