Probabilistic multiscale image segmentation

Abstract

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. The present paper deals with probabilistic (or multiparent) linking, i.e., a setup 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. 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.

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“…Other scale-space approaches with related aims have been developed by Lifshitz and Pizer (1990), Griffin et al (1992), Gauch and Pizer (1993), Burbeck and Pizer (1995), Olsen (1997) and Vincken et al (1997). Interesting works regarding hierarchical representations in biological vision have been presented by Riesenhuber and Poggio (1999).…”

Mutual Information Criterion-Based Optimal Scale Selection for Image Denoising and Segmentation

“…Equation (27) indicates that it is redundancy to compute some of the terms for the mutual information in (25). Thus, we simplify the i-Se algorithm to increase computation speed by deleting redundancy term.…”

“…The main idea behind the analysis for i-Se algorithms is to derive monotonic and smooth properties on the mutual information based formula of (25) and further to point out that the solution to the i-Se algorithm is convex. We begin with the following two inequality equations (proofs for the following two lemmas are given in the appendix).…”

“…The second type is derived from the diffusion process and based on partial differential equations [20]. It originates from the conventional isotropic heat flow equation and has been widespread used in image filtering [21][22][23][24], segmentation [25][26][27] and inpainting [28][29][30]. And the third type is based on the mathematical morphology [31][32][33].…”

Qualitative Multi-scale Feature Hierarchies for Object Tracking

“…In retrospect, a main reason why stability problems were encountered is that the pyramids involved a rather coarse sampling in the scale direction. (Koenderink 1984) defined links across scales using iso-intensity paths in scale-space, and this idea was made operational for medical image segmentation by (Lifshitz & Pizer 1990) and (Vincken et al 1997). (Lindeberg 1993) constructed a scale-space primal sketch, in which a morphological support region was associated with each extremum point and paths of critical points over scales were computed delimited by bifurcations.…”