The generalized Hough transform(GHough) can be used effectively for detecting and extracting an arbitrary-shaped 2-D model in an input image. However, the main drawbacks of the GHough are both heavy computation and an excessive storage requirement. Thus, most of the researches so far have focused on reducing both the time and space requirement of the GHough. But it is still not clear how well their improved algorithms will perform under various noise in an input image. Thus, this paper proposes a new framework that can measure the performance of the GHough quantitatively. For this purpose, we view the GHough as a detector in signal detection theory and the ROC curve will be used to specify the performance of the GHough. Finally, we show that we can evaluate the GHough under various noise conditions in an input image.