We present a novel simple technique for rapidly creating and presenting interactive immersive 3D exploration experiences of 2D pictures and images of natural and artificial landscapes. Various application domains, ranging from virtual exploration of works of art to street navigation systems, can benefit from the approach. The method, dubbed PEEP, is motivated by the perceptual characteristics of the human visual system in interpreting perspective cues and detecting relative angles between lines. It applies to the common perspective images with zero or one vanishing points, and does not require the extraction of a precise geometric description of the scene. Taking as input a single image without other information, an automatic analysis technique fits a simple but perceptually consistent parametric 3D representation of the viewed space, which is used to drive an indirect constrained exploration method capable to provide the illusion of 3D exploration with realistic monocular (perspective and motion parallax) and binocular (stereo) depth cues. The effectiveness of the method is demonstrated on a variety of casual pictures and exploration configurations, including mobile devices.