函数的光滑化或正则化卷积应用两个统计独立变量X与Y的和的概率密度函数是X与Y的概率密度函数的卷积

http://graphics.stanford.edu/courses/cs178/applets/convolution.html

Convolution is an operation on two functions f and g, which produces a third function that can be interpreted as a modified ("filtered") version of f. In this interpretation we call g the filter. If f is defined on a spatial variable like x rather than a time variable like t, we call the operation spatial convolution. Convolution lies at the heart of any physical device or computational procedure that performs smoothing or sharpening. Applied to two dimensional functions like images, it's also useful for edge finding, feature detection, motion detection, image matching, and countless other tasks. Formally, for functions f(x) and g(x) of a continuous variable x, convolution is defined as:

where * means convolution and · means ordinary multiplication. For functions of a discrete variable x, i.e. arrays of numbers, the definition is:

Finally, for functions of two variables x and y (for example images), these definitions become:

and

In digital photography, the image produced by the lens is a continuous function f(x,y), Placing an antialiasing filter in front of the sensor convolves this image by a smoothing filter g(x,y). This is the third equation above. Once the image has been recorded by a sensor and stored in a file, loading the file into Photoshop and sharpening it using a filter g[x,y] is the fourth equation.