Graduate Spline interpolation degree question

Click For Summary
SUMMARY

The discussion focuses on the instability of higher-order spline interpolation when applied to image tracking with missing pixels. The user discovered that degree 3 spline interpolation yields the best results, contrary to their initial belief that spline interpolation behaves consistently across datasets. The instability is attributed to varying distances between data points, which can lead to erratic behavior, especially during extrapolation. The implementation was conducted using the SciPy library in Python.

PREREQUISITES
  • Understanding of spline interpolation techniques
  • Familiarity with Python programming
  • Experience with the SciPy library
  • Knowledge of numerical stability in interpolation methods
NEXT STEPS
  • Research the properties of cubic spline interpolation
  • Explore the effects of data point distribution on interpolation accuracy
  • Learn about extrapolation issues in numerical methods
  • Investigate alternative interpolation techniques in SciPy
USEFUL FOR

Data scientists, image processing engineers, and developers working on numerical methods for interpolation and data reconstruction.

sandon
Messages
15
Reaction score
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
 

Attachments

  • BSpline4079_28.png
    BSpline4079_28.png
    15.3 KB · Views: 535
Physics news on Phys.org
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).
 

Similar threads

MATLAB Bilinear spline interpolation MATLAB using MESHGRID and SURF
  • · Replies 2 ·
Replies
2
Views
3K
How to determine the minimum grid length | Numerical Plasma Physics
  • · Replies 7 ·
Replies
7
Views
2K
Requesting suggestions for languages, libraries, and architectures for parallel (and sometimes non parallel) numerical and scientific computations
  • · Replies 8 ·
Replies
8
Views
4K
Polar and Cartesian graphs not matching up
  • · Replies 7 ·
Replies
7
Views
2K
Programs How good is this applied math program?
  • · Replies 13 ·
Replies
13
Views
3K
Homemade Quantum Eraser Experiment revisited with photos and full text
  • · Replies 13 ·
Replies
13
Views
7K
Attn Wii Gamers: Best HDTV for the Wii
  • · Replies 6 ·
Replies
6
Views
13K
The Scientist as Hero - or not
  • · Replies 1 ·
Replies
1
Views
3K
Medical The Human Mind and Predicting Behavior
  • · Replies 3 ·
Replies
3
Views
7K
Mathematica This Week's Finds in Mathematical Physics (Week 264)
  • · Replies 6 ·
Replies
6
Views
5K