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In this paper, we examine the problem of fitting a circle to a set of noisy measurements of points on the circle's circumference. to be convenient for its ease of analysis and computation. Using Chan's circular functional model to describe the distribution of points, we perform a statistical analysis of the estimate of the circle's centre, assuming… (More)

The accurate fitting of a circle to noisy measurements of circumferential points is a much studied problem in the literature. In this paper, we present an interpretation of the maximum-likelihood estimator (MLE) and the Delogne-Kåsa estimator (DKE) for circle-center and radius estimation in terms of convolution on an image which is ideal in a certain sense.… (More)

In this paper, we present an interpretation of the Maximum Likelihood Estimator (MLE) and the Delogne-Kåsa Estimator (DKE) for circle-parameter estimation via convolution. Under a certain model for theoretical images, this convolution is an exact description of the MLE. We use our convolution based MLE approach to find good starting estimates for the… (More)

Tracking is regarded as one of the most fundamental tasks in computer vision. It is used in many computer vision applications in fields such as surveillance, robotic navigation and 3D reconstruction to name but a few. Despite decades of research, the goal of fully automatic tracking of arbitrary types of objects in real world conditions is still an open… (More)

In this paper, we examine the problem of fitting a circle to a set of noisy measurements of points from the circle's circumference, assuming independent, identically distributed GAUSSIAN measurement errors. We propose an algorithm based on Branch and Bound to obtain the Maximum Likelihood Estimate and show that this algorithm obtains the optimal estimate.… (More)

The accurate fitting of a line to noisy measurements of points along its length is a much studied problem in the literature. In this paper, we interpret the maximum-likelihood estimator (MLE) for line-direction and perpendicular offset estimation in terms of convolution on the RADON Transform of an image which is ideal in a certain sense. We use our… (More)

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