图像处理中卷积理论的数学基础

为了使自然获取的图像利于人们判读或计算机识别,就要对图像进行增强或者复原处理,从而使图像增强与复原这两种看似矛盾的技术构成了数字图像处理领域的主要内容。众所周知,滤波器理论是这两门技术的核心内容。本文主要是从数字图像处理中所运用的滤波器的卷积理论入手,从数学角度严格的论述了数字图像处理中常用的滤波器的卷积理论的内容,完善其数学理论基础,以便在实际应用上能更准确和方便的应用相关理论。作为该理论演示,文章的最后给出了相关的实验结果。

Mathematical Theory Of Convolution On Image Processing

A mathematical method is offered for expressing some problems on digital image processing. The theory is mainly built on convolution. A strict proof about the theory is given firstly. Then, most attention is paid to explain the relationship between the digi-tal image processing and the convolution. Due to the mathematical foundation, the dilemma between the image detail and the image noise is clearly shown. Balance control on them is then weighed by a parameter. Finally experiment results are shown to test the the-ory at the end of the paper.