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Edge Detection
, 1985
"... For both biological systems and machines, vision begins with a large and unwieldy array of measurements of the amount of light reflected from surfaces in the environment. The goal of vision is to recover physical properties of objects in the scene, such as the location of object boundaries and the s ..."
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Cited by 1277 (1 self)
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For both biological systems and machines, vision begins with a large and unwieldy array of measurements of the amount of light reflected from surfaces in the environment. The goal of vision is to recover physical properties of objects in the scene, such as the location of object boundaries and the structure, color and texture of object surfaces, from the twodimensional image that is projected onto the eye or camera. This goal is not achieved in a single step; vision proceeds in stages, with each stage producing increasingly more useful descriptions of the image and then the scene. The first clue about the physical properties of the scene are provided by the changes of intensity in the image. The importance of intensity changes and edges in early visual processg has led to extensive research on their detection, description and .use, both in computer and biological vision systems. This article reviews some of the theory that underlies the detection of edges, and the methods used to carry out this analysis.
Digital step edges from zero crossing of second directional derivatives
 Pattern Analysis and Machine Intelligence, IEEE Transactions on
, 1984
"... AbstractWe use the facet model to accomplish step edge detection. The essence of the facet model is that any analysis made on the basis of the pixel values in some neighborhood has its final authoritative interpretation relative to the underlying gray tone intensity surface of which the neighborho ..."
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Cited by 202 (5 self)
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AbstractWe use the facet model to accomplish step edge detection. The essence of the facet model is that any analysis made on the basis of the pixel values in some neighborhood has its final authoritative interpretation relative to the underlying gray tone intensity surface of which the neighborhood pixel values are observed noisy samples. With regard to edge detection, we define an edge to occur in a pixel if and only if there is some point in the pixel's area having a negatively sloped zero crossing of the second directional derivative taken in the direction of a nonzero gradient at the pixel's center. Thus, to determine whether or not a pixel should be marked as a step edge pixel, its underlying gray tone intensity surface must be estimated on the basis of the pixels in its neighborhood. For this, we use a functional form consisting of a linear combination of the tensor products of discrete orthogonal polynomials of up to degree three. The appropriate directional derivatives are easily computed from this kind of a function. Upon comparing the performance of this zero crossing of second directional derivative operator with the Prewitt gradient operator and the MarrHildreth zero crossing of the Laplacian operator, we find that it is the best performer; next is the Prewitt gradient operator. The MarrHildreth zero crossing of the Laplacian operator performs the worst. Index TermsEdge operator, facet model, image processing, image segmentation, zero crossings of second directional derivative. I.
Integrated directional derivative gradient operator
 IEEE Trans. Syst., Man, Cybern
, 1987
"... AbstractAccurate edge direction information is required in many image processing applications. A variety of operators for computing local edge direction have been proposed, many of them estimating a kind of gradient. These operators face two major problems. One problem is the inherent bias in their ..."
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Cited by 11 (2 self)
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AbstractAccurate edge direction information is required in many image processing applications. A variety of operators for computing local edge direction have been proposed, many of them estimating a kind of gradient. These operators face two major problems. One problem is the inherent bias in their estimate of edge direction. The bias itself is a function of edge direction. Another problem is their sensitivity to the presence of noise in the image data. The second problem can be alleviated by an increase in the processing neighborhood size but usually at the expense of an increase in estimate bias and also inefrors in the processing ofsmall or thin objects. An operator based on the cubic facet model is discussed, which reduces sharply both estimate bias and noise sensitivity with no increase in computational complexity. The measure of gradient strength is the maximum value of the integral of the first directional derivative taken over a rectangular or square neighborhood, the maximum being taken over all possible directions for the directional derivative.The line direction which maximizes the integral defines the new estimate of gradient direction. Experimental results show the superiority of this operator to others such as the Roberts operator, the Prewitt operator, the Sobel operator, and the standard cubic facet gradient operator for step edges and ramp edges. Under zeronoise conditions the 7x 7 integrated directional derivative gradient operator has a worst bias of less than 0.090, and the 5 x 5 integrated directional derivative gradient operator has a worst bias of less than 0.26 ° on ramp edges. For comparison purposes the 7X 7 standard cubic facet gradient operator has a worst bias of about 1.20, and the 5x 5 standard cubic facet gradient operator has a worst bias of 0.50.The 7x 7 Prewitt operator has a worst bias of 50, and the 5x 5 Prewitt operator has a worst bias of4°. This improvement in worst bias stays with the contamination of edges by additive independent zeromean Gaussian noise. I.
Design and Evaluation of Feature Detectors
, 1998
"... Many applications in both image processing and computational vision rely upon the robust detection of parametric image features and the accurate estimation of their parameters. In this thesis, I address three fundamental questions related to the design and evaluation of parametric feature detectors. ..."
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Cited by 7 (0 self)
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Many applications in both image processing and computational vision rely upon the robust detection of parametric image features and the accurate estimation of their parameters. In this thesis, I address three fundamental questions related to the design and evaluation of parametric feature detectors. Most feature detectors have been designed to detect a single type of feature, more often than not, the step edge. A large number of other features are also of interest. Since the task of designing a feature detector is very time consuming, repeating the design effort for each feature is wasteful. To address this deficiency, in the first part of this thesis I develop an algorithm that takes as input a description of a parametric feature and automatically constructs a detector for it. The development of many feature detectors begins with an ideal model of the feature. Since image data are noisy, feature detectors must actually detect features that are almost, but not quite, ideal. Many exist...