Automatic detection and segmentation of evolving processes in 3D medical images: Application to multiple sclerosis – Summary
- The objective of this work was to automatically detect regions with apparent local volume variation with a vector field operator applied to the local displacement field obtained after a non-rigid registration between two successive temporal images.
- Quantitative measurements, such as the volume variation of lesions or segmentation of evolving lesions, are important.
- At this stage, we have only applied the approach to a few experimental cases. A clinical validation remains to be done.
- Qualitative information: Positions of lesions, segmentation of lesions.
- Quantitative information: Total volume of lesions, volume variation of lesions, segmentation of lesions.
- Images at different times are not directly comparable (movement of the patient, different machine, etc). We have to apply a transformation to compensate for the difference in position (translation) and orientation (rotation).
- Even with pre-processing, some perturbations can still disturd registration algorithms and in this case there is an inaccuracy in the alignment.
- Automatic methods to study lesions in time series:
- Thresholding does not always make it possible to distinguish the lesions from the white matter.
- Substract two images to find intensity changes. The substraction is dependent on the accuracy of the rigid registration. It is not trivial to distinguish global rigid changes from local rigid and non-rigid changes if the registration had issues.
Our idea is to avoid a voxel-by-voxel comparison using the ‘apparent’ motion between two images. We want to find a vector at each voxel that expresses its visual motion from one image to another by using a kind of optic flow algorithm. Stages:
- Images are aligned by rigid registration
- Compute the displacement field with non-rigis registration.
- Focus on the detection of regions of interest thanks to vector field operators.
- Use regions of interest to segment evolving lesions.
- We preferred a geometrical approach over an intensity-based method to be more robust.
- Extract feature points along the crest lines of the isosurface corresponding to the zero-crossing of the Laplacian of the image.
- Algorithm in [Pennec and Thirion, 1997]
- Compute a 3D displacement field with a non-rigid algorithm based on local difussion [Thirion, 1998; Cachier et al. 1999]
- It is an optical flow method the diffuses image 2 into image 1. Image 2 is iterativaly deformed.
- It works, even if the intensities are not equivalent.
- We use four multi-resolution levels with four iterations at the highest resolution level and the sigma for the Gaussian smoothing of the vector field is 1.0.
- At the end, each 3D point on image 1 has a vector
$u$ that gives its apparent displacementd. Field$u$ gives an idea of the temporal evolution between the images. - Objectives:
- Obtaining a scalar image enhancing time evolutions.
- Introduce operators that yield scalar values with a physical meaning for better interpretation.
- Inspired from [Davatzikos et al. 1996]
- The Jacobian of the deformation function gives the local variation of an elementary volume. It is a first order approximation.
- Jacobian > 1 -> local expansion. Jacobian < 1 -> local shrinking.
The Jacobian is invariant with respect to imperfect rigid registration. Of course, it requires that the non-rigid registration algorithm still computes a correct displacement field. This is actually the case as long as the original rigid alignment remains close to the ideal one.
It is therefore much less constrained than when employing the subtraction method where a precision of the initial rigid alignment typically better than one voxel is required.
- We need to compute the first nine derivatives of the displacement field
$u$ . - We use recursive filtering which gives an image for each derivative. We compute the Jacobian on sub-images and then fuse the
sub-results which include an overlapping border to avoid side effects.
- It is possible to compute a good approximation of the Jacobian at each point by calculating the determinant of the linear part of the
approximative local affine transformation.
- [Thirion and Calmon 1999]: Another vector field operator based on the divergence and the norm of the displacement field
$u$ . We have
no physical interpretation of the value, so it is difficult to automatically threshold the image to extract regions of interest.
- [Prima et al. 1998]
- [Rey et al. 1999]
- We can extract areas that correspond to significant temporal evolution since it is possible to find a uniform threshold over the
whole Jacobian image.
- They developed a simpler method: [Cacher and Rey, 2000]
- Skipped the rigid registration step for this case.
- Accuracy of the delimitation is qualitatively correct, but we observed a difference of between 5 ans 20% between the correct diameter
of the lesions and the measured diameter.
- Used a method based on “deformable models” [Montagnat and Delingette, 1998]. It combines both geometric and image information to perform
the segmentation.
- Gives a better result and makes it possible to perform quantitative measurements.
- This is not a clinical validation, which is much more complicated and will require a long period of time (2 years).
- Preliminary results: [Rey et al, 2000; Lebrun-Frenay et al, 2000]
Simply subtracting the images produces a very noisy result, while the results provided by this method remain similar to the results without the imperfect rigid registration.
- We believe that our approach will be useful to detect evolving regions corresponding to local apparent expansion or shrinking.
- At this stage, we have only applied the approach to a few experimental cases to demonstrate its potential.
- The method has the advantage of not being very dependent on the initial alignment given by a rigid registration stage, but still
gives poor results for segmentation. Thus we plan to use it in combination with deformable models algorithms.
- Clinical validation remains to be done, which will require additional work.