# Recognition and Fitting of Circles and Ellipses in Digital Image.

December 1993

## Date of Award

Winter 12-12-1994

## Institute Name (Publisher)

Indian Statistical Institute

## Document Type

Master's Dissertation

## Degree Name

Master of Technology

Computer Science

## Department

Computer Vision and Pattern Recognition Unit (CVPR-Kolkata)

## Supervisor

Chaudhuri, Bidyut Baran (CVPR-Kolkata; ISI)

## Abstract (Summary of the Work)

There are two stages of parametric shape analysis in image processing & pmttorn recognition.1) Detecting the points which belong to a particular shape.2) Optimum curve fitting from the set of points. For detection we will use Hough Transform ( H T ). Though Hough transform is a very useful method for shape detection & fitting but it does not optimize any criterion of fitting. For optimum fitting two methods can be mentioned.1) Conic section fitting by regression (2].2) Closed form expression [1]Both optimizing some objective criterion.In Chaudhuri[1) a generalized circle fitting on multidimensional weighted data is described. It is shown that the method is effective even if the data set makes an of 90 degree. this method is used in the program to find arc parameter (centre & radius) for a single circle. When a set of points are given we assume in this case that they belong to the same circle. Next, we tested if multiple circles can be fitted in a single image space using the same technique. The problem involves both localization and fitting of circles. We have observed that for two circles localization and fitting can be effectively done when they are separated by an order of (rl+r2) where rl and r2 are the radius of two circles.In the same paper[1] it is noted that iterative circle fitting Enethod [2] minimizes exactly same form of error function as in the method due to Thomas and Chan[3] and they should lead to the same value of circle parameters. It is proved that they are indeed the same. An interesting problem is to find the location of centre of a circle from the supplied points when the radius is knowm. Although less number of parameters are involved, it is seen that no closed form expression for the parameters are found by optimizing the objective function. On the other hand if the centre is given, the radius of the optimum circle can be found in closed form.

ProQuest Collection ID: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:28843326

ISI-DISS-1993-14