PROTOCOL FOR COMMUNICATING REGISTRATION TRANSFORMATIONS
Version 2.1 May 14th, 1997
This document serves to define the protocol for communicating geometrical transformations for volume images. The purpose of a transformation is to register one volume image with another.
The image volumes are those of
the project, “Retrospective Image Registration Evaluation”, 8R01EB002124-03, J.
Michael Fitzpatrick, Principal Investigator, Benoit M. Dawant,
Robert J. Maciunas, Robert M. Kessler, Investigators,
A description of the database
that contains the image volumes is given in the file format.txt. Ms. Ramya Balachandran of the Department of
Computer Science,
1. COMMUNICATION BY EMAIL
While the investigators at each site will copy the images via ftp from Vanderbilt, they will communicate their image transformations to Vanderbilt by email. (The schedule for these communications will be given later.)
These transformations will be sent in an ASCII file in a format that is specified below. They should be sent to Ms. Ramya Balachandran at
ramya.balachandran@vanderbilt.edu
2. PAIRS OF IMAGE VOLUMES
TO BE REGISTERED
For each patient included in the study there will be one CT and/or PET image volume and a subset of seven MR volumes (MP-RAGE; spin-echo T1, PD, T2 and the rectified versions of these three).
For each of these patients, each team of investigators will determine, based on their retrospective registration, a transformation from the CT volume, if present, to each of the MR volumes, and from the PET volume, if present, to each of the MR volumes. They may also determine a transformation from the MR MP-RAGE volume to the MR T2 weighted volume, in the cases where both of these are present. All registration pairs are indicated by the directed paths in the schematic below:
A given transformation maps points from one volume on the left, which we will call the “From” image, to one volume on the right, which we will call the “To” image.
Each transformation will be compared with a “gold standard” transformation for the corresponding From-To image pair. The gold standard will be a rigid body transformation. Thus it is expected that the transformations submitted by each team will also be rigid body transformations.
3. THE TRANSFORMATION PARAMETERS
There are many ways to specify a rigid body transformation, such as (a) three angles (e.g., the Euler angles) plus one translation vector, (b) one orthogonal three-by-three matrix plus one translation vector, (c) a quaternian plus one translation vector, (d) three translation vectors for each of three non-collinear points, and others. Additional implicit parameters must be agreed upon in advance or communicated with each of these methods: the position of the origin of the coordinate reference system and the directions of the x, y, and z axes. Additionally, methods (a) through (c) require the specification of the position of the center of rotation, and method (d) requires the specification of the positions of the three points.
In choosing our method of communication, we want to minimize the chances for miscommunication and error. Therefore, we have chosen a set of parameters that is easy to understand, is easy to calculate, includes redundancy, and has limited error propagation. The redundancy provides us a chance to check for errors without compromising the blindedness of our study. The error check is based on the assumption of rigid body motion (see Section 5). The error propagation refers to the relationship between the inevitable round-off errors associated with specifying parameters via a finite number of symbols and the resulting positional error produced at every point within the image volume (see Section 5).
Our method is as follows: A transformation will be specified by the set of original positions and transformed positions for each of the centers of the voxels at the eight corners of the “From” volume. Each position will be specified by its three coordinates, x, y, and z, in millimeters. Thus a transformation will be specified by 48 numbers: three numbers for the original position and three for the transformed position for each of eight positions. We call the coordinates of a transformed position, new_x, new_y, and new_z. Each number will be specified in fixed point with four digits to the right of the decimal place (to 1/10,000 millimeter). An example of a complete specification is provided in Section 4 below.
The origin of the coordinate reference system lies at the center of the first voxel in the voxel file. That file is described in Section 3.2 of the document PROTOCOLS FOR ACCESSING INFORMATION, Version 1.0 November 15, 1994. The x axis lies along the centers of the first row of voxels in the voxel file and is directed from the first voxel to the last on that row, the y axis lies along the centers of the first column and is directed from the first voxel to the last voxel on that column, and the z axis is perpendicular to the x and y axes and directed in the right-hand sense---from the first voxel in the file toward the first voxel in the last slice.
Consider for example the case
described in the PROTOCOLS document, in which the number of rows, columns, and
slices are, respecti
Display of slice 1---
1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
Display of slice 2---
16 17 18 19 20
21 22 23 24 25
26 27 28 29 30
The origin of the coordinate system lies at the center of voxel 1.
The x axis is directed from the center of voxel 1 to the center of voxel 5.
The y axis is directed from the center of voxel 1 to the center of voxel 11.
The z axis is directed from the center of voxel 1 to the center of voxel 16.
(Note that the resultant coordinate system is right-handed.)
It should perhaps be emphasized that all coordinates are in units of millimeters, as opposed to numbers of voxels or pixels. The conversion from voxel dimensions to millimeters should be done independently of the transformation that is being communicated. That conversion should be based on the pixel dimensions and slice thicknesses given in the header.ascii files associated with each image.bin file (see the PROTOCOLS document). Since all coordinates are in the same units, there is no need to include scale factors in the transformation to account for differences in voxel size. Indeed it would be wrong to do so.
4. THE FORMAT OF THE EMAIL MESSAGE
For each of the CT registrations (i.e., one for each of the MR images) the parameters should be emailed in the following form (the dashed lines are part of the form):
-----------------------------------------------------------------------------------
Transformation Parameters
Investigator(s): A. B. Cee, D. E. Eff, G. H. Eye, J. K. Ell, M. N. Oh,
and P. Q. Arr
Site:
Method: 1
Date: 12 December 1994
Patient number: 001
From: CT
To: MR-T1
Point x y z new_x new_y new_z
1 0.0000 0.0000 0.0000 6.1328 -33.4248 -20.2711
2 333.9870 0.0000 0.0000 339.1179 -60.8117 -19.2691
3 0.0000 333.9870 0.0000 33.5198 299.5603 -16.2633
4 333.9870 333.9870 0.0000 366.5048 272.1734 -15.2613
5 0.0000 0.0000 112.0000 5.6848 -34.7688 91.7289
6 333.9870 0.0000 112.0000 338.6699 -62.1557 92.7309
7 0.0000 333.9870 112.0000 33.0718 298.2163 95.7367
8 333.9870 333.9870 112.0000 366.0568 270.8293 96.7387
(All distances are in millimeters.)
-----------------------------------------------------------------------------------
Multiple sets of parameters can be sent in the same email message. The dashed lines serve as delimiters.
The title, “Transformation Parameters” will always be the same, as will be the headings,
Investigator(s):
Site:
Method:
Date:
Patient number:
From:
To:
Note that two lines are provided for each of the first two entries. If only one line is needed the second line should be left blank, as for the Site field in the example.
We will use the first three lines
as a unique label for each of the retrospective methods being evaluated in this
project. Thus they should not change
during the course of the project. If a
team of investigators wishes to employ two different methods of registration, a
separate set of transformations should be submitted for each of them, and they
should be labeled 1 or 2, respecti
The To: entry gives the modality of the MR image. The entry should be one of the following:
MR-MP_RAGE
MR-T1
MR-PD
MR-T2
MR-T1-rectified
MR-PD-rectified
MR-T2-rectified
5. ERROR CHECKING
When we receive a set of transformation parameters we will check them to determine whether they do in fact correspond to rigid body motion. We will accomplish that by calculating the rigid body motion that brings the original positions most nearly into coincidence with the new positions in the least-squares sense. (We employ the standard technique of performing the singular-value decomposition of the cross-covariance matrix to determine the optimal rotation matrix.) If the transformation is indeed a rigid body transformation, the root-mean-square (RMS) error should be on the order of the errors in the parameters. The errors in the parameters can be made as low as 0.0001 mm, but otherwise are controlled by the investigators. (For example, if a multiplication by a rotation matrix is involved, the accuracy is limited by the number of significant digits of the elements of the matrix.)
We wish to keep such errors an order of magnitude below the effects that we are measuring, namely positional differences between the retrospective registration and the gold standard prospective registration. Since the gold standard is itself in error by at least 0.1 mm, we will consider any RMS error of less than 0.01 mm to be acceptable. If the error is 0.01 mm or greater, we will alert the investigators and give them the option of checking for errors and resubmitting the transformation. We emphasize that this procedure does not compromise the blindedness of the study, since this error is unrelated to the registration error that we are attempting to assess and does not involve a comparison with the gold standard registration. It is merely an assessment of whether or not the submitted transformation is a rigid body transformation.
A benefit of having eight points instead of the minimum of three is that it greatly reduces the probability that erroneous numbers will produce a rigid transformation. We chose the particular number eight because it is larger than three and it equals the number of corners. The use of all the corners has a nice property regarding error propagation. Any error in the specification of the corner positions will produce errors in the transformation that will affect the interior positions. For any linear interpolant (including in particular rigid body motion) the error that propagates from the corners to the interior of the volume will be no greater than the largest error at the corners. Thus, each site can be sure that the rigid body transformation that they specify is in fact equal throughout the volume to the one that they have derived to within the accuracy of the corner positions.
In order to prevent, as much as possible, errors in the conversion from the coordinate and transform representation system used by investigators and that used for data submission, on receipt of a transformation table we will generate a reformatted image volume according to the transformation specified by the table. These images will be made accessible only to the investigator(s) who submitted the transform: their location and access method will be given to the submitting site. We suggest that all investigators check the reformatted volumes produced by their registration against the volume we provide, to insure that the intended transformation has been given to us.
6. TEMPLATES FOR THE
TRANSFORMATION PARAMETERS
To make it easier for each site to produce the transformation parameter message and to reduce further the chance for error, we will provide a template for each CT, PET and MP-RAGE image volume which includes part of the required information.
For example,
-----------------------------------------------------------------------------------
Transformation Parameters
Investigator(s):
Site:
Method:
Date:
Patient number: 001
From: CT
To:
Point x y z new_x new_y new_z
1 0.0000 0.0000 0.0000
2 333.9870 0.0000 0.0000
3 0.0000 333.9870 0.0000
4 333.9870 333.9870 0.0000
5 0.0000 0.0000 112.0000
6 333.9870 0.0000 112.0000
7 0.0000 333.9870 112.0000
8 333.9870 333.9870 112.0000
(All distances are in millimeters.)
-----------------------------------------------------------------------------------
There will be one such template for the CT volume, one for the PET volume, and one for the MP-RAGE volume for each patient, given that each volume is present. For a given patient number each site should copy the templates and fill in the identifying data in the first three lines. A copy of these filled-in templates should then be made for each transformation and the rest of the data filled in appropriately, specifically the Date:, the To: image volume, and the columns under new_x, new_y, and new_z.
These templates for the CT, PET
and MP-RAGE volumes will be found in files named ct.trans,
pet.trans and MP-RAGE.trans,
respecti
7. GOLD STANDARD TRANSFORMATIONS AND ORIGINAL
IMAGES
The “gold standard” transformations and original (fiducial marker containing) images can be found in the administration portion of the database in a directory called “fiducial”. Note that, in order to insure the blindedness of retrospective registration submission, these images and transforms are not accessible via the login and password used to obtain the rest of the data on this site.
A schematic of the database may be seen in Figure 1.
registration--\
|
|--admin-----------\
| |
| |--README
| |
| |--doc--\
| | |
| | |--format.txt
| | |--transformations.txt
| | | (this document)
| | ...
| |
| |--news--\
| | |
| | |--96-08-01 (name = date of news item)
| | ...
| |
| |--templates--\
| |
| |--patient_001--\
| | |
| | |--ct.trans
| | |--pet.trans
| |
| |--patient_002--\
| | |
| | ...
| ...
| |
| |--patient_101--\
| | |
| | |--ct.trans
| | |--MP_RAGE.trans
| ... ...
|
|--images--\
| |
| |--patient_001--\
| | |
| | ...
| |
| ...
|
|
|-fiducial-\
|--patient_001--\
| |
| ...
...
|
|--standard--\
|
|--patient_001--\
| |
| |--ct_T1.trans
| ...
...
FIGURE 1. Locations of Templates
and Standard Transformations in the Database
(The images portion of the
database is depicted in detail in the
file
format.txt located as shown above within the database.)
