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5 EDGE DETECTION
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Figure 51: One-dimensional edge profiles
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It is also possible for an edge to have both step and line characteristics For example, a surface that changes orientation from one flat surface to another will produce a step edge; but if the surface has a specular component of reflectance and if the surface corner is rounded, there can be a highlight due to the specular component as the surface orientation of the rounded corner passes the precise angle for specular reflection The edge profile generated by such a situation looks like a step edge with a superimposed line edge There are also edges associated with changes in the first derivative of the image intensity For example, mutual reflection from the sides of a concave corner generate roof edges Edges are important image features since they may correspond to significant features of objects in the scene For example, the boundary of an object usually produces step edges because the image intensity of the object is different from the image intensity of the background This chapter will deal almost exclusively with step edges, although many of the ideas can be adapted to other types of image intensity changes The profile of an ideal step edge and the profile of a real image that provides some examples of step edges are displayed in Figure 52 By definition, an edge is a significant local change in the image intensity The plot shows step
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CHAPTER 5 EDGE DETECTION
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Figure 52: (a) The top half of the connecting rod image (b) The profile of an ideal step change in image intensity is plotted to show that the edges are not perfectly sharp and the image is corrupted by noise The plot is a horizontal slice through the circular portion of the connecting rod corresponding to the bottom edge of the partial rod image shown above changes in image intensity that are edges because the changes are significant and local The plot also shows changes that are not edges, because they violate part of the definition The changes due to noise are not edges even though the changes are local, because the changes are not significant The changes due to shading, such as the ramp on the right side of the plot, are not edges even though the changes are significant, because the changes are not local Real images are very noisy It is difficult to develop an edge detection operator that reliably finds step edges and is immune to noise Before we discuss important considerations in edge detection operators, some terms must be carefully defined Definition 51 An edge point is a point in an image with coordinates [i,j] at the location of a significant local intensity change in the image Definition 52 An edge fragment corresponds to the i and j coordinates of an edge and the edge orientation e, which may be the gradient angle
51 GRADIENT
Definition 53 An edgedetector is an algorithmthat producesa set of edges
{edge points or edge fragments} from an image
Definition 54 A contour is a list of edgesor the mathematicalcurve that
models the list of edges Definition 55 Edge linking is the process of forming an ordered list of edges from an unordered list By convention, edges are ordered by traversal in a clockwise direction Definition 56 Edge following is the process of searching the {filtered} image to determine contours The coordinates of an edge point may be the integer row and column indices of the pixel where the edge was detected, or the coordinates of the edge location at subpixel resolution The edge coordinates may be in the coordinate system of the original image, but more likely are in the coordinate system of the image produced by the edge detection filter since filtering may translate or scale image coordinates An edge fragment may be conceptualized as a small line segment about the size of a pixel, or as a point with an
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