In medical imaging, model observers such as the "Hotelling observer" and the "Non Prewhitening Matched Filter" have been proposed to detect objects in X-ray images. These models, based on decision theory, are applied over the entire image. In this paper, we developed a model that mimics some processes of human visual perception. The proposed model is locally applied on some particular areas that correspond to the salient areas of the object. By doing this, the model mimics the sequence of eye fixations that we make when we explore an image for example in order to detect an object. The study is divided into three parts: a psychophysical experiment to obtain human's performance to detect various objects in noises, a theoretical part to develop the proposed model, and finally, a result part. During the experiment, several participants were asked to detect objects in noisy images using a free search task. The luminance contrast of objects was adaptively adjusted according to their responses to obtain a percentage of correct detection for each object of 50 %. The proposed model, based on decision theory, was applied locally on some areas of the image that has a size corresponding to the high visual acuity of foveal vision. Areas were chosen according to their high saliency values computed through a bio-inspired model of visual attention. For each area, our model returned a detectability index. By supposing statistical independence between areas, the local indexes are combined into a global detectability index. Results show that the proposed model fits the results of the psychophysical experiment and outperforms classical models of the literature.