fitting curve to binary object

hello, can any one please help me fit the best curve to the following binary image?

 i meaning some thing like the red curve.

[Guillaume]

What do you call a curve? A spline? A polynomial equation? What makes the red curve you've drawn any better than anything else?

Wouldn't the best curve be simply all the boundary pixels (which you'd obtain simply with bwboundaries)?

[Abo]

the red is just an example. i'm not sure how to call it!! curve, spline.. just wanna find it in some part of boundaries, like in the following photo, so can suggest any idea? thanks

[Guillaume]

In order to fit a set of points to something, you first need to define what that something. A curve can mean anything. a line, a spline, a quadratic (like in your first example), a half-ellipse (like in your second example), etc. Until you've decided what class of curve you want to fit, you won't be able to do any fitting.

As I said, the boundary pixels returned by bwboundaries is a curve.

[Abo]

what do you called the green line the last photo (above)? i meant the same thing. how can I find it by helping bwboundaries?

[Guillaume]

That green line looks like a half ellipse to me.