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37
Libs/boundedlines/Inpaint_nans/.gitignore
vendored
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Libs/boundedlines/Inpaint_nans/.gitignore
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# Compiled source #
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###################
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*.com
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*.class
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*.dll
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*.exe
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*.o
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*.so
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# Packages #
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############
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# it's better to unpack these files and commit the raw source
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# git has its own built in compression methods
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*.7z
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*.dmg
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*.gz
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*.iso
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*.jar
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*.rar
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*.tar
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*.zip
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# Logs and databases #
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######################
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*.log
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*.sql
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*.sqlite
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# OS generated files #
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######################
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.DS_Store
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.DS_Store?
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._*
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.Spotlight-V100
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.Trashes
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ehthumbs.db
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Thumbs.db
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161
Libs/boundedlines/Inpaint_nans/demo/html/inpaint_nans_demo.html
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Libs/boundedlines/Inpaint_nans/demo/html/inpaint_nans_demo.html
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<html xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">
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<head>
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<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
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<!--
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This HTML is auto-generated from an M-file.
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To make changes, update the M-file and republish this document.
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-->
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||||
<title>inpaint_nans_demo</title>
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<meta name="generator" content="MATLAB 7.0.1">
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<meta name="date" content="2006-06-28">
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<meta name="m-file" content="inpaint_nans_demo"><style>
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body {
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background-color: white;
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margin:10px;
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}
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h1 {
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color: #990000;
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font-size: x-large;
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h2 {
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color: #990000;
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font-size: medium;
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}
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p.footer {
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text-align: right;
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font-size: xx-small;
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font-weight: lighter;
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font-style: italic;
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color: gray;
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}
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pre.codeinput {
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margin-left: 30px;
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}
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span.keyword {color: #0000FF}
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span.comment {color: #228B22}
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span.string {color: #A020F0}
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span.untermstring {color: #B20000}
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span.syscmd {color: #B28C00}
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pre.showbuttons {
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margin-left: 30px;
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border: solid black 2px;
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padding: 4px;
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background: #EBEFF3;
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}
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pre.codeoutput {
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color: gray;
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font-style: italic;
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}
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pre.error {
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color: red;
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}
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/* Make the text shrink to fit narrow windows, but not stretch too far in
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wide windows. On Gecko-based browsers, the shrink-to-fit doesn't work. */
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p,h1,h2,div {
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/* for MATLAB's browser */
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width: 600px;
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/* for Mozilla, but the "width" tag overrides it anyway */
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max-width: 600px;
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/* for IE */
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width:expression(document.body.clientWidth > 620 ? "600px": "auto" );
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}
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</style></head>
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<body><pre class="codeinput"><span class="comment">% Surface fit artifact removal</span>
|
||||
[x,y] = meshgrid(0:.01:1);
|
||||
z0 = exp(x+y);
|
||||
|
||||
znan = z0;
|
||||
znan(20:50,40:70) = NaN;
|
||||
znan(30:90,5:10) = NaN;
|
||||
znan(70:75,40:90) = NaN;
|
||||
|
||||
z = inpaint_nans(znan,3);
|
||||
|
||||
<span class="comment">% Comparison to griddata</span>
|
||||
k = isnan(znan);
|
||||
zk = griddata(x(~k),y(~k),z(~k),x(k),y(k));
|
||||
zg = znan;
|
||||
zg(k) = zk;
|
||||
|
||||
close <span class="string">all</span>
|
||||
figure
|
||||
surf(z0)
|
||||
title <span class="string">'Original surface'</span>
|
||||
|
||||
figure
|
||||
surf(znan)
|
||||
title <span class="string">'Artifacts (large holes) in surface'</span>
|
||||
|
||||
figure
|
||||
surf(zg)
|
||||
title([<span class="string">'Griddata inpainting ('</span>,num2str(sum(isnan(zg(:)))),<span class="string">' NaNs remain)'</span>])
|
||||
|
||||
figure
|
||||
surf(z)
|
||||
title <span class="string">'Inpainted surface'</span>
|
||||
|
||||
figure
|
||||
surf(zg-z0)
|
||||
title <span class="string">'Griddata error surface'</span>
|
||||
|
||||
figure
|
||||
surf(z-z0)
|
||||
title <span class="string">'Inpainting error surface (Note z-axis scale)'</span>
|
||||
</pre><img vspace="5" hspace="5" src="inpaint_nans_demo_01.png"> <img vspace="5" hspace="5" src="inpaint_nans_demo_02.png"> <img vspace="5" hspace="5" src="inpaint_nans_demo_03.png"> <img vspace="5" hspace="5" src="inpaint_nans_demo_04.png"> <img vspace="5" hspace="5" src="inpaint_nans_demo_05.png"> <img vspace="5" hspace="5" src="inpaint_nans_demo_06.png"> <p class="footer"><br>
|
||||
Published with MATLAB® 7.0.1<br></p>
|
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<!--
|
||||
##### SOURCE BEGIN #####
|
||||
% Surface fit artifact removal
|
||||
[x,y] = meshgrid(0:.01:1);
|
||||
z0 = exp(x+y);
|
||||
|
||||
znan = z0;
|
||||
znan(20:50,40:70) = NaN;
|
||||
znan(30:90,5:10) = NaN;
|
||||
znan(70:75,40:90) = NaN;
|
||||
|
||||
z = inpaint_nans(znan,3);
|
||||
|
||||
% Comparison to griddata
|
||||
k = isnan(znan);
|
||||
zk = griddata(x(~k),y(~k),z(~k),x(k),y(k));
|
||||
zg = znan;
|
||||
zg(k) = zk;
|
||||
|
||||
close all
|
||||
figure
|
||||
surf(z0)
|
||||
title 'Original surface'
|
||||
|
||||
figure
|
||||
surf(znan)
|
||||
title 'Artifacts (large holes) in surface'
|
||||
|
||||
figure
|
||||
surf(zg)
|
||||
title(['Griddata inpainting (',num2str(sum(isnan(zg(:)))),' NaNs remain)'])
|
||||
|
||||
figure
|
||||
surf(z)
|
||||
title 'Inpainted surface'
|
||||
|
||||
figure
|
||||
surf(zg-z0)
|
||||
title 'Griddata error surface'
|
||||
|
||||
figure
|
||||
surf(z-z0)
|
||||
title 'Inpainting error surface (Note z-axis scale)'
|
||||
|
||||
|
||||
##### SOURCE END #####
|
||||
-->
|
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</body>
|
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</html>
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BIN
Libs/boundedlines/Inpaint_nans/demo/html/inpaint_nans_demo.png
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42
Libs/boundedlines/Inpaint_nans/demo/inpaint_nans_demo_old.m
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Libs/boundedlines/Inpaint_nans/demo/inpaint_nans_demo_old.m
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|
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% Surface fit artifact removal
|
||||
[x,y] = meshgrid(0:.01:1);
|
||||
z0 = exp(x+y);
|
||||
|
||||
znan = z0;
|
||||
znan(20:50,40:70) = NaN;
|
||||
znan(30:90,5:10) = NaN;
|
||||
znan(70:75,40:90) = NaN;
|
||||
|
||||
z = inpaint_nans(znan,3);
|
||||
|
||||
% Comparison to griddata
|
||||
k = isnan(znan);
|
||||
zk = griddata(x(~k),y(~k),z(~k),x(k),y(k));
|
||||
zg = znan;
|
||||
zg(k) = zk;
|
||||
|
||||
close all
|
||||
figure
|
||||
surf(z0)
|
||||
title 'Original surface'
|
||||
|
||||
figure
|
||||
surf(znan)
|
||||
title 'Artifacts (large holes) in surface'
|
||||
|
||||
figure
|
||||
surf(zg)
|
||||
title(['Griddata inpainting (',num2str(sum(isnan(zg(:)))),' NaNs remain)'])
|
||||
|
||||
figure
|
||||
surf(z)
|
||||
title 'Inpainted surface'
|
||||
|
||||
figure
|
||||
surf(zg-z0)
|
||||
title 'Griddata error surface'
|
||||
|
||||
figure
|
||||
surf(z-z0)
|
||||
title 'Inpainting error surface (Note z-axis scale)'
|
||||
|
||||
39
Libs/boundedlines/Inpaint_nans/doc/Nomination comments.rtf
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Libs/boundedlines/Inpaint_nans/doc/Nomination comments.rtf
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{\rtf1\mac\ansicpg10000\cocoartf102
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{\fonttbl\f0\fswiss\fcharset77 Helvetica;}
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{\colortbl;\red255\green255\blue255;}
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\margl1440\margr1440\vieww10780\viewh13720\viewkind0
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\pard\tx720\tx1440\tx2160\tx2880\tx3600\tx4320\tx5040\tx5760\tx6480\tx7200\tx7920\tx8640\ql\qnatural
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\f0\fs24 \cf0 Nomination comments:\
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\
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||||
Inpaint_nans fills a hole in matlab. (Yes, the pun was intentional.) But there\
|
||||
is indeed a niche that inpaint_nans falls into.\
|
||||
\
|
||||
The alternative to inpaint_nans is griddata (interp1 can be used for the 1-d \
|
||||
problems) but griddata fails to extrapolate well. Griddata also has serious\
|
||||
problems when its data already lies on a grid, due to its use of a Delaunay \
|
||||
triangulation. The other serious problem with the use of griddata is the\
|
||||
triangulation itself. The shape of the hole to be filled can sometimes result\
|
||||
in triangles with a poor aspect ratio (long, thin triangles) which are in turn\
|
||||
poor for interpolation. In fact, Griddata can even leave interior points\
|
||||
uninterpolated (see the tests.)\
|
||||
\
|
||||
A future plan for inpaint_nans is to add an option that will use a locally\
|
||||
anisotropic membrane model. This will allow better modeling for certain\
|
||||
classes of wavy surfaces. I'm also highly tempted to remove method 5.\
|
||||
I've never really liked it, having put it in at the request of one user. It has\
|
||||
no valid theory behind it in the context of inpaint_nans.\
|
||||
\
|
||||
In the interest of openness, I'll also say what inpaint_nans does not do. It\
|
||||
does not handle non-uniform grids. It is limited by the amount of memory \
|
||||
in the size of the arrays it can handle, although some of the methods were\
|
||||
explicitly provided to be more memory efficient than others. Inpaint_nans\
|
||||
also makes heavy use of sparse matrices, so surprisingly large problems\
|
||||
are accessible.\
|
||||
\
|
||||
Finally, while inpaint_nans does work for 1-d problems, they are not my\
|
||||
target. Interp1 (with 'spline' as the method) is as accurate, and should be\
|
||||
faster in general.\
|
||||
\
|
||||
John\
|
||||
}
|
||||
187
Libs/boundedlines/Inpaint_nans/doc/methods_of_inpaint_nans.m
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Libs/boundedlines/Inpaint_nans/doc/methods_of_inpaint_nans.m
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%{
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|
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The methods of inpaint_nans
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|
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Digital inpainting is the craft of replacing missing elements in an
|
||||
"image" array. A Google search on the words "digita inpainting" will turn
|
||||
up many hits. I just tried this search and found 18300 hits.
|
||||
|
||||
If you wish to do inpainting in matlab, one place to start is with my
|
||||
inpaint_nans code. Inpaint_nans is on the file exchange:
|
||||
|
||||
http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=4551&objectType=file
|
||||
|
||||
It looks for NaN elements in an array (or vector) and attempts to interpolate
|
||||
(or extrapolate) smoothly to replace those elements.
|
||||
|
||||
The name "inpainting" itself comes from the world of art restoration.
|
||||
Damaged paintings are restored by an artist/craftsman skilled in matching
|
||||
the style of the original artist to fill in any holes in the painting.
|
||||
|
||||
In digital inpainting, the goal is to interpolate in from the boundaries
|
||||
of a hole to smoothly replace an artifact. Obviously, where the hole is
|
||||
large the digitally inpainted repair may not be an accurate approximation
|
||||
to the original.
|
||||
|
||||
Inpaint_nans itself is really only a boundary value solver. The basic idea
|
||||
is to formulate a partial differential equation (PDE) that is assumed to
|
||||
apply in the domain of the artifact to be inpainted. The perimeter of the
|
||||
hole supplies boundary values for the PDE. Then the PDE is approximated
|
||||
using finite difference methods (the array elements are assumed to be
|
||||
equally spaced in each dimension) and then a large (and very sparse) linear
|
||||
system of equations is solved for the NaN elements in the array.
|
||||
|
||||
I've chosen a variety of simple differental equation models the user can
|
||||
specify to be solved. All the methods current use a basically elliptic
|
||||
PDE. This means that the resulting linear system will generally be well
|
||||
conditioned. It does mean that the solution will generally be fairly smooth,
|
||||
and over large holes, it will tend towards an average of the boundary
|
||||
elements. These are characteristics of the elliptic PDEs chosen. (My hope
|
||||
is to expand these options in the future.)
|
||||
|
||||
%}
|
||||
|
||||
%%
|
||||
|
||||
% Lets formulate a simple problem, and see how we could solve it using
|
||||
% some of these ideas.
|
||||
A = [0 0 0 0;1 NaN NaN 4;2 3 5 8];
|
||||
|
||||
% Although we can't plot this matrix using the functions surf or mesh,
|
||||
% surely we can visualize what the fudamental shape is.
|
||||
|
||||
% There are only two unknown elements, the artifacts that inpaint_nans
|
||||
% would fill in: A(2,2) and A(2,3).
|
||||
|
||||
% For an equally spaced grid, the Laplacian equation (or Poisson's equation
|
||||
% of heat conduction at steady state if you prefer. Or, for the fickle,
|
||||
% Ficke's law of diffusion would apply.) All of these result in the PDE
|
||||
%
|
||||
% u_xx + u_yy = 0
|
||||
%
|
||||
% where u_xx is the second partial derivative of u with respect to x,
|
||||
% and u_yy is the second partial with respect to y.
|
||||
%
|
||||
% Approximating this PDE using finite differences for the partial
|
||||
% derivatives, implies that at any node in the grid, we could replace
|
||||
% it by the average of its 4 neighbors. Thus the two NaN elements
|
||||
% generate two linear equations:
|
||||
%
|
||||
% A(2,2) = (A(1,2) + A(3,2) + A(2,1) + A(2,3)) / 4
|
||||
% A(2,3) = (A(1,3) + A(3,3) + A(2,2) + A(2,4)) / 4
|
||||
%
|
||||
% Since we know all the parameters but A(2,2) and A(2,3), substitute their
|
||||
% known values.
|
||||
%
|
||||
% A(2,2) = (0 + 3 + 1 + A(2,3)) / 4
|
||||
% A(2,3) = (0 + 5 + A(2,2) + 4) / 4
|
||||
%
|
||||
% Or,
|
||||
%
|
||||
% 4*A(2,2) - A(2,3) = 4
|
||||
% -A(2,2) + 4*A(2,3) = 9
|
||||
%
|
||||
% We can solve for the unkowns now using
|
||||
u = [4 -1;-1 4]\[4;9]
|
||||
|
||||
A(2,2) = u(1);
|
||||
A(2,3) = u(2);
|
||||
|
||||
% and finally plot the surface
|
||||
close
|
||||
surf(A)
|
||||
title 'A simply inpainted surface'
|
||||
|
||||
% Neat huh? For an arbitrary number of NaN elements in an array,
|
||||
% the above scheme is all there is to method 2 of inpaint_nans,
|
||||
% together with a very slick application of sparse linear algebra
|
||||
% in Matlab.
|
||||
|
||||
% Method 0 is very similar, but I've optimized it to build as
|
||||
% small a linear system as possible for those cases where an array
|
||||
% has only a few NaN elements.
|
||||
|
||||
% Method 1 is another subtle variation on this scheme, but it
|
||||
% tries to be slightly smoother at some cost of efficiency, while
|
||||
% still not modifying the known (non-NaN) elements of the array.
|
||||
|
||||
% Method 5 of inpaint_nans is also very similar to method 2, except
|
||||
% that it uses a simple average of all 8 neighbors of an element.
|
||||
% Its not actually an approximation to our PDE.
|
||||
|
||||
% Method 3 is yet another variation on this theme, except the PDE
|
||||
% model used is one more suited to a model of a thin plate than for
|
||||
% heat diffusion. Here the governing PDE is:
|
||||
%
|
||||
% u_xxxx + 2*u_xxyy + u_yyyy = 0
|
||||
%
|
||||
% again discretized into a linear system of equations.
|
||||
|
||||
%%
|
||||
|
||||
% Finally, method 4 of inpaint_nans has a different underlying
|
||||
% model. Pretend that each element in the array was connected to
|
||||
% its immediate neighbors to the left, right, up, and down by
|
||||
% "springs". They are also connected to their neighbors at 45
|
||||
% degree angles by springs with a weaker spring constant. Since
|
||||
% the potential energy stored in a spring is proportional to its
|
||||
% extension, we can formulate this again as a linear system of
|
||||
% equations to be solved. For the example above, we would generate
|
||||
% the set of equations:
|
||||
|
||||
% A(2,2) - A(1,2) = 0
|
||||
% A(2,2) - A(2,1) = 0
|
||||
% A(2,2) - A(3,2) = 0
|
||||
% A(2,2) - A(2,3) = 0
|
||||
% (A(2,2) - A(1,1))/sqrt(2) = 0
|
||||
% (A(2,2) - A(1,3))/sqrt(2) = 0
|
||||
% (A(2,2) - A(3,1))/sqrt(2) = 0
|
||||
% (A(2,2) - A(3,3))/sqrt(2) = 0
|
||||
% A(2,3) - A(1,3) = 0
|
||||
% A(2,3) - A(2,2) = 0
|
||||
% A(2,3) - A(3,3) = 0
|
||||
% A(2,3) - A(2,4) = 0
|
||||
% (A(2,3) - A(1,2))/sqrt(2) = 0
|
||||
% (A(2,3) - A(1,4))/sqrt(2) = 0
|
||||
% (A(2,3) - A(3,2))/sqrt(2) = 0
|
||||
% (A(2,3) - A(3,4))/sqrt(2) = 0
|
||||
|
||||
% Substitute for the known elements to get
|
||||
|
||||
% A(2,2) - 0 = 0
|
||||
% A(2,2) - 1 = 0
|
||||
% A(2,2) - 3 = 0
|
||||
% A(2,2) - A(2,3) = 0
|
||||
% (A(2,2) - 0)/sqrt(2) = 0
|
||||
% (A(2,2) - 0)/sqrt(2) = 0
|
||||
% (A(2,2) - 2)/sqrt(2) = 0
|
||||
% (A(2,2) - 5)/sqrt(2) = 0
|
||||
% A(2,3) - 0 = 0
|
||||
% A(2,3) - A(2,2) = 0
|
||||
% A(2,3) - 5 = 0
|
||||
% A(2,3) - 4 = 0
|
||||
% (A(2,3) - 0)/sqrt(2) = 0
|
||||
% (A(2,3) - 0)/sqrt(2) = 0
|
||||
% (A(2,3) - 3)/sqrt(2) = 0
|
||||
% (A(2,3) - 8)/sqrt(2) = 0
|
||||
|
||||
% This system is also solvable now:
|
||||
r2 = 1/sqrt(2);
|
||||
M=[1 0;1 0;1 0;1 -1;r2 0;r2 0;r2 0;r2 0;0 1;-1 1;0 1;0 1;0 r2;0 r2;0 r2;0 r2];
|
||||
v = M\[0 1 3 0 0 0 2*r2 5*r2 0 0 5 4 0 0 3*r2 8*r2]'
|
||||
|
||||
A(2,2) = v(1);
|
||||
A(2,3) = v(2);
|
||||
|
||||
% and finally plot the surface
|
||||
surf(A)
|
||||
title 'A simply inpainted surface using a spring model'
|
||||
|
||||
%%
|
||||
|
||||
% Why did I provide this approach, based on a spring metaphor?
|
||||
% As you should have observed, methods 2 and 4 are really quite close
|
||||
% in what they do for internal NaN elements. Its on the perimeter that
|
||||
% they differ significantly. The diffusion/Laplacian model will
|
||||
% extrapolate smoothly, and as linearly as possible. The spring model
|
||||
% will tend to extrapolate as a constant function.
|
||||
BIN
Libs/boundedlines/Inpaint_nans/garden50.jpg
Normal file
BIN
Libs/boundedlines/Inpaint_nans/garden50.jpg
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 22 KiB |
1
Libs/boundedlines/Inpaint_nans/inpaint_nans.m
Normal file
1
Libs/boundedlines/Inpaint_nans/inpaint_nans.m
Normal file
File diff suppressed because one or more lines are too long
1
Libs/boundedlines/Inpaint_nans/inpaint_nans_bc.m
Normal file
1
Libs/boundedlines/Inpaint_nans/inpaint_nans_bc.m
Normal file
File diff suppressed because one or more lines are too long
43
Libs/boundedlines/Inpaint_nans/inpaint_nans_demo.m
Normal file
43
Libs/boundedlines/Inpaint_nans/inpaint_nans_demo.m
Normal file
@@ -0,0 +1,43 @@
|
||||
%% Surface Fit Artifact Removal
|
||||
|
||||
%% Construct the Surface
|
||||
[x,y] = meshgrid(0:.01:1);
|
||||
z0 = exp(x+y);
|
||||
|
||||
close all
|
||||
figure
|
||||
surf(z0)
|
||||
title 'Original surface'
|
||||
|
||||
znan = z0;
|
||||
znan(20:50,40:70) = NaN;
|
||||
znan(30:90,5:10) = NaN;
|
||||
znan(70:75,40:90) = NaN;
|
||||
|
||||
figure
|
||||
surf(znan)
|
||||
title 'Artifacts (large holes) in surface'
|
||||
|
||||
%% In-paint Over NaNs
|
||||
z = inpaint_nans(znan,3);
|
||||
figure
|
||||
surf(z)
|
||||
title 'Inpainted surface'
|
||||
|
||||
figure
|
||||
surf(z-z0)
|
||||
title 'Inpainting error surface (Note z-axis scale)'
|
||||
|
||||
%% Comapre to GRIDDATA
|
||||
k = isnan(znan);
|
||||
zk = griddata(x(~k),y(~k),z(~k),x(k),y(k));
|
||||
zg = znan;
|
||||
zg(k) = zk;
|
||||
|
||||
figure
|
||||
surf(zg)
|
||||
title(['Griddata inpainting (',num2str(sum(isnan(zg(:)))),' NaNs remain)'])
|
||||
|
||||
figure
|
||||
surf(zg-z0)
|
||||
title 'Griddata error surface'
|
||||
24
Libs/boundedlines/Inpaint_nans/license.txt
Normal file
24
Libs/boundedlines/Inpaint_nans/license.txt
Normal file
@@ -0,0 +1,24 @@
|
||||
Copyright (c) 2009, John D'Errico
|
||||
All rights reserved.
|
||||
|
||||
Redistribution and use in source and binary forms, with or without
|
||||
modification, are permitted provided that the following conditions are
|
||||
met:
|
||||
|
||||
* Redistributions of source code must retain the above copyright
|
||||
notice, this list of conditions and the following disclaimer.
|
||||
* Redistributions in binary form must reproduce the above copyright
|
||||
notice, this list of conditions and the following disclaimer in
|
||||
the documentation and/or other materials provided with the distribution
|
||||
|
||||
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
|
||||
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
|
||||
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
|
||||
ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
|
||||
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
|
||||
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
|
||||
SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
|
||||
INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
|
||||
CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
|
||||
ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
|
||||
POSSIBILITY OF SUCH DAMAGE.
|
||||
BIN
Libs/boundedlines/Inpaint_nans/monet_adresse.jpg
Normal file
BIN
Libs/boundedlines/Inpaint_nans/monet_adresse.jpg
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 145 KiB |
178
Libs/boundedlines/Inpaint_nans/test/test_main.m
Normal file
178
Libs/boundedlines/Inpaint_nans/test/test_main.m
Normal file
@@ -0,0 +1,178 @@
|
||||
%% Repair to an image with 50% random artifacts
|
||||
|
||||
% Garden at Sainte-Adresse (Monet, 1867)
|
||||
garden = imread('monet_adresse.jpg');
|
||||
G = double(garden);
|
||||
G(rand(size(G))<0.50) = NaN;
|
||||
Gnan = G;
|
||||
|
||||
G(:,:,1) = inpaint_nans(G(:,:,1),2);
|
||||
G(:,:,2) = inpaint_nans(G(:,:,2),2);
|
||||
G(:,:,3) = inpaint_nans(G(:,:,3),2);
|
||||
|
||||
figure
|
||||
subplot(1,3,1)
|
||||
image(garden)
|
||||
title 'Garden at Sainte-Adresse (Monet)'
|
||||
|
||||
subplot(1,3,2)
|
||||
image(uint8(Gnan))
|
||||
title 'Corrupted - 50%'
|
||||
|
||||
subplot(1,3,3)
|
||||
image(uint8(G))
|
||||
title 'Inpainted Garden'
|
||||
|
||||
%% Surface fit artifact removal
|
||||
|
||||
[x,y] = meshgrid(0:.01:1);
|
||||
z0 = exp(x+y);
|
||||
|
||||
znan = z0;
|
||||
znan(20:50,40:70) = NaN;
|
||||
znan(30:90,5:10) = NaN;
|
||||
znan(70:75,40:90) = NaN;
|
||||
|
||||
tic,z = inpaint_nans(znan,3);toc
|
||||
|
||||
tic
|
||||
k = isnan(znan);
|
||||
zk = griddata(x(~k),y(~k),z(~k),x(k),y(k));
|
||||
zg = znan;
|
||||
zg(k) = zk;
|
||||
toc
|
||||
|
||||
figure
|
||||
surf(z0)
|
||||
title 'Original surface'
|
||||
|
||||
figure
|
||||
surf(znan)
|
||||
title 'Artifacts (large holes) in surface'
|
||||
|
||||
figure
|
||||
surf(zg)
|
||||
title(['Griddata inpainting (',num2str(sum(isnan(zg(:)))),' NaNs remain)'])
|
||||
|
||||
figure
|
||||
surf(z)
|
||||
title 'Inpainted surface'
|
||||
|
||||
figure
|
||||
surf(zg-z0)
|
||||
title 'Griddata error surface'
|
||||
|
||||
figure
|
||||
surf(z-z0)
|
||||
title 'Inpainting error surface (Note z-axis scale)'
|
||||
|
||||
%% Comparison of methods
|
||||
|
||||
[x,y] = meshgrid(-1:.02:1);
|
||||
r = sqrt(x.^2 + y.^2);
|
||||
z = exp(-(x.^2+ y.^2));
|
||||
|
||||
z(r>=0.9) = NaN;
|
||||
|
||||
z((r<=.5) & (x<0)) = NaN;
|
||||
|
||||
figure
|
||||
pcolor(z);
|
||||
title 'Surface provided to inpaint_nans'
|
||||
|
||||
% Method 0
|
||||
tic,z0 = inpaint_nans(z,0);toc
|
||||
|
||||
% Method 1
|
||||
tic,z1 = inpaint_nans(z,1);toc
|
||||
|
||||
% Method 2
|
||||
tic,z2 = inpaint_nans(z,2);toc
|
||||
|
||||
% Method 3
|
||||
tic,z3 = inpaint_nans(z,3);toc
|
||||
|
||||
% Method 4
|
||||
tic,z4 = inpaint_nans(z,4);toc
|
||||
|
||||
% Method 5
|
||||
tic,z5 = inpaint_nans(z,5);toc
|
||||
|
||||
figure
|
||||
surf(z0)
|
||||
colormap copper
|
||||
hold on
|
||||
h = surf(z);
|
||||
set(h,'facecolor','r')
|
||||
hold off
|
||||
title 'Method 0 (Red was provided)'
|
||||
|
||||
figure
|
||||
surf(z1)
|
||||
hold on
|
||||
h = surf(z);
|
||||
set(h,'facecolor','r')
|
||||
hold off
|
||||
title 'Method 1 (Red was provided)'
|
||||
|
||||
figure
|
||||
surf(z2)
|
||||
hold on
|
||||
h = surf(z);
|
||||
set(h,'facecolor','r')
|
||||
hold off
|
||||
title 'Method 2 (Red was provided) - least accurate, but fastest'
|
||||
|
||||
figure
|
||||
surf(z3)
|
||||
hold on
|
||||
h = surf(z);
|
||||
set(h,'facecolor','r')
|
||||
hold off
|
||||
title 'Method 3 (Red was provided) - Slow, but accurate'
|
||||
|
||||
figure
|
||||
surf(z4)
|
||||
hold on
|
||||
h = surf(z);
|
||||
set(h,'facecolor','r')
|
||||
hold off
|
||||
title 'Method 4 (Red was provided) - designed for constant extrapolation!'
|
||||
|
||||
figure
|
||||
h = surf(z5);
|
||||
set(h,'facecolor','y')
|
||||
hold on
|
||||
h = surf(z);
|
||||
set(h,'facecolor','r')
|
||||
hold off
|
||||
title 'Method 5 (Red was provided)'
|
||||
|
||||
|
||||
%% 1-d "inpainting" using interp1
|
||||
|
||||
x = linspace(0,3*pi,100);
|
||||
y0 = sin(x);
|
||||
y = y0;
|
||||
% Drop out 2/3 of the data
|
||||
y(1:3:end) = NaN;
|
||||
y(2:3:end) = NaN;
|
||||
|
||||
% inpaint_nans
|
||||
y_inpaint = inpaint_nans(y,1);
|
||||
|
||||
% interpolate using interp1
|
||||
k = isnan(y);
|
||||
y_interp1c = y;
|
||||
y_interp1s = y;
|
||||
y_interp1c(k) = interp1(x(~k),y(~k),x(k),'cubic');
|
||||
y_interp1s(k) = interp1(x(~k),y(~k),x(k),'spline');
|
||||
|
||||
figure
|
||||
plot(x,y,'ro',x,y_inpaint,'b+')
|
||||
legend('sin(x), missing 2/3 points','inpaint-nans','Location','North')
|
||||
|
||||
figure
|
||||
plot(x,y0-y_inpaint,'r-',x,y0-y_interp1c,'b--',x,y0-y_interp1s,'g--')
|
||||
title 'Inpainting residuals'
|
||||
legend('Inpaint-nans','Pchip','Spline','Location','North')
|
||||
Reference in New Issue
Block a user