[Octave-bug-tracker] [bug #61754] Bicubic interpolation in interp2() incompatible with Matlab

[Christof Kaufmann]

URL:
  <https://savannah.gnu.org/bugs/?61754>

                 Summary: Bicubic interpolation in interp2() incompatible with
Matlab
                 Project: GNU Octave
            Submitted by: christofkaufmann
            Submitted on: Mon 03 Jan 2022 01:25:04 AM UTC
                Category: Octave Function
                Severity: 3 - Normal
                Priority: 5 - Normal
              Item Group: Matlab Compatibility
                  Status: None
             Assigned to: None
         Originator Name: Christof Kaufmann
        Originator Email: 
             Open/Closed: Open
                 Release: dev
         Discussion Lock: Any
        Operating System: Any

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Details:

Using "cubic" for the method argument of interp2 is just an alias for "pchip"
(piecewise cubic Hermite interpolating polynomial). However in Matlab a cubic
convolution is used, as stated in their documentation of interp2
<https://www.mathworks.com/help/matlab/ref/interp2.html#inputarg_method>. This
method is also described on Wikipedia's Bicubic Interpolation
<https://en.wikipedia.org/wiki/Bicubic_interpolation#Bicubic_convolution_algorithm>
page.

A tiny example to show the difference:
Octave:

> interp2(magic(4), 1, 1.5, 'cubic')
ans = 8.1875

Matlab (R2021a):

> interp2(magic(4), 1, 1.5, 'cubic')
ans = 8.6250


The topic has already been discussed in bug #60322 (regarding imresize) and
there is even a patch for imresize available to reach Matlab compatibility.
Maybe this patch can be adapted for interp2 as well? What is your opinion on
this?




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