ArbitrayAxisOfRotation

[AmazingYi]

I have some questions in demo 18 ArbitraryAxisOfRotation . Firstly, the Euler angles in the demo . Can it be understood as the source is in the sphrical center, the detector is tangent to the sphere ,on the surface. And the ZYZ angles determined where the detector is ?
If so, I draw the coordinates of these angels , It is werid path that I‘m not sure if it is right.

And I also have a question that if tigre Arbitrary Axis can solve this CT structure in below.

A point is source, and the purple circle AD is a sphere that it's center is the source. the green line is the detector. It is tangent to the sphere .

Line GI is actually a circle ,which is the path of the detector . BC in blue is the platform place the object . and it will move a little right or left to make sure objcet point F is in the center of th image.
As you can see ,the x_ray is cone . I ’m not sure if the AD center of cone x ray was reqiured always perpendicular to detector . but our source is not movable. I want ask that if tigre can cover this structure.

[AnderBiguri]

Can it be understood as the source is in the sphrical center, the detector is tangent to the sphere

No, the origin is in the spherical center. The XYZ axis, that you can see in the TIGRE paper or Demo 1. Around those axis, Euler ZYZ rotation is provided, i.e. rotation around the moved axis.

About your geometry: Yes, TIGRE does all possible geometries, so it can do this one. However, there is no easy way to do this one. You will need to interpret each projection uniquely, and compute the appropuiate parameters for rotation and trasnlation of object and detector. Ultimately you need to find a way to describe your geometry with respect to a standard circular CBCT acquisition, which is the reference. This is not trivial at all, but of course, possible.

[AmazingYi]

Can it be understood as the source is in the sphrical center, the detector is tangent to the sphere

No, the origin is in the spherical center. The XYZ axis, that you can see in the TIGRE paper or Demo 1. Around those axis, Euler ZYZ rotation is provided, i.e. rotation around the moved axis.

About your geometry: Yes, TIGRE does all possible geometries, so it can do this one. However, there is no easy way to do this one. You will need to interpret each projection uniquely, and compute the appropuiate parameters for rotation and trasnlation of object and detector. Ultimately you need to find a way to describe your geometry with respect to a standard circular CBCT acquisition, which is the reference. This is not trivial at all, but of course, possible.

OK , I  got it.  

in the picture above ,I want to ask that where is the initial position of the detector .For eample , is it in the - X axis ? and perpendicular to - X axis ?

I also update my diagram below.

A is the source , the green circle in the picture is a sphere where detector is ,D is it's center . green line k is the detector now in the picture . orange line HK actually is a circle ,the path of the detector. Detector rotate around line AF the center of cone x-ray .
OK I have question that in this case ,D point is the origin ,DSD is AH, DSO should be AD or A to the cross of line CJ and AH?

I explian it more detaily . green line h is the initial position of detector . DE is the object need to check . so in the begining,DE is in the center of the detector or in the center of the image .as the detector going to H from F。 BC should move to MN like picture below . so that the D the same as M is always in the center of image.

So,I wanto ask that DSO is AM or AD since the path of deteoctor is a circle HK.

[AnderBiguri]

in the picture above ,I want to ask that where is the initial position of the detector .For eample , is it in the - X axis ? and perpendicular to - X axis ?

Correct.

About your diagrams: apologies, but these are a bit complicated and I really don't have the time to study them, and writting the translation form circular CBCT to these is not trivial at all. Unfortunately I don't have the time to write it for you. I suggest you study TIGRE's geometry (read the papers too) and try it yourself, you can let me know if you are struggling with it then.

[AmazingYi]

in the picture above ,I want to ask that where is the initial position of the detector .For eample , is it in the - X axis ? and perpendicular to - X axis ?

Correct.

About your diagrams: apologies, but these are a bit complicated and I really don't have the time to study them, and writting the translation form circular CBCT to these is not trivial at all. Unfortunately I don't have the time to write it for you. I suggest you study TIGRE's geometry (read the papers too) and try it yourself, you can let me know if you are struggling with it then.

Thanks for your reply , I find an example in discussions "offset origin and offset detector" in this example #649 . I knew that , source and detector , the "cone like "path they combine is caused by "offset detector " and "offset origin".,rather that ZYZ angles. Buy what‘s different between this and mine is that the detctor is on spherical surface and this seems flat.

In demo 17 detector rotation . I try to use a cubic stick made by numpy ,such as stick=np.zeros[64,64,64]
stick[ 22:42 ,22:42, :]=1 to replace the "head" voxels which is hard to identify its angles. finally I only set pitch an angle 40 dgree . it ' s the angle detectot move from the top of sphere to te left site .

But When I input my images ,the result is wrong. I'm now confused that. In the situation of discusions 649 , will the detector roll that it point to the center of the circle，or just move staight ,if there are not any detector rotation prameters set . I took a sketch to illustrate it。

And I also wonder that if I set "offet origin", I should to caculate the detector rotation using new origin or the old one.

[AnderBiguri]

@AmazingYi The detector is always perpendicular to the source-origin axis, unless rotated. so by default, A is correct.

The best way to think about it is again to think of standard CBCT circular scanning. The default TIGRE parameters do that, so you need to descrive your rotations, offsets, etc as a shift from that standard.

[AmazingYi]

@AnderBiguri Oh! Thanks for your reply , I noticed that the example above , detector and object are moving a paths like A . But in my case, the object is moving like B ,because the platform can not rotate.,it can only move along x axis or y axis . But the detector is moving like A . So, is there any method in tigre to make object moving like B ? does the object rotated through Offset or ZYZ angles?
And I'm still confused about Rotation of detector example. For example , I created a little cubic object to see the synthesis result instead of the " head " . then use opencv to see the "projections".

The other parameters are the same as   "zeminLi 66"'s  example , when I set detector rotation parameter like below , it is OK  

03.mp4

But When I set picth to 40 , the cube is  "streched "  for an unusual angle.  

05.mp4

In short , what i expect picth of detectort is like below , is it reference for surface of detector ? if not ,what is the "pitch" reference frame for ?

[AnderBiguri]

Yes, pitch is what you say it is indeed. But I am not sure why you think the projections you get are wrong. Can you tell me what you expect instead? can you show me the full geometry?

[AmazingYi]

@AnderBiguri I'm sorry for not providing a detiailed description. what i expect is like video 1 . the cubic stick is only 4 voxels hight ,so the detector is highter than the object, that the procettion shows different angles of this cube in above . So it should be sinilar to every angle ,even if set pitch because the detector moved a circular path
but in video 2 this cube image somtines is longer ,sometimes is shoter .

only the detector is in a very low position can cause this,I think ,but I set pitch to 40 in every angle.

Sure ,geo is in below . it is the same to "zeminLi 66"'s example

[AnderBiguri]

Are you sure you are not just plotting it transposed? Try your plotting technique but for a circular CBCT. Surely your plotting function is missing a few things, like for example a reasonable display range, as its all white saturated.

[AmazingYi]

Are you sure you are not just plotting it transposed? Try your plotting technique but for a circular CBCT. Surely your plotting function is missing a few things, like for example a reasonable display range, as its all white saturated.

Yes ，plotting fuc is not very complex  ,just using opencv to see image  in every angle  . what different  is  that  in demo 18 ,  load a head voxel  to  synthesis  different angles  ，but  this "head " is too  complex to figure out  the positon  of detector .  
I not sure if it a bug  of  "tigre.Ax()  " function   or something wrong in my  code  or something I used incorrect  .    Therefore,  the rest code   is showing  below .  videos  showed above   are  produced by the "for ..."  loop.  I only resized  the image  to 3  times  its size for a better view. 

The white saturated image  ,I think is cause by  I set the cube  voxel  "1"  value   which  means  X-rays cannot go through it at all , because the max of the head voxel is 0.9xxx  .  you can imagine that  it is a cube made of  Pb or Cu  . Anyway , it is for convenience  to estimate the position of detector,because I an not sure the geo of mine is right.

Yes ,I tried CBCT. In circular CBCT , I only set Z1 (0-2pi ,108 slice) and pitch 60 degree . It 's OK,too. you can see the top of the cube is bigger than the bottom because the pitch of detector . I 'm now wondering that if offset of detector and origin will influence the rotation of detector . such as pitch and yaw 。

09.mp4

[AmazingYi]

Oh , I find the reason that this image is too white. I fogot to conver "np.fp32 " to " np.uint8 " . But it doesn't matter for estimating the position of detector .

[AnderBiguri]

@AmazingYi if you use plotProj() function from TIGRE, do you still get the same gifs, or are they transposed?

[AmazingYi]

@AnderBiguri Yes, I tried again. plotProj() and opencv plot show the same result . I only set pitch 40 for detector rotation the same as above. here is the result. ( the cube is 10 voxel height for a better view of plotProj() func )

12.mp4

opencv

13.mp4

[AnderBiguri]

@AmazingYi have you tried with roll?

[AmazingYi]

@AnderBiguri Roll works well. I set it to 0- 2pi , the cube rolled as we set in the image ( the detector rolled ,in fact )