It is widely recognized that the accuracy of colocalization measurements is dependent upon the quality of the source images. We demonstrate that, as the image quality increases, the measured colocalization, using the Pearson and Spearman rank correlation coefficients, approaches the true colocalization asymptotically. This means that in practice it is difficult to obtain images of sufficient quality for accurate measurements. We introduce the replicate-based noise corrected correlation (RBNCC) which aligns the measured colocalization with the true colocalization: a noise measurement is made for each fluorophore from a pair of replicate images, the two noise measurements are combined to generate a correction factor which is applied to the measured colocalization between the two fluorophores. In consequence, accurate measurements can be obtained even with noisy images, making RBNCC especially attractive for live imaging. Even with images of apparently good quality we found an average discrepancy of about 20% between the measured and corrected colocalization. A case is made for using the Spearman rank coefficient instead of the Pearson coefficient to measure colocalization.