Dear Biomch-l,

I have the following problem:

Using image processing algorithms (sub-voxel accuracy) on medical

imaging datasets, four marker centroids are determined, combined

and normalized to define a local reference frame Rloc within a

global reference frame Rglob.

The next step is to find the transformation matrix between both Rloc

and Rglob. To do this I am using, the unit vectors of both Rloc and

Rglob into a SVD algorithm (Challis, J. of Biomechanics, 28, 733-

737, 1995). Root Mean Square Error (RMS) the position was found

as well (Soderkvist, J. of Biomechanics, 26, 1473-1477). Mean

Absolute Relative Difference (MARD) as well (see Challis).

It seems to work because further use of the results are satisfactory.

My problem is the following:

the RMS errors I found are very small (between 0.000016 mm and

0.00004 mm) and are not accepted by one of the reviewers of a

paper we are trying to publish.

I agree very much that such error, I quote the reviewer, "is

unrealistically small" ... but we checked, re-checked our code, let

our data processed by an external dept. and cannot locate any

problems in our protocol: the above error seems really real, except

of course if we are missing something ...

I would greatly appreciate if somebody could process the following

data and compared it to our following results. Could you, please,

take a look at it ? Many thanks !!

THE DATA

1 0 134.820068 110.476936 -383.543427

1 1 134.725296 111.466965 -383.647430

1 2 135.702469 110.512123 -384.012543

1 3 134.359253 110.340698 -384.420410

2 0 0.000000 0.000000 0.000000

2 1 1.000000 0.000000 0.000000

2 2 0.000000 1.000000 0.000000

2 3 0.000000 0.000000 1.000000

First digit indicates the frame (1: Rloc, 2: Rglob).

Second digit indicates the landmark.

Then, the X Y Z coordinates of each of the 4 landmarks.

THE RESULTS

Transformation matrix

-0.094769 0.990052 -0.104002 -136.490646

0.882429 0.035186 -0.469128 -302.787415

-0.460802 -0.136233 -0.876985 -259.185822

0.000000 0.000000 0.000000 1.000000

RMS error

0.000016 (small, isn't !?, is it normal or not ?).

MARD error

inf (to small to be handled in single floating point precision ...)

Rotation amplitude in radians (in degrees).

0.252528 (14.468779)

Translation (mm)

-251.301172

To me, such a small error can be explained by the fact we are using

the unit vectors of both reference systems into the SVD routines to

process the transformation matrix, meaning the cluster is very rigid

and therefore the matrix well defined.

Please, can you comment this ?

Again, thank you very much in advance !!

Serge

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Serge VAN SINT JAN, Ph.D. | Marie Curie Fellow

VAKHUM project Co-ordinator | phone: + 32 2 555 6325

Dept. of Anatomy (CP 619) | + 32 2 555 6376

University of Brussels | fax: + 32 2 555 6378

808 Lennik Street | email: sintjans@ulb.ac.be

1070 Brussels - Belgium | WWW: http://homepages.ulb.ac.be/~sintjans

VAKHUM project: http://www.ulb.ac.be/project/vakhum

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