Only a scale operation will keep all the ratios.

My guess is that a perspectivistic operation keeps the ratios as well?

I found out that the image I made with Darktable can be reproduced by Gimp's perspective tool.
So the algorithm's are the same

Wrong guess... The perspective doesn't keep the aspect ratios. Try applying it to a square grid. The only things that it keeps (and this is more important) is the straight lines: for instance, a diagonal in the grid remains straight... even though it then goes across non-square tiles.

Nutello,

I did some work. But it isn't solved yet..

First, with LibreCAD I found the principal point for this image:



I assume the tower had a square circumference.
The principal point (view point) isn't in the center of your image. So your image is cropped or made with a tilt shift camera or it is tilted in the photo-lab. Maybe a combination of those. But for editing it makes no difference.

here is the image with expanded canvas (no other editing). Now you can see de difference between the center of the image ( blue lines) and the principal point ( yellow lines crossing, the "horizontal" yellow line is the horizon) So the viewpoint/ principal point is almost in the center of the left door/entrance:



The (expanded canvas) image can now be used well for a perspective match, for example in Blender. When modeling the tower, it will now be square shaped, because of the expanded canvas and therefore new center:





(with expanded canvas) Field of view is: 81° / Focal length 18.74mm.

Question: Is the new church tower build on the same place as the old tower? Or is the new tower more to the front?

We can now start thinking about "untilt" and "unshift". When we "untilt", we will make a three points perspective from a two points perspective (complicated). But I want in the new three point perspective image the church tower also have a square outline. In other words: The new three points perspective image must be properly edited and give the same ratios when using this new image in Blender or Sketchup. Maybe other people have good ideas here too? To be continued......

Iarga, that is some serious scientific work you do!!

I have a question: in my opinion, when looking to the horizon from a low viewpoint, I look via a horizontal line.
This way, the yellow line can not be the horizon because if it were, the building in the background wouldn't be horizontal.

Looking at the background building, the horizon should be where one of the lines a, b, c and d is perpendicular to the red line (the vertical). So the horizon should be close to where the blue line is.

The new tower is indeed not on the same spot as the old one. It moved some 8 meters or so streetwards.
Thanks for your work

Nutello,

You are right. Good observation. The perspective lines from those houses don't match de perspective lines from the tower, otherwise that perspective lines would converge to the same horizon.

Logic: two horizons can't be, so the original image has some "warp". Maybe manipulated with ancient photo techniques in darkroom?

The big part of the church, on the right side of the image, has also different perspective lines (not same as tower), but that lines do converge to the same horizon as from the tower.

Maybe that part was a little bit rotated relative to the tower (about 1°-2°)? Because when the perspective lines meet on another place on the horizon, the plane from those perspective lines is not parallel to the plane from the other perspective lines.

AFAIK, and according to Wikepedia the "tilt" in photography doesn't change the perspective, it lets you define a plane of focus which isn't parallel to the film/sensor. In the case at hand, given the depth of field (the wheelbarrow on the left is also in focus) there is likely no tilt at all. The "shift" does not change the perspective either, it is more a way to select the adequate part of the lens projection. This is the same (except for the resulting pixel count) as shooting with a wide angle lens on a strictly horizontal camera (so that you get the whole building without convergent verticals) and then cropping the relevant part.

What would have happened in that shot is that it was taken with a small/medium format (slightly pointing up, so with converging verticals), and then, in the enlarger, copied over a sheet of paper that was slightly sloping to correct this.

Nutello,

You are totally right here. You take me on the right track. Thank you. There are no different horizons. I'm doing the whole procedure again. "Your" horizon is the right one.

Also Ofnuts tells something important here: tilt and shift don't change perspective.

I will look at the image now as if it is a one point perspective. The nice thing is:

The image is not in a strange way manipulated.

But now the different rotation of the church in relation to the street will be the thing I'm going to investigate. To be continued....

I don't think so. Shifting makes convergent lines parallel, which is not the case with that wide angle lens.

What make the lines parallel is that the plane of your sensor is vertical (which means that the axis of your lens is horizontal, not point up or down). With a wide angle, you scan shoot strictly horizontally and crop out the bottom half. With a shift lens you just don't need to throw away half the pixels (nice schema in the Wikipedia article, next to "Perspective-control lenses").

You can experiment with you smartphone camera. Put a sheet of paper on a flat horizontal surface. Take a shot, trying to keep the edges of the paper parallel to the edge of the screen. When this happens you phone is exactly horizontal.

Nutello,

I corrected for the horizon. Starting from one point perspective was no succes, so I repeated the same procedure as above. I studied the tower on different images. I'm almost sure it was square based. So the square is my reference.

find viewpoint:



So now the viewpoint is also corrected. The cyan lines are helplines for the procedure to match the camera with the perspective:



again in blender:



I used this add-on in blender to match the perspective:
https://github.com/mrossini-ethz/camera-calibration-pvr
https://blenderartists.org/t/add-on-cam ... rectangles

I totally agree with that yellow horizon line.
I'm not quite sure how you found that principal point. Is it coincidence it's on the horizon? Does that mean the camera was perfectly horizontal?

This property is connected to a two-point-perspective. When the vertical lines are parallel, it is a two point perspective.

In a three point perspective the principal point is not on the horizon. Then there is a perspective triangle. The principal point is the orthocenter of this perspective triangle.

We can know the position of the camera, but we don't know of it is made with tilt-shift, corrected afterwards or cropped afterwards.