Many quality metrics have been proposed for the compliance perception to assess haptic device performance and perceived results. Perceived compliance may be influenced by factors such as object properties, experimental conditions and human perceptual habits. In this paper, analysis of softness perception was conducted to find out relevant quality metrics dominating in the compliance perception system and their correlation with perception results, by expressing these metrics by basic physical parameters that characterizing these factors. Based on three psychophysical experiments, just noticeable differences (JNDs) for perceived softness of combination of different stiffness coefficients and damping levels rendered by haptic devices were analyzed. Interaction data during the interaction process were recorded and analyzed. Preliminary experimental results show that the discrimination ability of softness perception changes with the ratio of damping to stiffness when subjects exploring at their habitual speed. Analysis results indicate that quality metrics of Rate-hardness, Extended Rate-hardness and ratio of damping to stiffness have high correlation for perceived results. Further analysis results show that parameters that reflecting object properties (stiffness, damping), experimental conditions (force bandwidth) and human perceptual habits (initial speed, maximum force change rate) lead to the change of these quality metrics, which then bring different perceptual feeling and finally result in the change of discrimination ability. Findings in this paper may provide a better understanding of softness perception and useful guidance in improvement of haptic and teleoperation devices.