Spline interpolation degree question

In summary, the conversation discusses the issue of unstable high order spline interpolation in image tracking, with the best result being degree 3. The speaker questions the behavior of spline interpolation and wonders if there is a numerical explanation for it. They also mention using the Python Scipy library for their interpolation. It is suggested that the issue could be due to large differences in the distances between data points.
  • #1
sandon
18
1
Hi,

I working on code that does image tracking with missing pixels, but I noticed that higher ordered spline interpolation is unstable. Found through trial and error that the best result is degree 3, picture related. I always thought that spline interpolation does not display behaviours shown in the picture because they are conducted piece by piece over the data set. Is there a numerical explanation for this behaviour?

P.S interpolation done in python with scipy library
 

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  • #2
If the distances between your data points differ by large factors I'm not surprised that high order splines do strange things. It is the same behavior you see outside the interpolation range (as extrapolation).
 

1. What is spline interpolation degree?

Spline interpolation degree is a term used in mathematics and computer science to describe the number of polynomial segments used to approximate a curve or function. It determines the level of smoothness of the interpolated curve.

2. How is spline interpolation degree calculated?

The spline interpolation degree is calculated based on the number of data points and the desired level of smoothness. It is typically denoted by the letter "k" and can range from 1 (linear) to n-1 (where n is the number of data points) for a spline interpolation curve to be continuous and differentiable.

3. What is the difference between a low and high spline interpolation degree?

A low spline interpolation degree (such as 1 or 2) results in a less smooth curve that may not pass through all the data points. A high spline interpolation degree (such as n-1) results in a smoother curve that passes through all the data points, but may not accurately reflect the true behavior of the underlying function.

4. How does the choice of spline interpolation degree affect the accuracy of the curve?

The choice of spline interpolation degree can greatly impact the accuracy of the interpolated curve. A low degree may result in a curve that is too rigid and does not accurately fit the data, while a high degree may result in a curve that is too flexible and overfits the data. It is important to choose a degree that balances smoothness and accuracy for the specific data set.

5. Are there any limitations to using spline interpolation degree?

While spline interpolation can be a useful tool for approximating curves and functions, it does have some limitations. These include the inability to extrapolate beyond the given data points, and the potential for errors if the data points are not evenly spaced. Additionally, the choice of spline interpolation degree may be subjective and may not accurately reflect the true behavior of the underlying function in some cases.

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