# Building the ijk to RAS transform from a nrrd file

**URL:** <https://discourse.slicer.org/t/building-the-ijk-to-ras-transform-from-a-nrrd-file/1513>\
**Category:** Support\
**Tags:** nrrd\
**Created:** [November 23, 2017, 11:58pm UTC](https://discourse.slicer.org/t/building-the-ijk-to-ras-transform-from-a-nrrd-file/1513 "2017-11-23T23:58:04Z")\
**Posts on this page:** 6\
**Page:** 1

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**Author:** ![dcantor](https://sea2.discourse-cdn.com/flex002/user_avatar/discourse.slicer.org/dcantor/32/782_2.png) [@dcantor](https://discourse.slicer.org/u/dcantor)\
**Post date:** [November 23, 2017, 11:58pm UTC](https://discourse.slicer.org/t/building-the-ijk-to-ras-transform-from-a-nrrd-file/1513/1 "2017-11-23T23:58:04Z")

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Hi Slicers,

I am working on a project with Slicer generated nrrd files and after looking at the nrrd header I notice there is no info about the ijk to RAS matrix yet when I load that nrrd file into Slicer I obtain the matrix. So I think I figured out how to build it in code and I am looking for validation from someone who is more experienced than me. This is what I am doing:

1. I read the nrrd header and obtain the _space direction_ vectors (say **a** , **b** , **c** )

2. I build a 3x3 matrix (A) where the columns correspond to **a** , **b** , and **c**.

3. Given the **t** translation column vector (as defined in the nrrd _space origin_ header), I can obtain world coordinates **x** for the index column vector **v** by:

> x = A\*v + t

1. since my nrrd volume appears to be in LPS frame (as per the _space_ header), I have to multiply **x** by the LPS to RAS transform.

Say that’s T = [-1 0 0; 0 -1 0; 0 0 1], so:

> x\_ras = T \* x

Is this correct?

Now, the IJK to RAS direction matrix reported in Slicer (Volumes module) seems to be:

> T\*A

is this correct?

Thanks!

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<div class="post-metadata">

**Author:** ![lassoan](https://sea2.discourse-cdn.com/flex002/user_avatar/discourse.slicer.org/lassoan/32/13_2.png) [@lassoan](https://discourse.slicer.org/u/lassoan)\
**Post date:** [November 24, 2017, 1:05am UTC](https://discourse.slicer.org/t/building-the-ijk-to-ras-transform-from-a-nrrd-file/1513/2 "2017-11-24T01:05:47Z")

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Almost correct. IJKToRAS is a homogeneous transformation matrix, which contains axis directions in the top-left 3x3 sub-matrix, origin in the first 3 values of 4th column, and [0,0,0,1] in the 4th row (so you don’t “add” the translation component but concatenate). In Matlab syntax:

```
ijk_to_lps = [[space_directions, space_origin]; [0 0 0 1]]
lps_to_ras = diag([-1 -1 1 1])
ijk_to_ras = lps_to_ras * ijk_to_lps
```

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<div class="post-metadata">

**Author:** ![dcantor](https://sea2.discourse-cdn.com/flex002/user_avatar/discourse.slicer.org/dcantor/32/782_2.png) [@dcantor](https://discourse.slicer.org/u/dcantor)\
**Post date:** [November 24, 2017, 3:40am UTC](https://discourse.slicer.org/t/building-the-ijk-to-ras-transform-from-a-nrrd-file/1513/3 "2017-11-24T03:40:44Z")

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Ok, the confusion was because in the volumes module the matrix appears as a 3x3 matrix. But it doesn’t matter, anyways the 4x4 form is equivalent as you show since you are operating in homogeneous coordinates.  
Thank you Andras.

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**Author:** ![Optics\_Bioeng](https://sea2.discourse-cdn.com/flex002/user_avatar/discourse.slicer.org/optics_bioeng/32/66534_2.png) [@Optics\_Bioeng](https://discourse.slicer.org/u/Optics_Bioeng)\
**Post date:** [June 25, 2023, 6:04am UTC](https://discourse.slicer.org/t/building-the-ijk-to-ras-transform-from-a-nrrd-file/1513/4 "2023-06-25T06:04:47Z")

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Hello Slicers

OS: Windows11  
Slicer5.2.2

I’m beginner of 3DSlicer. I am working on a project with Slicer generated nrrd files too. This is what I want to do:

Step1. Forearm segmentation in Slicer and output as nrrd data.

 ![スクリーンショット 2023-06-25 143847](https://us1.discourse-cdn.com/flex002/uploads/slicer/original/3X/3/f/3f04c2e26e7f848f5f846e07c15d3e838889f7aa.jpeg)

Step2. Calculate the centre of gravity for a particular slice using python and obtain its coordinate ijk

```python
import nrrd
tensor, header = nrrd.read("C:\\Users.....\\Segmentation.seg.nrrd", index_order ='C')
import cv2
def calc_center_gravity(tensor, gk):
    gravity = []
    img = tensor[gk]
    contours, _ = cv2.findContours(img, cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)
    for cnt in contours:
        M = cv2.moments(cnt)
        if M["m00"] == 0:
            continue
        gx = int(M["m10"] / M["m00"])
        gy = int(M["m01"] / M["m00"])
        plt.plot(gi, gj, marker='.')
        gravity.append((gi, gj, gk))
    plt.imshow(img, cmap="gray")
    plt.title(f"centre of gravity index\n (i, j, k)=({gi}, {gj}, {gk})")
    plt.show()
    return gravity
gravity = calc_center_gravity(tensor, 24)

```

![スクリーンショット 2023-06-25 145035](https://us1.discourse-cdn.com/flex002/uploads/slicer/original/3X/0/4/041b24419e1324ce74e7f121c807900df8aa52f2.png)

```python
space_directions = header["space directions"]
space_origin = header["space origin"]
ijk2lps = np.vstack([np.hstack([space_directions, space_origin.reshape(-1, 1)]), np.array([0, 0, 0, 1])])
lps2ras = np.diag([-1, -1, 1, 1])
ijk2ras = np.dot(lps2ras, ijk2lps)
​
gravity_ijk = np.append(np.array(gravity[0]), 1).reshape(-1, 1)
gravity_ras = np.dot(ijk2ras, gravity_ijk)
gravity_ras

```

Step3. transform the acquired coordinate ijk to ras and markup it again in Slicer.

 ![スクリーンショット 2023-06-25 145822](https://us1.discourse-cdn.com/flex002/uploads/slicer/original/3X/e/1/e16a2332c24267bca969603c0484aeb8a80f1284.jpeg)

Problem  
Cannot convert nrrd centre-of-gravity coordinates ijk to slicer coordinates ras between step2 and 3  
Could you tell me what is wrong? Thank you!

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<div class="post-metadata">

**Author:** ![pieper](https://sea2.discourse-cdn.com/flex002/user_avatar/discourse.slicer.org/pieper/32/8_2.png) [@pieper](https://discourse.slicer.org/u/pieper)\
**Post date:** [June 25, 2023, 6:07pm UTC](https://discourse.slicer.org/t/building-the-ijk-to-ras-transform-from-a-nrrd-file/1513/5 "2023-06-25T18:07:34Z")

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You should be able to work from this example:  
[Script repository — 3D Slicer documentation](https://slicer.readthedocs.io/en/latest/developer_guide/script_repository.html#get-centroid-of-a-segment-in-world-ras-coordinates)

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<div class="post-metadata">

**Author:** ![Optics\_Bioeng](https://sea2.discourse-cdn.com/flex002/user_avatar/discourse.slicer.org/optics_bioeng/32/66534_2.png) [@Optics\_Bioeng](https://discourse.slicer.org/u/Optics_Bioeng)\
**Post date:** [June 27, 2023, 7:17am UTC](https://discourse.slicer.org/t/building-the-ijk-to-ras-transform-from-a-nrrd-file/1513/6 "2023-06-27T07:17:46Z")

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Thank you. I will have a try.