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Saliency detection is one of the key issues in simulating visual attention selection. Most attention models adopt the competitive structure to simulate the human visual system. Although these models provide remarkable results and convincing biological plausibility, they are still confronted with many difficulties in practical applications because of their extreme time cost and parameter sensitivity. Recently, a new saliency detection approach based on Fourier transform, as represented by spectral residual (SR) and phase Fourier transform (PFT), has been attracting much attention for its excellent accuracy and computational speed. All these models can be unified into one framework called amplitude spectrum modulation (ASM). The aim of this paper is to explore the intrinsic mechanism of ASM and develop an advanced ASM model. After analyzing SR and PFT, we give a mathematical description for the fundamental idea and the inherent limitations of the existing ASM models. A new saliency detective model, based on the scale-invariant ASM, scene and context-based modulation, and competitive structure, is also proposed breaking through the limitations of the traditional ASM models. Simulation results suggest that the proposed model is more accurate in predicting human eye fixation and is more robust against different types of stimulus when compared with competing models.