# The global behavior of solutions of a certain third order differential equation

Cardinal Scholar
 dc.contributor.advisor Puttaswamy, T. K. en_US dc.contributor.author Shi, Changgui en_US dc.date.accessioned 2011-06-03T19:36:01Z dc.date.available 2011-06-03T19:36:01Z dc.date.created 1992 en_US dc.date.issued 1992 dc.identifier LD2489.Z78 1992 .S55 en_US dc.identifier.uri http://cardinalscholar.bsu.edu/handle/handle/184401 dc.description.abstract In computer vision, object recognition involves segmentation of the image into separate components. One way to do this is to detect the edges of the components. Several algorithms for edge detection exist and one of the most sophisticated is the Canny edge detector.Canny [2] designed an optimal edge detector for images which are corrupted with noise. He suggested that a Gaussian filter be applied to the image and edges be sought in the smoothed image. The directional derivative of the Gaussian is obtained, then convolved with the image. The direction, n, involved is normal to the edge direction. Edges are assumed to exist where the result is a local extreme, i.e., where∂2 (g * f) = 0.(0.1)_____∂n2In the above, g(x, y) is the Gaussian, f (x, y) is the image function and The direction of n is an estimate of the direction of the gradient of the true edge. In this thesis, we discuss the computational algorithm of the Canny edge detector and its implementation. Our experimental results show that the Canny edge detection scheme is robust enough to perform well over a wide range of signal-to-noise ratios. In most cases the Canny edge detector performs much better than the other edge detectors. dc.description.sponsorship Department of Mathematical Sciences dc.format.extent ii, 30 leaves ; 28 cm. en_US dc.source Virtual Press en_US dc.subject.lcsh Differential equations -- Asymptotic theory. en_US dc.title The global behavior of solutions of a certain third order differential equation en_US dc.description.degree Thesis (M.S.) dc.identifier.cardcat-url http://liblink.bsu.edu/catkey/834515 en_US
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• Master's Theses [5454]
Master's theses submitted to the Graduate School by Ball State University master's degree candidates in partial fulfillment of degree requirements.