Detecting Edges

by Sam Maniscalco

Submitted : Spring 2009

In human vision the first level of processing is edge detection. Edges are determined by the transitions from dark points to bright points in an image. For this edge detection project I was given an edge profile model representing a boundary or edge in an image. From this model we can determine the strength or repose of the edge, the width of the edge, and either the transition from dark to bright to dark or the transition from bright to dark to bright. The first task of the project was to take the given edge profile and determine the type of edge that is represented and the characteristic of the edge such as that of the varying width of the edge as the variable a is either increased or decreased. With the next problem, using the fact that an exponential function is a derivative of itself and the chain rule, the derivate of the edge profile model was calculated. After finding the derivative of the edge profile model the final questions involved utilizing the properties of the function defined by the derivative. Finding the derivate of the derivate of the edge profile model allowed the discovery of the maximum and minimum values of x for the derivate of the edge profile model, at the time as graphing the derivate of the edge profile model allows an understanding of how the variable a affects the function. In the final step, using the characteristic of the derivative of the edge profile, it can be seen that only the numerator portion of the derivate needs to be examined to find the location where the value of the derivate is equal to zero.

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