convolution

Convolution operation plays a vital role in image processing. This is used in many applications in image processing, such as blurring, sharpening, embossing and edge detection etc. By studying this article, one can understand the concept of Convolution operation in image processing in theoretical and practical manner. In addition, it explains the differences between convolution and correlation operations in mathematical and practical manner.

Before understanding the convolution operation, first let me explain the correlation operation in theoretical and mathematical manner. If we want to apply correlation or convolution operation in image processing, we have to define a kernel . The kernel is a small matrix. In general, the kernel is square matrix and the dimension is in odd, for example, 3 x 3, 5 x 5, 7 x 7 ........ etc. The following 3 X 3 kernel has been taken to explain the correlation and convolution operations in this article.

Correlation

correlation is the process of adding each element of the image to its local neighbors by the weighted kernel. For better understanding, the part of image of size 3 x 3 has been taken as follows.

The correlation is the process of finding the sum of product of similar entries between the kernel and part of the image. Mathematically, it can be expressed as depicted in Equation 1.

In the resulting image, the element at coordinates [1,1] is updated with the resultant value of correlation as shown in Equation 1. This process is subsequently applied to find the rest of the values of elements in the resulting image as depicted in following.

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