Counting Number of Voxels between 2 points without drawing lines

Hi All,

I have curve volumes and I know the coordinates of each and every voxels including the endpoints. I have many curve volumes like this and, I would like to know the straight distance of endpoints(A-B) by VOXELS. I calculated the distance using Pythagoras therom using the X,Y, Z coordinates.But I would like to know the straight distance by voxels WITHOUT drawing a line between those two points. I have lots of volumes like this and I cannot draw lines between those openning points hence it takes high computational power. Appreciate your comments.

Answer 1

[Matt J]

Assuming you have a binarized image and the curve is the only object in that image,

[I,J]=find( bwmorph(yourImage,'endpoints'));

distance=norm([I(1), J(1)] - [I(2),J(2)]),

[Hege]

Hi Matt,

Thank you very much for your reply!

Actually, my expectation is not calcualte the distance. I used all formulas what you explained above. I got all the endpoints, coordinates of each and every voxel and already calculated the distance between endpoints.

I would like to know, how many voxels will be there if I connect these enpoints using a straight line without drawing a line.Bascially, it should be an integer value. On the hand, I checked the norm distance and, compared my answer by drawing a voxel line between those two endpoints(I calculated using the Pythogoras therom as well). But answers are very different which means it seems that, I will not get the number of voxels between those two endpoints using these norm or pythogorm calculations

Appreciate your comments!

[Matt J]

"I would like to know, how many voxels will be there if I connect these enpoints using a straight line without drawing a line"

This is by definition the distance between the two points. I'm not sure what distinction you're attempting to draw. Let's take a simpler picture. What is the number of voxels separating the line end points in the image below? Which voxels are counted in the separation?

[Hege]

Thank you very much for your reply!

number of voxels which is seperated by the line is 5. I would like to know how I should get the answer as 5. Earlier, I draw a voxel line that connect these 2 endpoints and got the number of voxels using the regionprops3(). But, I want to know this number of voxels(ex:5) without connecting those 2 endpoints which means without drawing lines. I know all the details of the endpoints. But I want to know how I should get this number 5?

[Matt J]

That will just be

distance=norm(  [I(1), J(1)] - [I(2),J(2)]   ,1)  - 1,

[Hege]

Hi Matt,

Thank you very much for your answer and I really appreciate it.

Before I write this comment, I tried many times and many ways to implement your answer to voxel. But I am getting very big values of distances and I could not find where the problem is.

I would really appreciate if you could please give me a tip atleast how to implement your answer for 3D domains.

[I,J,K]=find( bwmorph3(yourImage,'endpoints'));

Note: I am getting K as a logical array

Appreciate your feedback!

[Matt J]

That would be,

[I,J,K]=ind2sub(  size(yourImage)  ,   find( bwmorph(yourImage,'endpoints'))   );

[Hege]

Hi Matt,

I am really sorry to ask you a simple question again and it would be great if you could kindly descibe how to compute the distance using the 'norm'. I tried to get the norm value of my volume in the 3D domain. But I am getting a deviated value rather than I expected. really appreciate your support with the explanation. Simply, what I ask is, how to apply this 'norm' to my 3D domain as you you applied to 2D domain.

Thank you in Advance!

[Matt J]

You mean how to generalize

distance=norm(  [I(1), J(1)] - [I(2),J(2)]   ,1)  - 1,

to 3D. It's just

distance=norm(  [I(1), J(1), K(1)] - [I(2),J(2),K(2)]   ,1)  - 1,

[Hege]

Hello Matt,

To be honest, I tried many ways to solve this issue in last couple of days using the above answer in different ways. but the problem is still there . Simply, if we draw voxel line between two points, regionprops3() says it obtains 51 voxels.

But above answer( distance=norm( [I(1), J(1), K(1)] - [I(2),J(2),K(2)] ,1) - 1, ) gives me 56 voxels.

Coordinates

x0=22; y0=52; z0=10;

x1=77; y1=52; z1=10;

I appreciate if you could give me a tip why and how this occurs!

[Matt J]

Simply, if we draw voxel line between two points, regionprops3() says it obtains 51 voxels.

That's not what I see from regionprops3:

x0=22;  y0=52;  z0=10;
x1=77;  y1=52;  z1=10; 

L=zeros(100,100,100);

L(x0,y0,z0)=1;
L(x1,y1,z1)=1;

regionprops3(L,'ConvexVolume')

ans = table
    ConvexVolume
    ____________

         56     

[Hege]

Hello Matt,

Really sorry for getting back to you late. As I am using curve and linear models(including complex curves), I am unable to use convex volume values. I use only' regionprops3(L,'Volume') .So I can get the voxel along that path(curve or linear).when I use regionprops3(L,'Volume') I got different values comapring to the 'norm' function . However, I decided to solve the problem by drawing 1 width voxel lines.

I really appreiate your great help and thank you very much for it.

Again, Thank you in Advance!

[Matt J]

I am not sure how you are "drawing" the 1-width voxel lines. The details in that would explain why you might be getting differences from norm().

One thing I should probably point out is that the norm() command calculates the line length assuming the line is drawn without allowing diagonal steps. That was the rule you held yourself to in the small you gave me above with the green squares. In that example, you said the number of squares separating the end-voxels should be 5 as shown by the green squares, but had you allowed diagonal steps, there could have been as few as 3 green squares.

[Hege]

Hi Matt,

Yes. It is my mistake. Sorry.

Simply, I want know the number of all voxels which contributes to generate a line.

What I meant by one voxels width line is, skeletonized voxel line(this inlcudes the diagonal steps as well). But, this obtains very high computational time and power as my model is huge and complex. However, it gives me the correct answer.

I appreciate if you could suggest any idea if there is any simple solution.

Sorry again for the misunderstanding of wrong explanation.

[Matt J]

The shortest voxelized line which can take diagonal steps is of length,

distance = norm(Pt1-Pt2, inf) - 1

assuming as before that you exclude the end-voxels.

[Hege]

Hi Matt,

Thank you so much and this is a great solution for my work. I applied it many different ways and it works. Thank you again!!