图像维数计算方法及其实质研究

Study of the Calculation Method of True Color Image Dimension and Its Nature

基于颜色单元体模型,本文提出了一种间接量测表面形貌的新方法——真彩图像维数计算方法,并通过激光表面仪扫描实验对此进行了验证。该计算方法的提出,使在表面形貌的实验研究中用拍摄数码照片方法取代激光表面仪扫描成为可能。比较研究显示,该方法具有简单、方便、直观和扫描范围大等优势,是表面形貌实验研究手段上的一大改进。本文还分别探讨了二值化图像,灰度图像,真彩图像的分形特性,剖析了三类图像维数的物理实质。比较研究结果显示,对于同一试样,真彩图像维数最大,灰度图像次之,二值化图像维数最小,其维数在区间[1,2]内。以此说明,二值化图像维数是曲线维数,灰度图像维数仅考虑了颜色明度值的影响,只有真彩图像维数充分考虑了色彩、色饱和度和明度值的"贡献",该维数才是"全局"意义上的图像维数。

Rough color surface of joint is established by color unit model. Its fractality is investigated by cubic covering method. Dimension theory of true color images is proposed in this paper. Validation of image dimension calculation theory was carried out by numerical experiment and laser profilometer experiment, which indicates that principle of image dimension is reliable. Fractal characteristics of binary image, gray one and true color image were also investigated and presented in this paper; and their physical nature was analyzed. Comparison proves that true color image has the most dimension, gray image possesses the second position and binary image is listed last, which range is greater than 1 and less than 2 under same specimen condition. It indicates that binary image dimension is curve dimension and gray image dimension only takes into account effect of illumination and it is true color image dimension that takes into account sufficiently contribution of hue, color saturation, illumination. So it is ＂global image dimension＂.