Oceanic eddies have a large impact on climate and human activities; consequently, it is worthwhile to characterise them. One of their main features is size; however, it is a difficult task to obtain user-independent estimates of this feature from brightness temperature maps for eddies near the Iberian Peninsula. The reason is that the current methods in the scientific literature are unable to handle the variability in the shape and size of these eddies as well as the weak temperature gradients associated with them, especially those found off Iberia or those methods employ user-defined values that influence the estimate of the eddies' sizes. Our new method solves these problems using orientation fields and clustering methods. Its outcome is an ellipse that characterizes the size of the eddies with good precision.