Smooth Jagged Lines into Curves

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If there are algorithms that approximates curves into jagged lines, is there any way to do it in reverse? Given a jagged lines, we have to smoothens the lines into forming curves?

My purpose is I want to smoothen the first image borders but not removing the curves. I want it to look naturally as the second image.

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Given a smooth curve, take discrete points along it and join adjacent pairs by line segments.

Given such a sequence of connected line segments, find their intersection points and use a B spline fit.