8 bit灰度图像分层信息量研究

Research on the Information Content of 8 Bit Gray Image

灰度图像按比特位从高到低可以分为8 bit。其中,高比特平面包含大量有视觉意义的数据,而低比特平面只含有少量有视觉意义的数据。这个特性在图像识别和压缩等领域有重要的应用。对此,应用信息论的方法证明其中原因。首先,用直方图数据说明低比特平面灰度直方图的分布比高比特平面平滑,从而说明视觉信息与熵值有关;其次,从数学上严谨地证明,同一图像比特平面从高到低,其熵值单调递增,从而证明比特平面包含的视觉信息是单调递减的;最后,通过实验对不同图像的比特平面进行熵值计算,得到的结果与之前的证明完全一致。

Grayscale images can be divided into 8 bit from high to low.Among them,the high bit plane contains a large amount of visually meaningful data,while the low bit plane only contains a small amount of visually meaningful data.This feature has important applications in fields such as image recognition and compression.This article adopts the method of information theory to prove the reason for this.Firstly,using histogram data to illustrate that the distribution of low bit plane grayscale histograms is smoother than that of high bit planes,thus demonstrating that visual information is related to entropy value;secondly,mathematically rigorously prove that the entropy value of the same image bit plane increases monotonically from high to low,thereby proving that the visual information contained in the bit plane decreases monotonically;finally,entropy calculation was performed on the bit planes of different images through experiments,and the results obtained were completely consistent with the previous proof.