Basic info can be read in Wikipedia: Receiver operating characteristic, https://en.wikipedia.org/wiki/Receiver_operating_characteristic

ROC curves – what are they and how are they used?

https://acutecaretesting.org/en/articles/roc-curves-what-are-they-and-how-are-they-used

Dr. Alshujeary,

Considering that ROC is receiver operating characteristic, maybe this article will help you: Article 3D ROC Analysis for Medical Imaging Diagnosis

Well , realistic (rather easier) is either a polygon (with limited number of sides - rectangle ) curve is better !!

Generating a parametric circle equation and matching with the ROI of interest needs - center fixing / radius calculation for which we need bounds (at least) .

Look @ my RG page you have script for circle generation (for Iris ) feel free to use .

An interesting and useful alternative to ROC analysis is AUC (area under curve) - see Ling С. AUC: a statistically consistent and more discriminating measure than accuracy / С. X. Ling, J. Huang, H. Zhang // Proceedings of IJCAI 2003. - Acapulco, Mexico, 2003. - P. 519-524. It allows characterizing detection by the only parameter

Accuracy (Acc), Sensitivity (Sn), Specificity (Sp), and the area under a Receiver Operating Characteristic (ROC) curve, also known as Area Under the Curve (AUC) are four commonly used parameters to compare the performance of the competing techniques.

Accuracy shows the overall segmentation performance. Sensitivity indicates effectiveness in detection of pixels with positive values: specificity measure the detection of pixels with negative values.

Important parameter is ROC curve, also known as AUC, it has the ability to reflect the trade-offs between the sensitivity and specificity. Note that an AUC of 0.50 means that the classification is equivalent to a pure random guess, and an AUC of 1.0 means that the classifier distinguishes class examples perfectly. The most frequently used performance measure extracted from the ROC curve is the value of the AUC which is 1 for an optimal system.

Article A Morphological Hessian Based Approach for Retinal Blood Ves...

The ROC curve is a fundamental tool for diagnostic test evaluation. In a ROC curve the true positive rate (Sensitivity) is plotted in function of the false positive rate (100-Specificity) for different cut-off points of a parameter.

Each point on the ROC curve represents a sensitivity/specificity pair corresponding to a particular decision threshold. The area under the ROC curve (AUC) is a measure of how well a parameter can distinguish between two diagnostic groups (diseased/normal).