Non-linear Voxel-based 2D/3D Registration using Differential Properties
Problem
Image registration is a problem often encountered in digital medical imaging. In this work we developed an atlas-based matching algorithm, which can be used to establish a fully-automatic segmentation application, by transferring the atlas information (anatomic labels) directly to the patient dataset [1]. Naturally the atlas data differs from the patient data. In this case a registration approach is necessary to match these two datasets.
One of the main problems the voxelbased registration algorithm has to deal with is detecting the anatomically correlating voxels in both datasets. Well established distance measures, like least squares distance or variance of ratio, are using intensity information only. For the majority of cases this is insufficient for identifying correlating voxels.
Therefore we expand the least squares distance by differential informations, assuming that the more specific characterization of each point improve the identification of correlating voxels. Consequently the segmentation of the patient dataset becomes more accurate.
Methods
In this work each voxel is characterized by its intensity value, normals and curvature value. The intensity is automatically taken from the images. Calculating normals and curvature needs to approximate the first derivation. For this approximation we use the Deriche operator [2], which can be implemented recursively and in parallel. Via this gradient we can estimate normals by definition and curvature values by using the Foerstner operator [3].
Our algorithm computes the transformation of corresponding anatomical regions in these two datasets. These computations are done in an iterative way, where each iteration step is subdivided in two main parts. The first one calculates a force-field as proposed in Besl’s [4] iterative closest point algorithm (ICP). Here, we estimate a force vector for each point of the patient dataset by searching the atlas volume for a corresponding point in a specific spherical region. The point with the minimal distance concerning the measure is taken as the corresponding point in the patient volume. In the second step we have to update the transformation with the force field from step one. We take a temporary transformation by summing up the entries of the old transformation and the entries of the actual force field. In order to estimate a smooth transformation we have to convolve the temporary transformation with a Gauss filter. This procedure was established by Thirion [5]. After that we have to transform the atlas with this resulting transformation. This atlas is then used as the new atlas input for the next iteration.
These iteration steps will be terminated if the maximum number of iterations is reached or if no more changes occur regarding the distance between the patient and the atlas.
To illustrate the performance of the new multi information distance we present two experiments using patient datasets of the human pelvis and the visible human dataset as atlas.
Figure 1: Illustration of the reference dataset and one reference point (left), the multi-information distance (middle) between the reference point and all points of the model dataset (right). The marker in the upper right corner shows the position with minimal distance consequently the corresponding point .
In our first experiment we use a simple visualization tool for the distance measure. This tool calculates the distances between one point in the patient data and all points in the atlas data. We expect the minimum value at the position of the anatomically corresponding atlas voxel (see Figure 1).
Experimentally we have compared the least squares distance with the multi information distance. We found that using the least squares measure does not allocate corresponding voxel pairs as well as our new multi information approach using curvature and normal characteristics.
At this point we have to note that defining the corresponding voxel is a subjective process and there are no objective measures to identify this voxel.
In the second experiment we implement multi information registration. We compare the results of the grey value based distance and the multi information distance applied to the patient images and the visible human atlas. The 3D images have initially been registered by an affine transformation and segmented manually. For both applications we use comparable parameters. After matching the pelvis datasets with the visible human dataset (see Figure 2), we use the estimated transformation for transferring the label information of the visible human atlas directly to the patient data. We compare the segmentation results with the manual segmentation. It can be seen that the full automatic segmentation based on multi information distance identifies more voxels exactly.
Figure 2: Illustration of the reference dataset with an edge overlay of the unregistered model dataset (left) and the result of the multi-information registration (right).
Selected Publications
[1] J. Ehrhardt, H. Handels, S. J. Pöppl: Atlas-based determination of anatomical landmarks to support the virtual planning of hip operations. CARS 2003: 99-104
[2] R. Deriche, Using Canny's criteria to derive a recursively implemented optimal edge detector. IJCV,1: 167-187, 1987
[3] K. Rohr. Differential operators for detecting point landmarks. Image and Vision Computing, 15(3):219-233, 1997
[4] P. J. Besl and N. D. McKay. A method for registration of 3-D shapes. IEEE Transaction on Pattern Analysis and machine Intelligence, 14(2):239-258, February 1992.
[5] J.-P. Thirion, Image matching as a diffusion process: an analogy with Maxwell’s demons, Medical Image Analysis 2 (1998), no. 3, 243-260
[6] D. Säring, J. Ehrhardt, H. Handels, S. J. Pöppl: Nicht-lineare voxelbasierte Registrierung unter Einbeziehung von Differentialeigenschaften. Bildverarbeitung für die Medizin 2004: 284-288
Project Team
D. Säring,
J. Ehrhardt,
H. Handels
