cubic convolution interpolation at boundaries?
- From: Markus <iandjohn@xxxxxxxxx>
- Date: 24 Apr 2007 23:35:14 -0700
I am using the symmetric cubic convolution kernel ("Catmull-Rom
splines") to interpolate data over a limited range in a variable x.
For the interpolation I am using between 8 and 12 nodes which are
equidistant in x.
Example: The interpolated function between nodes 4 and 5 is computed
based on the data points at nodes 3,4,5,6
My question is: how should I treat the ranges near the boundary?
If I am using 10 nodes, how should I interpolate the data between node
9 and 10? So far I am using linear interpolation here - but this is
conceptually ugly (and it's not precise, although the latter is not my
biggest problem since I want a _nice_ solution).
I am especially worried that in my current approach the interpolated
function has no continuous 1st derivative at node 9.
Is there a solution, in which I could use e.g. a non-symmetric
convolution kernel to interpolate between nodes 9 and 10, based on the
nodes 8,9,10 or maybe 7,8,9,10 - and which results in a continuous 1st
derivative everywhere?
I have not found any discussion about the boundary-treatment in the
literature (and neither on the Google-wide web). In image processing
sometimes people mirror the image at the boundaries (i.e. they would
introduce a hypothetical 11th node for which the data value is set
equal to the data at the 9th node and interpolate using the data
points at nodes 8,9,10,11) - but this would not work in my case.
Any help is appreciated!
Markus
.
- Prev by Date: cubic convolution interpolation at boundaries?
- Next by Date: Hodge decomposition
- Previous by thread: Re: cubic convolution interpolation at boundaries?
- Next by thread: cubic convolution interpolation at boundaries?
- Index(es):
Relevant Pages
|
