Image quality evaluation accurately is vital in developing image stitching algorithms as it directly reflects the algorithms progress. However, commonly used objective indicators always produce inconsistent and even conflicting results with subjective indicators. To enhance the consistency between objective and subjective evaluations, this paper introduces a novel indicator the Frechet Distance for Stitched Images (SI-FID). To be specific, our training network employs the contrastive learning architecture overall. We employ data augmentation approaches that serve as noise to distort images in the training set. Both the initial and distorted training sets are then input into the pre-training model for fine-tuning. We then evaluate the altered FID after introducing interference to the test set and examine if the noise can improve the consistency between objective and subjective evaluation results. The rank correlation coefficient is utilized to measure the consistency. SI-FID is an altered FID that generates the highest rank correlation coefficient under the effect of a certain noise. The experimental results demonstrate that the rank correlation coefficient obtained by SI-FID is at least 25% higher than other objective indicators, which means achieving evaluation results closer to human subjective evaluation.