Multimodal Segmentation

The validity of the multimodal approach is evaluated on the basis of the highly complex task of segmentation of the small intestine. Currently, no satisfying solutions exist to deal with this problem. Although the small intestine has a complex spatial structure, from a topological point of view it is a rather simple linear tube with exactly defined start- and endpoint. Therefore, the key to solving the segmentation problem is to make use of the topological causality of the structure. The overall extraction process has to be mapped onto the linear structure of the intestinal system to simplify the task.

The initial step of our multimodal technique is the haptically assisted extraction of the centerline of the tubular structures. The underlying idea is to create guiding force maps, similar to the notion of virtual fixtures found in teleopera-tion [63,64]. These forces can be used to assist a user's movement through the complex dataset.

To do this we first create a binarization of our data volume V by thresholding. The threshold is chosen dependent on the grayscale histogram, but can also be specified manually. We have to emphasize that this step is not sufficient for a complete segmentation of the datasets we are interested in. This is due to the often low quality of the image data. Nevertheless, in the initial step we are not interested in a topologically correct extraction. On the contrary, we only need a rough approximation of our object of interest. From the resulting dataset W

we generate an Euclidean distance map by computing the value

DM(x, y, z) = min _d[(x, y, z), (xi, y,, zi)], (14.41)

for each (x, y, z) e W, where d denotes the Euclidean distance from a voxel that is part of the tubular structure to a voxel of the surrounding tissue W = V \ W.

In the next step we negate the 3-D distance map and approximate the gradients by central differences. Moreover, to ensure the smoothness of the computed forces, we apply a 5 x 5 x 5 binomial filter. This force map is precomputed before the actual interaction to ensure a stable force-update. Because the obtained forces are located at discrete voxel positions, we have to do a trilinear interpolation to obtain the continuous gradient force map needed for stable haptic interaction. Furthermore, we apply a low-pass filter in time to further suppress instabilities. The computed forces can now be utilized to guide a user on a path close to the centerline of the tubular structure. In the optimal case of good data quality, the user falls through the dataset guided along the 3-D ridge created by the forces. However, if the 3-D ridge does not exactly follow the centerline the user can guide the 3-D cursor by exerting a gentle force on the haptic device to leave the precalculated curve.

While moving along the path, points near the centerline are set. These points can be used to obtain a B-spline, which approximates the path. In the next step this extracted centerline is used to generate a good initialization for a deformable surface model. To do this, a tube with varying thickness is created according to the precomputed distance map. This resulting object is then deformed subject to a thin plate under tension model. Details of the algorithmic background of this deformable model approach are described in section 14.4.2.

Because of the good initialization, only a few steps are needed to approximate the desired object [65]. The path initialization can be seen in Fig. 14.18(a). Note, that the 3-D data is rendered semitransparent to visualize the path in the lower left portion of the data. Figure 14.18(b) depicts the surface model during deformation.

In order to further improve the interaction with complicated datasets a step-by-step segmentation approach can be adopted by hiding already segmented loops. This allows a user to focus attention on the parts that still have to be extracted. For this purpose the 3-D surface model is turned back into voxels and removed from the dataset (Fig. 14.19). This step can be carried out in

(a) Intialized path. (b) Deforming tube.

Figure 14.18: Interactive segmentation.

(a) Intialized path. (b) Deforming tube.

Figure 14.18: Interactive segmentation.

real-time by using a hardware accelerated, 2-buffer based approach as described in [66].

In order to validate the described system, it was used to generate topo-logically correct models of the small intestine. The application studies of the system required interaction times of 20-30 min, which compares favorably to the reported times of 1-2 h in previous research. It was possible to extract the centerlines of the complicated datasets, obtain the segmentations, and create

(a) Voxelization. (b) Removed segemented part.

Figure 14.19: Hiding segmented parts.

(a) Voxelization. (b) Removed segemented part.

Figure 14.19: Hiding segmented parts.

virtual fly-throughs. Further evaluation studies were performed, which show a statistically significant performance improvement in the trial time when using haptically enhanced interaction in 3-D segmentation. Also in the haptic condition the quality of segmentation was always superior to the one without force feedback.

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