武汉理工大学数字图像处理英文课件 Chapter1（2）.pptVIP

Entropy Image Entropy Uniform Random Noise * Entropy is a concept which originally arose from the study of the physics of heat engines. It can be described as a measure of the amount of disorder in a system. An organized structure, such as a crystal or a living organism, is very highly ordered and consequently has low entropy. When the crystal is heated sufficiently, it melts and becomes liquid, a much less ordered state. When the organism dies, it decays and becomes completely disrupted. In either system, its entropy increases. Another way of expressing entropy is to consider the spread of states which a system can adopt. A low entropy system occupies a small number of such states, while a high entropy system occupies a large number of states. In the case of an image, these states correspond to the gray levels which the individual pixels can adopt. For example, in an 8-bit pixel there are 256 such states. If all such states are equally occupied, as they are in the case of an image which has been perfectly histogram equalized, the spread of states is a maximum, as is the entropy of the image. On the other hand, if the image has been thresholded, so that only two states are occupied, the entropy is low. If all of the pixels have the same value, the entropy of the image is zero. Note that, in this progression, as the entropy of the image is decreased, so is its information content. We moved from a full gray scale image, with high entropy, to a thresholded binary image, with low entropy, to a single-valued image, with zero entropy. Information, in this context, refers to the announcement of the unexpected. If the pixels of an image were inspected, and found to be the same. This information could have been communicated in a very short message. The information content is said to be low simply because it can be communicated in a short message. If the pixels are changing in unexpected ways, however, longer messages are required to communicate this fact and the infor