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<p><b>Abstract</b>—A method is presented to segment multidimensional images using a multiscale (hyperstack) approach with probabilistic linking. A hyperstack is a voxel-based multiscale data structure whose levels are constructed by convolving the original image with a Gaussian kernel of increasing width. Between voxels at adjacent scale levels, child-parent linkages are established according to a model-directed linkage scheme. In the resulting tree-like data structure, roots are formed to indicate the most plausible locations in scale space where segments in the original image are represented by a single voxel. The final segmentation is obtained by tracing back the linkages for all roots.</p><p>The present paper deals with probabilistic (or multiparent) linking, i.e., a set-up in which a child voxel can be linked to more than one parent voxel. The multiparent linkage structure is translated into a list of probabilities that are indicative of which voxels are partial volume voxels and to which extent. Probability maps are generated to visualize the progress of weak linkages in scale space when going from fine to coarser scale. This is shown to be a valuable tool for the detection of voxels that are difficult to segment properly.</p><p>The output of a probabilistic hyperstack can be directly related to the opacities used in volume renderers. Results are shown both for artificial and real world (medical) images. It is demonstrated that probabilistic linking gives a significantly improved segmentation as compared with conventional (single-parent) linking. The improvement is quantitatively supported by an objective evaluation method.</p>
Image segmentation, multiscale analysis, scale space, probability maps, partial volume artifact, object definition.

K. L. Vincken, A. S. Koster and M. A. Viergever, "Probabilistic Multiscale Image Segmentation," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 19, no. , pp. 109-120, 1997.
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