ImageTransformation and corresponding points

Question

I have identified a list of corresponding points on two different images manually. I have found the geometrical transformation between such sets of points using FindGeometricTransform and I would now like to transform one of my images according to such transformation. When I do so, however, Mathematica gives me a completely black image and I don't understand how to get the first image transformed.

Here are the images:

I import them with:

i10 = Import["https://i.stack.imgur.com/cdx00.jpg"];
i15 = Import["https://i.stack.imgur.com/XApmx.jpg"];

The lists of corresponding points are:

pts10 = {{1934.77615025538`, 
1576.1190734112033`}, {2058.4519305241565`, 
1405.2746195470152`}, {1594.8656770702503`, 
1522.0661370677385`}, {1717.5432392405596`, 
1641.0491448965918`}};

pts15 = {{1821.159315341623`, 
2432.200159743154`}, {1935.081765338483`, 
2254.0263438834454`}, {1476.992138438835`, 
2391.701747362471`}, {1604.3856168362227`, 2505.453543001129`}};

This command finds the transformation:

f = FindGeometricTransform[pts15, pts10, TransformationClass -> "Rigid"][[2]]

The following command, however, gives a black image:

ImageTransformation[i10, f]

Am I doing something wrong? Thanks

Answer 1

I get different corresponding points when evaluating: pts=ImageCorrespondingPoints[i10,i15]? See: MapThread[HighlightImage[#1, #2] &, {{i10, i15}, ImageCorrespondingPoints[i10, i15]}].

You probably selected them manually? Since you are working with pixel positions I would propose that you display a plot of the coordinates, e.g. of pts10, pts15 and transformed data of pts10.

pts10 = {{1934.77615025538`, 
1576.1190734112033`}, {2058.4519305241565`, 
1405.2746195470152`}, {1594.8656770702503`, 
1522.0661370677385`}, {1717.5432392405596`, 
1641.0491448965918`}};

pts15 = {{1821.159315341623`, 
2432.200159743154`}, {1935.081765338483`, 
2254.0263438834454`}, {1476.992138438835`, 
2391.701747362471`}, {1604.3856168362227`, 2505.453543001129`}};

I use here for demonstration TransformationClass -> "Translation":

{e, t} = FindGeometricTransform[pts15, pts10, TransformationClass -> "Translation"];

transformedData = t[pts10]

(* {{1818.89,2430.52},{1934.78,2254.31},{1476.9,2391.75},{1604.78,2505.12}} *)

symbolPlus = Graphics[{Blue, Line[{{{-1, 0}, {1, 0}}, {{0, -1}, {0, 1}}}]}];
symbolCross = Graphics[{Line[{{{-1, -1}, {1, 1}}, {{-1, 1}, {1, -1}}}]}];

ListPlot[{pts10, transformedData, pts15}, 
 PlotMarkers -> {{symbolPlus, 0.04}, {symbolCross, 0.04}, {symbolCross, 0.04}}, Frame -> True, 
 PlotStyle -> {Blue, Red, Green}, FrameLabel -> {{"y (pixels)", ""}, {"x (pixels)", ""}}, 
 BaseStyle -> {FontWeight -> "Bold", FontSize -> 15, FontFamily -> "Calibri"}, ImageSize -> 600, 
 AspectRatio -> Automatic, PlotRange -> {{1400, 2100}, {1300, 2600}}]

When I use another TransformationClass then the transformed data of pts10 (red) and the data pts15 (green) fit nearly exactly on top of each other. The blue plus signs correspond to the orginal points pts10.

Answer 2

Assuming that corresponding points are found correctly, you may still see black image because transformed image is out of frame of original image. To fix that, I suggest adding following options:

ImageTransformation[i10, f, DataRange -> Full, PlotRange -> All]

This should ensure that no data points are lost and field of view covers them all.