A semi-localized elastic net for surface reconstruction of objects from multislice images

The traveling salesman problem (TSP) is a prototypical problem of combinatorial optimization and, as such, it has received considerable attention from neural-network researchers seeking quick, heuristic solutions. An early stage in many computer vision tasks is the extraction of object shape from an image consisting of noisy candidate edge points. Since the desired shape will often be a closed contour, this problem can be viewed as a version of the TSP in which we wish to link only a subset of the points/cities (i.e. the "noisefree" ones). None of the extant neural techniques for solving the TSP can deal directly with this case. In this paper, we present a simple but effective modification to the (analog) elastic net of Durbin and Willshaw which shifts emphasis from global to local behavior during convergence, so allowing the net to ignore some image points. Unlike the original elastic net, this semi-localized version is shown to tolerate considerable amounts of noise. As an example practical application, we describe the extraction of "pseudo-3D" human lung outlines from multiple preprocessed magnetic resonance images of the torso. An effectiveness measure (ideally zero) quantifies the difference between the extracted shape and some idealized shape exemplar. Our method produces average effectiveness scores of 0.06 for lung shapes extracted from initial semi-automatic segmentations which define the noisefree case. This deteriorates to 0.1 when extraction is from a noisy edge-point image obtained fully-automatically using a feedforward neural network.