掩模的矩阵乘法表示及其应用

Matrix Multiplicative Representation of Mask and Its Application

通过对掩模的作用原理进行研究,首先给出了行列成比例的二维掩模的矩阵乘法表示,进而得到了掩模的矩阵乘法实现方法,该方法不仅提高了掩模实现的速度,而且避免了处理图像时的加边运算;其次,提出了基于边界的掩模概念,并给出了相应的矩阵乘法表示,在保持原图像大小不变的前提下,避免了算术均值掩模处理后图像的黑边现象;最后,仿真实验验证了以上结论的正确性。尽管以上结论是针对行列成比例的掩模得到的,但仍不失一般性,因为大部分的掩模均可转化为行列成比例的掩模的和或差。

Through studying the principle of mask, firstly it gives the matrix multiplicative representation of mask and the fast implementing method of mask which largely improve the speed of mask implementing and avoid the operation of adding edge before processing under keeping the size of the original image. Secondly,it proposes a concept of edge - based mask,and gives the matrix multiplicative representation correspondingly that can avoid black edge in the processed image by the mean mask. The results of digital experiments indicate the involved conclusion. Although this conclusion is obtained by a special kind of masks that row and column are proportioned, it is also universal. Because most of masks can be represented by the summation or difference of the proportioned masks.