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Perspective transform revisited
#21
(11-16-2020, 06:11 PM)akovia Wrote: Really nice plugin.

Just using it for straightening perspective DVD cover images like Amazon and other outlets will use sometimes, and it worked perfectly.

Thanks!

Great! It is always a relief to hear such outcomes!
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#22
I made another plugin, and with it I think this package is finished. The plugins are at

http://kmarkku.arkku.net/Perspective_tra...aster.html

When you put the file perspective_transform.py in your Gimp's plug-ins folder, you find at Filters > Distorts > Perspective transform four plugins:

  1. Perspective transform - 1+2+3 points to circle (center and 2+3 points)
  2. Perspective transform - 4 points to 4 points
  3. Perspective transform - 4 points to circle (clock face)
  4. Perspective transform - 4 points to rectangle corners

The first is the new plugin and I explain it in this post. The other three are the old plugins; I changed only wordings but they work just as before.

The new plugin "Perspective transform - 1+2+3 points to circle (center and 2+3 points)" is meant to correct a distorted circle. In that sense it does the same thing as the third of the plugins, but the inputs are different. This one may be easier to use (no hours).

I made the following test figure. On the left we have a regular figure. I distorted it with Gimp's Perspective Transform tool to get what is on the right. That is the test figure. Now I want to correct the distortion back.

   

You must imagine now a distorted circle (an ellipse) around the figure though I didn't draw it there. That is the distorted circle we should now corrected to a true circle.

The plugin takes as input one path with three strokes:

  1. One stroke has 1 anchor. The anchor is supposed to be the point which should become, after correction, the center of the circle.
  2. Another stroke has 2 anchors. They must be points on the distorted circle. Also, they determine the position to which the final figure should be rotated (see below).
  3. The third stroke has 3 anchors. They are just some three other points on the distorted circle.
It does not matter in which order the 3 strokes are in the path.

In the following picture, on the left we see the path I used. The 1-anchor path is the little circle in the middle. The other two strokes you recognize certainly: one has 2 anchors, and one has 3 anchors.

   

With this path and otherwise with default values, the plugin produced the figure on the right. Rather good, isn't it?

I attach the .xcf file of the distorted figure and the path in case you want to look at it more closely.


.xcf   example.xcf (Size: 188.12 KB / Downloads: 3)

The plugin offers a method to set to which position the corrected circle will be rotated. The plugin uses the direction of the 2-anchors stroke for this, and you have three alternatives to choose from:
  • Make it vertical (default)
  • Make it horizontal
  • Keep its direction as it is
You notice that in the example figure I put the 2-anchors stroke to the two petals with blue dots. When I ran the plugin with the default value, the line segment between the blue dots was turned vertical.

But in general, the final figure may turn out to be rotated by 180 degrees from what you wanted. The plugin has an option to correct that. You can also define extra rotation in degrees.

You may be wondering: Why the strokes with 2 and 3 anchors? The 2-anchors stroke has the function that its direction is used to determine the rotation. But why the 3-anchors stroke? Why 5 (=2+3) points on the distorted circle? And why the center point? I cannot resist explaining a little about the ideas behind the plugin, since this all is not quite obvious.

<skip if not interested...>
The plugin is designed to correct a distorted circle to a true circle. The distorted circle is assumed to be what we get when we take a photo of a circle in an angle. In the photo the circle is distorted; it becomes an ellipse, approximately (but that depends on the lens and is not always true). We just assume here that it is an ellipse. To be precise, what the plugin does is that it corrects an ellipse to a circle, and in addition it corrects the distortion also globally in the plane, not only the curve (the ellipse).

An ellipse is determined completely from its 5 points. That is the reason for inputting 5 points on the distorted circle: they enable the plugin to compute everything of the ellipse: center, axes, and whatever. And correcting the ellipse to a circle is then easy.

But if we used only the 5 points and corrected the ellipse (the curve) to a circle, then everything else on the plane would still come out uncorrected. For example, the point that the correction should take to the center of the circle, would generally be still offset from the center. But a remarkable fact is that if we also know which point should become the center of the circle, then we can correct the distortion globally (up to rotation and perhaps reflection)!

Namely, it can be shown that, given an ellipse and one point inside it, there is a projective transformation that maps the ellipse onto a given circle, at the same time sending that specified point to the center of the circle. Moreover, such transformation is unique up to a rotation and possibly a reflection! Therefore, any distortion of a circle, caused by a projective (perspective) mapping (like taking a photo), can be corrected in a unique way using the scheme in the plugin (five points, center, direction, and keeping ccw as ccw). When we know that, writing such plugin means only  constructing that correcting transformation.

I don't give any details about the construction but you may wish to look at the code and the comments therein. This part is the most interesting in the whole process, and I am still amazed at the way it did come through.
</skip...>

That's that. If you have any problems with the plugin, please just ask.
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#23
This other plugin is welcome! I didn't find it as intuitive as the previous ones, but maybe I haven't understood it as I should yet.
In the image made available in .xcf I could try the correction even using paths other than the one provided and the result was practically the same; pretty satisfactory.
However, I particularly prefer the previous plugins, in this case the 4-point to 4-point generated an image closer to the original with better control over the desired center of the corrected image.
   
Thanks for keeping perfecting this plugin!
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#24
(Yesterday, 12:45 PM)Krikor Wrote: This other plugin is welcome! I didn't find it as intuitive as the previous ones, but maybe I haven't understood it as I should yet.
In the image made available in .xcf I could try the correction even using paths other than the one provided and the result was practically the same; pretty satisfactory.
However, I particularly prefer the previous plugins, in this case the 4-point to 4-point generated an image closer to the original with better control over the desired center of the corrected image.

Thanks for keeping perfecting this plugin!

Yes, 4 to 4 is good if you know where to put the 4 target points.

In this particular figure it is practically guessing where to put the center, so the result is not perhaps so good. But in some other picture the center point may be easy to set.

Thanks for trying the plugins!
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