Distance of what to what?

You need two regions of interest to compare (contours for example). Then you can think of Dice coefficient, Hausdorff distance and Jaccard index.

Thanks Michel K Herde .

I have a doubt regarding their distance measure.

They have written that

"..input points are the coordinates of a binary skeleton of the fixed image. In the script, the distance between a pair of points is calculated (m), as i

s the distance between the deformed coordinates (m’, see Supplemental Fig. 3). The absolute value of the difference is the error."

It is not clear why they are assuming distance between pair of points will persist. Please comment

Lambert Zijp Distance measure of points before and after registration. Can you tell me how to calculate 3D hausdorff distance? Does it do overlap or point matching to calculate distance? how doest it work?

If you only have points in both datasets, I hope you also have a one to one correspondence map. If so, I would calculate the mean squared distance (3D Pythagoras without taking sqrt, add them, divide by NbPointPairs) between those points. The three criteria I mentioned earlier are only applicable to ROIs.

Lambert Zijp Sorry I didn't get you. Suppose I have two image previously fixed image A and moving image B. I have found that transformation T makes A similar to B. No I can apply T on A to get a new image A'.

I can compare A' and B. But how?

Suppose I have a point (1,1) in A and it becomes (2,1) after applying T on A. Now how to measure distance with B is not clear. Or how to measure hausdorff distance here. Please suggest. Thanks

I get it that you DO NOT have two sets of Points Of Interest; only two volumes. Or are you registering a volume on itself? If not, you don't know which point in A (with or without applying the transform) corresponds to which point in B.

Then my question in my first post remains: Distance of what to what?

You need to create contours in both volumes (marching for example) or create two sets of POIs.

Or, if you want to compare a couple of registration methods, you could use mean squared pixelvalue differences over the common volume.

Lambert Zijp You are correct! I need to calculate Hausdorff distance between two 3D volume. Is it possible? How does it work? Is there any other volumetric distance measures for these images?

Thanks

No, Hausdorf, Jaccard and Dice, all need contours or surfaces as input.

Mean squared pixelvalue differences seems the only option if you do not want to create POIs or ROIs. But if you match a volume on itself, you have got an enormous amount of corresponding point pairs!

Lambert Zijp Thanks for your kind reply. As per my knowledge in case of Jaccard / Dice measure, two binary image volume mask would suffice. They don't need to provide surface explicitly. But I am not sure in the case of hausdorff distance. How does it calculated? In my case, I am registering two different modality image volumes. I can segment a ROI or the whole image itself from the background(the contour), but it is not clear what to give in input to hausdorff distance.

Michel K Herde Thanks for your answer. I have a doubt.

" The absolute value of the difference (or root mean square thereof) is a measure for how well both images register. "

What I have understood is the below steps:-

1. Suppose I have two image previously fixed image A and moving image B. I have found that transformation T makes A similar to B. So, I have applied T on A to get a new image A'.

2. I have sampled n points on both B and A'.

3. Now I have calculated point wise distance in B and A' individually.

4. RMSE calculated on these distance measures.

5. RMSE value determines the quality of resistance.

Is it fine?

I don't get it Subhajit: you sample points (xyz coordinates) in A and A'. The distance between them is exactly zero!!

Michel is talking about a skeleton. A skeleton can only be created when you have binary images (just a foreground and a background value). Creating a skeleton (medial axis transform, or 'peeling') is well defined in the continuous domain, but is ill defined in pixeled data: what are features to be preserved, and what are merely tessellation artifacts...

If you have binary images, Dice is easily calculated, and going to contours/surfaces is trivial: each pixel having a neighbor with a different pixelvalue, belongs to the contour/surface (depending on the connectedness you want).

Nice discussion by the way.

Lambert Zijp A' is the transformed image of A. B is the moving image.

Why do you think the distance will be zero if I use sample points from A?

What I have got from the previous conversation is that:-

1. Let's say I select each pixels after 10 pixel in my skeleton or sampling set S(A).

2. Suppose I have a point (1,1,1) in S(A) and after applying T , I get (1,2,1), which is in S'(A).

3. calculate distance(RMSE_1) between each point from S and S'.

4. What this distance imply is not clear to me . This is just displacement or deformed distance measure. How is this can be treated as a parameter for registration accuracy?

5. Are we referring RMSE_2 of the distance measured between S(A) and S(B) as a ground truth?

Michel K Herde Please throw some light on this.

It would be great if you tell me how hausdorff distance has been measured if I have two binary image volumes. I am little jeopardized how hausdorff distance measure finds corresponding matching points between two image volumes? Because It finds the max distance of most mismatched point between two image volumes. Please elaborate a little about that also.

Lambert Zijp and Michel K Herde Thanks for all of your kind comments and efforts.

Forget about the distance being zero, I wanted to say that if you sample xyz points in A and B', the distance is zero (there is only a pixelvalue difference).

For Dice and Jaccard, two binary ROIs (masks as you call it) is enough.

The Hausdorff distance will always be between a point in A and B' that are both located on the edge.

I am a C programmer, and the volumes in medical imaging are not 'too' large, so I calculate Hausdorff by brute force:

(pseudo code)

GlobalHausdorff = 0

for each contour point of A

{ LocalHausdorff = 100000000

for each contour point of B'

{ if deltaX or deltaY or deltaZ greater than LocalHausdorff continue

NewLocalHausdorff = Pythagoras

if LocalHausdorff greater than NewLocalHausdorff

LocalHausdorff = NewLocalHausdorff

}

if LocalHausdorff greater than GlobalHausdorff

GloballHausdorff = LocalHausdorff

}

You do deformable registration of breast MRI with CT? If so, Dice and Jaccard are not very helpful. Hausdorff of the skin is just one criterion. Maybe you can find a couple of landmarks in the breast? If you segment something other than skin, it is hard to discern segmentation error from registration error.

Visual inspection of the result and of the deformation vector-field is always good, but will not give you a 'number'.

Lambert Zijp Thanks a lot.

What I understood from your last comment is that , I need to get edge contour to get hausdorff distance. I can not use whole binary image mask as an input(?).

Yes, I wanted to validate my breast MRI data after registration. I am looking for a volumentric distance measure, which has quantifiable value. I thought hausdorff would work, but now I can see, it is hard to find only boundary of the shape. I was thinking if I Can I the other method suggested by Michel K Herde .

Hi Michel K Herde , I could not able to understand your statement " there is good overlap in fine details ..". So, you are saying lesser the value of RMSE, higher chance of alignment perfectly between fixed and moving image? Is that true? If so, don't your think sample should be taken from both fixed and moving image. So, what I was thinking of applying Transformation on the sample points from moving images and calculate RMSE with sample from fixed image. So, in a multimodal setting, I just want to show if method A is better than method B, by using RMSE value from fixed and moving images. Is it possible? I could not able to understand how to find sample points from fixed and moving images, how can I assure both are same set of points?

1. Get sample S from fixed images using some logic, get sample points S' using the previous logic from moving image.

2. Apply known transformation on S' to get S''.

3. Calculate RMSE between S and S'' for different methods and compare.

Am I right here?

what you suggested me before was to get S' , by applying transformation on S, and then calculate RMSE. I am not sure what RMSE will yield here. Because S' is deformed set, so the value of RMSE may be bigger or lesser in value, depending upon the deformation. But it doesn't tell about how good a registration was. That must depend upon the overlap or alignment between fixed and moving images.

I know, its pretty silly to ask you same question. But please clarify with a small example if you can (about how to compare registration method A with B, using fixed and moving images).

Thanks