What is the right term for this task - blurring or edge smoothing

I am new to image processing, so please bear with me for this basic question.

I have done some searches but still not sure about the best keyword for finding more help. What I want to achieve is this:

An image of wood patterns with dark and light areas. Between the dark and light areas, there are sharp edges. What I want to do is to make the change very smooth and slow (without sharp edges). How smooth and slow depends on the distance between the edges (or size of the light areas between any two dark areas). I was thinking about using opencv. Can someone give a hint on what exactly this is? I found some tutorials but this doesn’t sound like blurring. Is this edge smoothing or what? Thanks so much.

This is promissing: Fast blur in JAVA2D

Try to keep post that are of the same topic under the same heading aka. same post. Keeps from spreading same topic all over the forum.