# Efficient Curve Detection using the Gauss-Newton Method

# Efficient Curve Detection using the Gauss-Newton Method

The problem of finding curves, like straight lines, circles, or ellipses in images is very important in computer vision. There are already well-established approaches to such problems that rely on voting cells in the parameter space (Rough transform) or sampling techniques like RANSAC.In this talk we will present a new approach, based on continuous optimization methods, that does not depend on votes or sampling. In our approach, model fitting is expressed as a Low Order-Value optimization (LOVO) problem, which consists of the minimization of an order-value function. An efficient Gauss-Newton algorithm is then used to solve the LOVO problem from many starting points.

We will also present some initial numerical testing, focusing on searching for circles, comparing the LOVO approach to classical computer vision methods. The LOVO approach proves to be robust, precise and to possess a speed advantage as the size of the image increases.