This paper presents a detailed error analysis of geometric hashing for 2D object recogition. We analytically derive the probability of false positives and negatives as a function of the number of model and image, features and occlusion, using a 2D Gaussian noise model. The results are presented in the form of ROC (receiver-operating characteristic) curves, which demonstrate that the 2D Gaussian error model always has better performance than that of the bounded uniform model. They also directly indicate the optimal performance that can be achieved for a given clutter and occlusion rate, and how to choose the thresholds to achieve these rates.