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Salient areas in natural scenes are generally regarded as areas which the human eye will typically focus on, and finding these areas is the key step in object detection. In computer vision, many models have been proposed to simulate the behavior of eyes such as SaliencyToolBox (STB), Neuromorphic Vision Toolkit (NVT), and others, but they demand high computational cost and computing useful results mostly relies on their choice of parameters. Although some region-based approaches were proposed to reduce the computational complexity of feature maps, these approaches still were not able to work in real time. Recently, a simple and fast approach called spectral residual (SR) was proposed, which uses the SR of the amplitude spectrum to calculate the image's saliency map. However, in our previous work, we pointed out that it is the phase spectrum, not the amplitude spectrum, of an image's Fourier transform that is key to calculating the location of salient areas, and proposed the phase spectrum of Fourier transform (PFT) model. In this paper, we present a quaternion representation of an image which is composed of intensity, color, and motion features. Based on the principle of PFT, a novel multiresolution spatiotemporal saliency detection model called phase spectrum of quaternion Fourier transform (PQFT) is proposed in this paper to calculate the spatiotemporal saliency map of an image by its quaternion representation. Distinct from other models, the added motion dimension allows the phase spectrum to represent spatiotemporal saliency in order to perform attention selection not only for images but also for videos. In addition, the PQFT model can compute the saliency map of an image under various resolutions from coarse to fine. Therefore, the hierarchical selectivity (HS) framework based on the PQFT model is introduced here to construct the tree structure representation of an image. With the help of HS, a model called multiresolution wavelet domain foveation (MWDF) is p- - roposed in this paper to improve coding efficiency in image and video compression. Extensive tests of videos, natural images, and psychological patterns show that the proposed PQFT model is more effective in saliency detection and can predict eye fixations better than other state-of-the-art models in previous literature. Moreover, our model requires low computational cost and, therefore, can work in real time. Additional experiments on image and video compression show that the HS-MWDF model can achieve higher compression rate than the traditional model.