Computational models for image quality assessment (IQA) have been developed by exploring effective features that are consistent with the characteristics of a human visual system (HVS) for visual quality perception. In this paper, we first reveal that many existing features used in computational IQA methods can hardly characterize visual quality perception for local image characteristics and various distortion types. To solve this problem, we propose a new IQA method, called the structural contrast-quality index (SC-QI), by adopting a structural contrast index (SCI), which can well characterize local and global visual quality perceptions for various image characteristics with structural-distortion types. In addition to SCI, we devise some other perceptually important features for our SC-QI that can effectively reflect the characteristics of HVS for contrast sensitivity and chrominance component variation. Furthermore, we develop a modified SC-QI, called structural contrast distortion metric (SC-DM), which inherits desirable mathematical properties of valid distance metricability and quasi-convexity. So, it can effectively be used as a distance metric for image quality optimization problems. Extensive experimental results show that both SC-QI and SC-DM can very well characterize the HVS's properties of visual quality perception for local image characteristics and various distortion types, which is a distinctive merit of our methods compared with other IQA methods. As a result, both SC-QI and SC-DM have better performances with a strong consilience of global and local visual quality perception as well as with much lower computation complexity, compared with the state-of-the-art IQA methods.