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. / Department of Mathematical Sciences

In this master thesis, it is proposed to solve in the large thedifferential equationZ2(d2y/dz2) + z (dy/dz) (b0+b1zm) + (c0+c1zm)y = 0Here, m is an arbitrary positive integer, the variable z is complex as are the constants bi, ci (i = 0, 1). It is also assumed that the roots of the indicial equation about the regular singular point z=0 are such that their difference is incongruent to zero modulo m.

Under consideration are two-point boundary value problems for a system of second order differential equations which contains a small parameter multiplying the highest dereivatives. We prove the existence of solutions exhibiting left and right boundary layers by constructing upper and lower solutions of the system. The behavior of the solutions as the parameter tends to zero is also established. Of special interest is the existence of a compound boundary layer (i.e., one involving two scales) at the left endpoint of the interval.

No description available.

The asymptotic behaviour of nonoscillatory solutions of second order nonlinear ordinary differential equations is studied. Necessary and sufficient conditions are given for the existence of positive solutions with specified asymptotic behaviour at infinity. Existence of nonoscillatory solutions is established using the Schauder-Tychonoff fixed point theorem. Techniques such as factorization of linear disconjugate operators are employed to reveal the similar nature of asymptotic solutions of nonlinear differential equations to that of linear equations. Some examples illustrating the asymptotic theory of ordinary differential equations are given. / Science, Faculty of / Mathematics, Department of / Graduate

Abstract not available

In order to introduce the investigation contemplated in this thesis, let us consider the differential equation d3y d2y dyz3 ____+ z2___(b0 + blzm) + z - (c0 + clzm) dz3 dz2 dz+ (d0 + dlzm + d2z2m) y = 0Here, m is an arbitrary positive integer and the variable z is complex as are the constantsbi,ci (i=0,1) and di (i=0,1,2) with d2≠0. It is also assumed that the difference of no two roots of the indicial equation about z = 0 is congruent to zero modulo m.Ball State UniversityMuncie, IN 47306

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