The four registration methods were also applied to three actual time series.
For these datasets, the activation profile used to compute cross-correlation was obtained by convolving the task timing with the SPM99 hemodynamic model.
A moving average was removed from the estimated motion parameters before computing the correlation in order to discard slow motion trends. In the case of the DLS method, the number of activated voxels in the three mask comprised, respectively, 19%, 22% and 18% of the brain size.
Reducing Activation-Related Bias in FMRI Registration 283
Fig. 3. Registration errors for the parameters and for the simulated time series with true correlated motion (true motion was removed). Graphs refer to LS1 and LS2 (left) and to DLS and SRA methods (right).
The results obtained with the three actual time series also indicate a reduc- tion in the correlation between the motion estimates and the activation paradigm for the DLS and SRA. This is particularly visible in the (and parameter (see Figure 4). Correlation values are presented in Table 2.
For the first actual time series, one can see that the different methods do not generally agree in the estimation of (and parameter (see Figure 4).
This effect, which is also observed for the other two time series, may be due to the fact that the methods do not share the same computational framework, as mentioned above.
4 Discussion
The problem of minimizing the bias introduced by the presence of activation is of particular importance due to the use of high field magnets (> 3T), which increase
284 L. Freire et al.
Fig. 4. Detrended registration parameters and for the first actual time series. Graphs refer to LS1 and LS2 (left) and to DLS and SRA methods (right).
activation amplitude. The work presented in this paper shows that the SRA and DLS methods seem suitable for the problem of motion compensation of FMRI studies, even in a situation where true activation-correlated subject motion is present. Indeed, this is an important issue when assessing the robustness of a registration method. The explanation is twofold: the first deals with the fact that interpolation errors during registration could be confounded with an activation- like bias; the second, to the well known fact that registration error (generally) increases with the initial misalignement.
The three actual time series used in this work were selected from among 14 subjects because they clearly presented a strong correlation with activation paradigm. Nevertheless, the true motion for these subjects is unknown and may or may not be correlated to the stimulus. However, the results obtained from the experiments performed in this paper clearly support the idea that the bias in motion estimates was due, at least in part, to presence of activation. Indeed, incorporating the activation profile into the SRA method or discarding about 20% of the voxels in the DLS method substantially reduces the correlation with the task.
A few plots obtained from the actual data show a disagreement between the different registration methods. In our opinion, this situation may stem from the fact that the time series include spatial distortions induced by the fast acquisi- tion scheme. Indeed, there is an interaction between these distortions and head movement and therefore, the rigid registration approach cannot perfectly align the time series. In such ill-posed situations, similarity measures are prone to sev- eral local minima, which are due to local good matches between object features, possibly caused by the fact that both methods rely on different interpolation methods. This may explain why the two different computational frameworks
Reducing Activation-Related Bias in FMRI Registration 285 sometimes provide slightly different solutions for the rotation parameters for LS1 and LS2.
The success of the SRA method described in this paper calls for the devel- opment of integrated methods mixing motion estimation, activation detection and distortion correction. Like activation detection, however, distortion correc- tion may require additional information, such as a magnetic field phase map obtained from the MR scan [9], adding another level of complexity because this phase map may depend on the head position in the scanner.
5 Conclusion
During the last decade, numerous general purpose similarity measures have been proposed to tackle medical image registration problems. They have led to a lot of success with important impact on neuroscience and clinical applications. The assumptions underlying these similarity measures, however, often neglect some features specific to FMRI data, leading to the kind of bias mentioned in this paper. In our opinion, tuning registration methods to account for these features, as demonstrated for the DLS and SRA methods, will be a necessary and fruitful endeavour.
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A Robust Algorithm for Nerve Slice Contours Correspondence
Shaorong Wang1,2, Liyan Liu1,2, Fucang Jia1,2, Hua Li1
1Key Lab of Intelligent Information Processing, Institute of Computing Technology Chinese Academy of Sciences, Beijing, 100080
{shrwang, lyliu, fcjia, lihua}@ict.ac.cn, www.ict.ac.cn
2Graduate School of the Chinese Academy of Sciences, Beijing 100039
Abstract. In this paper, the three-dimensional reconstruction of consecutive brachial plexus slices is discussed. To get precise results, the contour-based re- construction method is adopted. As the contour correspondence problem is of great importance to the reconstruction, a cluster method is firstly used to get rid of the offsets between the contours introduced during the stage of data acquisi- tion. Besides correspondence check, a robust similarity-based correspondence algorithm is proposed which results in an automatic correspondence rate more than 97%.
1 Introduction
The repair and regeneration of damaged brachial plexus has always been a focus in orthopaedics. Until now there still exists imperfectness in the restore of nerve func- tion. The main reason lies in the wrong anastomose of nerve fibers between sense and motor ones. So it’s an urgent problem in basic and clinical researches to know the exact structure of brachial plexus [16].
The structure of brachial plexus is very complicated. The nerve bundles branch, cross and recombine one another. Sense fibers and motor ones in nerve bundles mix together to combine a commix bundle in every part of brachial plexus. In this case, a three-dimensional model would provide a good understanding of the nerve structure where the traditional two-dimensional nerve atlas suffered.
In this paper, the contour-based method is introduced to reconstruct brachial plexus’s three-dimensional structure, including both out contour and the ultra- complicated pathways of nerve bundles inside. A robust similarity-based contour correspondence algorithm is proposed to guarantee a precise and correct result.
2 Related Work
The volume data visualization methods can be grouped in two classes according to different problems and data characteristics [14]: surface-based reconstruction [12]
and direct volume rendering [13].
G.-Z. Yang and T. Jiang (Eds.): MIAR 2004, LNCS 3150, pp. 286-293, 2004.
© Springer-Verlag Berlin Heidelberg 2004
A Robust Algorithm for Nerve Slice Contours Correspondence 287 Surface-based reconstruction also has two categories, two-dimensional contour- based reconstruction [12] and iso-surface extracting-based reconstruction [2].
The former is a commonly used and effective visualization method. It means to re- construct surfaces of three-dimensional objects based on a collection of planar con- tours representing cross-sections through the objects. It is mainly composed of three problems [3]: correspondence problem, tilling problem, and branching problem.
Among them, contour correspondence, whose goal is to obtain correspondence rela- tionship of contours on two adjacent slices, is vital to the whole progress. [5] com- putes the overlapping area of contours on adjacent slices as the correspondence crite- rion. [1],[9] approximate the contours by ellipses and then assemble them into cylin- ders to determine the correspondence. [4] uses domain knowledge to constrain the problem. [7] realizes automatic reconstruction through Greeb graph. [6] uses a method of distance transform and region correspondence. [8] realizes a nerve recon- struction tracing system, in which the primary rule for correspondence is to compute the overlapping area and distance between the centers of the contours on adjacent slices.
3 Nerve Reconstruction
In this paper, we realize a nerve reconstruction system to deal with 842 brachial plexus slices. In order to obtain precise three-dimensional structure of all nerve bun- dles and display clearly their relationship, the contour-based reconstruction method is adopted.
The whole process can be divided into several steps including image adjustment, image segment, contour correspondence, contour reconstruction and rendering. The source data is a series of two-dimensional images containing brachial plexus informa- tion. Fig.1-a is one of these slices with the thickness of 15 micron and interval of 0.2mm.
Image adjustment: Based on the markers on the original images, the adjust- ment is accomplished by matching corresponding landmarks in both images through an affine transformation.
Image segmentation: Firstly each adjusted image is binarized, and then the con- tours on each slice are extracted by use of watershed-based algorithm. Due to the complexity of nerve structure, automatic segmentation associated necessary human intervention is adopted.
Contour correspondence: To find correct connection relationship between contours on adjacent slices. This is the main topic of this paper, and we will give a more de- tail description later.
Contour reconstruction: [10],[11]’s methods are used here to reconstruct the three- dimensional surface structure of the brachial plexus.
Rendering: The final stage of the process is to render the results of reconstruction on the screen.
288 S. Wang et al.
The main contributions of this paper are listed as following:
Cluster small contours into big circles. Perform the correspondence on the scale of big circles firstly to get rid of offset errors introduced during the data acquisition.
Execute the correspondence progress repeatedly and in each loop put those corre- sponded contours as benchmarks for next correspondence.
Check intermediate results by the constrain criterion and recorrespond the uncorre- sponded contours with a new method by a new set correspondence intensity.
4 Contour Correspondence
Correspondence problem is the most important and difficult problem of the contour- based reconstruction method. In our case, the structure of brachial plexus is very complicated and the offsets between the contours on the adjacent slices are sometimes very large. So the general contour-based methods suffer here.
[15] uses (1) to compute the discrepancy of two contours. If the discrepancy is lower than a given value, there exists correspondence between the two contours.
Through this method an automatic correspondence rate of near 90% is obtained.
Careful observation of the slices shows that the contours representing nerve fibers assemble into several big circles or ellipses, which represent nerve bundles. And offsets of the fibers in the same bundles are very similar between the adjacent slices.
According to above characteristics, we present our algorithm as following:
1.
2.
3.
For each slice, cluster the small contours into several big circles.
Correspond the big circles, compute the corresponding circles’ offsets and add them to the small contours.
Correspond the small contours.