Fast and numerically stable circle fit

We develop a new algorithm for fitting circles that does not have drawbacks commonly found in existing circle fits. Our fit achieves ultimate accuracy (to machine precision), avoids divergence, and is numerically stable even when fitting circles get arbitrary large. Lastly, our algorithm takes less than 10 iterations to converge, on average.Comment: 16 page

The unsupervised learning algorithm for detecting ellipsoid objects

This paper is devoted to the analysis and implementation of the algorithms for automatic detection of the circular objects in the image. The practical aim of this task is development of the algorithm for automatic detection of log abuts in the images of roundwood batches. Based on literature review four methods were chosen for the further analysis and the best performance out of them was provided by ELSD algorithm. Some modifications were implemented to the algorithm to fulfill the requirements of the given task. After all, the modified ELSD algorithm was tested on the dataset of the images. The relative accuracy of the algorithm in comparison with manual measurement is 95.2% for the images with total area of background scene less than 20%. © 2019 International Association of Computer Science and Information Technology

Maximum likelihood estimation for disk image parameters

We present a novel technique for estimating disk parameters (the centre and the radius) from its 2D image. It is based on the maximal likelihood approach utilising both edge pixels coordinates and the image intensity gradients. We emphasise the following advantages of our likelihood model. It has closed-form formulae for parameter estimating, requiring less computational resources than iterative algorithms therefore. The likelihood model naturally distinguishes the outer and inner annulus edges. The proposed technique was evaluated on both synthetic and real data.Comment: 13 pages, 4 figures. in IEEE Signal Processing Letter

Maximum likelihood estimation of circle parameters via convolution

Copyright © 2006 IEEEThe 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. We use our convolution-based MLE approach to find good estimates for the parameters of a circle in digital images. In digital images, it is then possible to treat these estimates as preliminary estimates into various other numerical techniques which further refine them to achieve subpixel accuracy. We also investigate the relationship between the convolution of an ideal image with a “phase-coded kernel” (PCK) and the MLE. This is related to the “phase-coded annulus” which was introduced by Atherton and Kerbyson who proposed it as one of a number of new convolution kernels for estimating circle center and radius. We show that the PCK is an approximate MLE (AMLE). We compare our AMLE method to the MLE and the DKE as well as the Cramér–Rao Lower Bound in ideal images and in both real and synthetic digital images.Emanuel E. Zelniker, Student Member, IEEE, and I. Vaughan L. Clarkso