scispace - formally typeset
Search or ask a question
Journal ArticleDOI

A Computational Approach to Edge Detection

01 Jun 1986-IEEE Transactions on Pattern Analysis and Machine Intelligence (IEEE Computer Society)-Vol. 8, Iss: 6, pp 679-698
TL;DR: There is a natural uncertainty principle between detection and localization performance, which are the two main goals, and with this principle a single operator shape is derived which is optimal at any scale.
Abstract: This paper describes a computational approach to edge detection. The success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points. These goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution. We define detection and localization criteria for a class of edges, and present mathematical forms for these criteria as functionals on the operator impulse response. A third criterion is then added to ensure that the detector has only one response to a single edge. We use the criteria in numerical optimization to derive detectors for several common image features, including step edges. On specializing the analysis to step edges, we find that there is a natural uncertainty principle between detection and localization performance, which are the two main goals. With this principle we derive a single operator shape which is optimal at any scale. The optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a Gaussian-smoothed image. We extend this simple detector using operators of several widths to cope with different signal-to-noise ratios in the image. We present a general method, called feature synthesis, for the fine-to-coarse integration of information from operators at different scales. Finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge.
Citations
More filters
Book
01 Jan 1998
TL;DR: An introduction to a Transient World and an Approximation Tour of Wavelet Packet and Local Cosine Bases.
Abstract: Introduction to a Transient World. Fourier Kingdom. Discrete Revolution. Time Meets Frequency. Frames. Wavelet Zoom. Wavelet Bases. Wavelet Packet and Local Cosine Bases. An Approximation Tour. Estimations are Approximations. Transform Coding. Appendix A: Mathematical Complements. Appendix B: Software Toolboxes.

17,693 citations

01 Jan 2001
TL;DR: This book is referred to read because it is an inspiring book to give you more chance to get experiences and also thoughts and it will show the best book collections and completed collections.
Abstract: Downloading the book in this website lists can give you more advantages. It will show you the best book collections and completed collections. So many books can be found in this website. So, this is not only this multiple view geometry in computer vision. However, this book is referred to read because it is an inspiring book to give you more chance to get experiences and also thoughts. This is simple, read the soft file of the book and you get it.

14,282 citations

Journal ArticleDOI
TL;DR: A new definition of scale-space is suggested, and a class of algorithms used to realize a diffusion process is introduced, chosen to vary spatially in such a way as to encourage intra Region smoothing rather than interregion smoothing.
Abstract: A new definition of scale-space is suggested, and a class of algorithms used to realize a diffusion process is introduced. The diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing. It is shown that the 'no new maxima should be generated at coarse scales' property of conventional scale space is preserved. As the region boundaries in the approach remain sharp, a high-quality edge detector which successfully exploits global information is obtained. Experimental results are shown on a number of images. Parallel hardware implementations are made feasible because the algorithm involves elementary, local operations replicated over the image. >

12,560 citations

Journal ArticleDOI
TL;DR: This paper has designed a stand-alone, flexible C++ implementation that enables the evaluation of individual components and that can easily be extended to include new algorithms.
Abstract: Stereo matching is one of the most active research areas in computer vision. While a large number of algorithms for stereo correspondence have been developed, relatively little work has been done on characterizing their performance. In this paper, we present a taxonomy of dense, two-frame stereo methods designed to assess the different components and design decisions made in individual stereo algorithms. Using this taxonomy, we compare existing stereo methods and present experiments evaluating the performance of many different variants. In order to establish a common software platform and a collection of data sets for easy evaluation, we have designed a stand-alone, flexible C++ implementation that enables the evaluation of individual components and that can be easily extended to include new algorithms. We have also produced several new multiframe stereo data sets with ground truth, and are making both the code and data sets available on the Web.

7,458 citations


Cites background from "A Computational Approach to Edge De..."

  • ...Other traditional matching costs include normalized cross-correlation [51, 93, 19], which behaves similar to sumof-squared-differences (SSD), and binary matching costs (i.e., match / no match) [73], based on binary features such as edges [4, 50, 27 ] or the sign of the Laplacian [82]....

    [...]

Journal ArticleDOI
TL;DR: It is observed that the ranking of the descriptors is mostly independent of the interest region detector and that the SIFT-based descriptors perform best and Moments and steerable filters show the best performance among the low dimensional descriptors.
Abstract: In this paper, we compare the performance of descriptors computed for local interest regions, as, for example, extracted by the Harris-Affine detector [Mikolajczyk, K and Schmid, C, 2004]. Many different descriptors have been proposed in the literature. It is unclear which descriptors are more appropriate and how their performance depends on the interest region detector. The descriptors should be distinctive and at the same time robust to changes in viewing conditions as well as to errors of the detector. Our evaluation uses as criterion recall with respect to precision and is carried out for different image transformations. We compare shape context [Belongie, S, et al., April 2002], steerable filters [Freeman, W and Adelson, E, Setp. 1991], PCA-SIFT [Ke, Y and Sukthankar, R, 2004], differential invariants [Koenderink, J and van Doorn, A, 1987], spin images [Lazebnik, S, et al., 2003], SIFT [Lowe, D. G., 1999], complex filters [Schaffalitzky, F and Zisserman, A, 2002], moment invariants [Van Gool, L, et al., 1996], and cross-correlation for different types of interest regions. We also propose an extension of the SIFT descriptor and show that it outperforms the original method. Furthermore, we observe that the ranking of the descriptors is mostly independent of the interest region detector and that the SIFT-based descriptors perform best. Moments and steerable filters show the best performance among the low dimensional descriptors.

7,057 citations

References
More filters
Journal ArticleDOI
TL;DR: The theory of edge detection explains several basic psychophysical findings, and the operation of forming oriented zero-crossing segments from the output of centre-surround ∇2G filters acting on the image forms the basis for a physiological model of simple cells.
Abstract: A theory of edge detection is presented. The analysis proceeds in two parts. (1) Intensity changes, which occur in a natural image over a wide range of scales, are detected separately at different scales. An appropriate filter for this purpose at a given scale is found to be the second derivative of a Gaussian, and it is shown that, provided some simple conditions are satisfied, these primary filters need not be orientation-dependent. Thus, intensity changes at a given scale are best detected by finding the zero values of delta 2G(x,y)*I(x,y) for image I, where G(x,y) is a two-dimensional Gaussian distribution and delta 2 is the Laplacian. The intensity changes thus discovered in each of the channels are then represented by oriented primitives called zero-crossing segments, and evidence is given that this representation is complete. (2) Intensity changes in images arise from surface discontinuities or from reflectance or illumination boundaries, and these all have the property that they are spatially. Because of this, the zero-crossing segments from the different channels are not independent, and rules are deduced for combining them into a description of the image. This description is called the raw primal sketch. The theory explains several basic psychophysical findings, and the operation of forming oriented zero-crossing segments from the output of centre-surround delta 2G filters acting on the image forms the basis for a physiological model of simple cells (see Marr & Ullman 1979).

6,893 citations


"A Computational Approach to Edge De..." refers background or methods in this paper

  • ...This is similar to the selection criterion proposed by Marr and Hildreth [18] for choosing between different Laplacian of Gaussian channels....

    [...]

  • ...In fact, a one-dimensional Marr-Hildreth edge detector is almost identical with the operator we have derived because maxima in the output of a first derivative operator will correspond to zero-crossings in the Laplacian operator as used by Marr and Hildreth....

    [...]

  • ...The effect of the window function becomes very marked for large operator sizes and it is probably the biggest single reason why operators with large support were not practical until the work of Marr and Hildreth on the Laplacian of Gaussian....

    [...]

  • ...Directional operators very much like the ones we have derived were suggested by Marr [17], but were discarded in favor of the Laplacian of Gaussian [18]....

    [...]

  • ...There are also strong links with the Laplacian of Gaussian operator suggested by Marr and Hildreth [18]....

    [...]

Journal ArticleDOI
TL;DR: In this paper, the authors used the representations of the noise currents given in Section 2.8 to derive some statistical properties of I(t) and its zeros and maxima.
Abstract: In this section we use the representations of the noise currents given in section 2.8 to derive some statistical properties of I(t). The first six sections are concerned with the probability distribution of I(t) and of its zeros and maxima. Sections 3.7 and 3.8 are concerned with the statistical properties of the envelope of I(t). Fluctuations of integrals involving I2(t) are discussed in section 3.9. The probability distribution of a sine wave plus a noise current is given in 3.10 and in 3.11 an alternative method of deriving the results of Part III is mentioned. Prof. Uhlenbeck has pointed out that much of the material in this Part is closely connected with the theory of Markoff processes. Also S. Chandrasekhar has written a review of a class of physical problems which is related, in a general way, to the present subject.22

5,806 citations

Journal ArticleDOI

2,140 citations


"A Computational Approach to Edge De..." refers methods in this paper

  • ...It is also possible to include additional constraints by using a penalty method [15]....

    [...]

Book
01 Jan 1979
TL;DR: In this paper, the authors used the methodology of artificial intelligence to investigate the phenomena of visual motion perception: how the visual system constructs descriptions of the environment in terms of objects, their three-dimensional shape, and their motion through space, on the basis of the changing image that reaches the eye.
Abstract: This book uses the methodology of artificial intelligence to investigate the phenomena of visual motion perception: how the visual system constructs descriptions of the environment in terms of objects, their three-dimensional shape, and their motion through space, on the basis of the changing image that reaches the eye. The author has analyzed the computations performed in the course of visual motion analysis. Workable schemes able to perform certain tasks performed by the visual system have been constructed and used as vehicles for investigating the problems faced by the visual system and its methods for solving them.Two major problems are treated: first, the correspondence problem, which concerns the identification of image elements that represent the same object at different times, thereby maintaining the perceptual identity of the object in motion or in change. The second problem is the three-dimensional interpretation of the changing image once a correspondence has been established.The author's computational approach to visual theory makes the work unique, and it should be of interest to psychologists working in visual perception and readers interested in cognitive studies in general, as well as computer scientists interested in machine vision, theoretical neurophysiologists, and philosophers of science.

2,070 citations


Additional excerpts

  • ...Shape from motion [29], [13] can be used to infer the structure of three-dimensional objects from the motion of edge contours or edge points in the image plane....

    [...]