| Summary: | <p>Newly emerging medical image modalities, large high-dimensional images with resolution and quality improved over time, introduce new challenges for traditionally sequential segmentation procedures. We contribute to three aspects of medical image segmentation, and we provide a new, more reliable way to evaluate the results of segmentation.</p>
<p>The watershed transform is a popular image partitioning procedure from mathematical morphology, used in many applications of computer vision. Our first contribution is to automate an organ segmentation procedure. The algorithm is sequential and is based on the construction of an image partition forest—a watershed-based hierarchical partitioning of a 3D image—followed by the fast marching method for hypersurface front propagation.</p>
<p>Secondly, we parallelise the watershed procedure. Our algorithm constructs paths of steepest descent and reduces these paths into direct pointers to catchment basin minima in logarithmic time, also crucially incorporating successful resolution of plateaux. Three GPU implementation variants and their parameters are analysed through experiments on 2D and 3D images.</p>
<p>Thirdly, we propose the fast dashing parallel method for hypersurface front propagation in a partitioned image. This new parallel procedure solves the eikonal equation at voxels on partitioning region boundaries and ‘dashes’ with constant arrival time inside partitioning regions. Experiments on 2D and 3D data show that the GPU implementation of fast dashing executes faster than traditional eikonal solvers and produces qualitative results that fit better for medical image segmentation.</p>
<p>Our novel way to evaluate segmentation results relies on a new family of metrics, with hybrid characteristics. These metrics quantify the similarity or difference of segmented regions by considering their average overlap in fixed-size neighbourhoods of points on the boundaries of those regions. Our metrics are more sensitive to combinations of segmentation error types than other metrics in the existing literature. We compare the metric performance on collections of segmentation results sourced from carefully compiled 2D synthetic data and 3D medical images. We show that our metrics: (1) penalise errors successfully, especially those around region boundaries; (2) avoid overly inflated scores; and (3) score segmentation results over a wider range of values.</p>
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