Property of correlation between entropy and focus

It makes all the difference whether one recognizes objects through the clear or fuzzy image through a video. That is a so-called garbage in garbage out. In an imaging automatic identification system, in order to recognize the objects in a frame of a video correctly, it is very important to extract the clearest frame from the video. Based on observing the distribution of histogram for each frame from a section of video with the same scene, we find that the distribution range of histogram is wider if the frame is clear, otherwise, the distribution range of histogram is narrower when the frame is fuzzy. On the other hand, clear image contains higher entropy and fuzzy image contains lower entropy. According to this fact, the relationship between entropy and the clarity of an image is proposed in this paper. By using this property, the clearest image is extracted from a section of video with the same scene automatically. Experiments are carried out for some samples with scenes of different distance to demonstrate the correctness of the proposed property.