Non-parametric Nearest-Neighbour (NN) image classification is desired in certain applications, because no intensive learning is required. Naive Bayes Nearest Neighbour (NBNN) and its improved version, Local Naive Bayes Nearest Neighbour (Local NBNN), are two impressive classifiers that keep a good balance between algorithm accuracy and complexity. Instead of computing image-to-image (I2I) distances, these two algorithms calculate image-to-class (I2C) distances. As a consequence, the local image descriptors are not quantised and the performance of such an image classifier is thereby enhanced. In this paper, by applying the concept of saliency detection to the calculation of I2C distances, we separate each training image from each category into two parts: foreground and background. Then we calculate I2C distances for foreground and background to classify the test image. Afterwards, the scores presented by the foreground and the background are used to correct the responses generated by the original NBNN or Local NBNN. Moreover, it is observed that a prior clustering inside each training category is able to reduce time consumption significantly without sacrificing system performance. By combining the contributions above, our approach is superior to the original NBNN and Local NBNN classifiers in terms of both efficiency and accuracy on three datasets: Pami-09, 15-Scene and Caltech-5.