Segmentation of medical images is very important for clinical research and diagnosis, leading to a requirement for robust automatic methods. This paper reports on the combined use of a neural network (a multilayer perceptron, MLP) and active contour model ('snake') to segment structures in magnetic resonance (MR) images. The perceptron is trained to produce a binary classification of each pixel as either a boundary or a non-boundary point. Subsequently, the resulting binary (edge-point) image forms the external energy function for a snake, used to link the candidate boundary points into a continuous, closed contour. We report here on the segmentation of the lungs from multiple MR slices of the torso; lung-specific constraints have been avoided to keep the technique as general as possible. In initial investigations, the inputs to the MLP were limited to normalised intensity values of the pixels from an (7 × 7) window scanned across the image. The use of spatial coordinates as additional inputs to the MLP is then shown to provide an improvement in segmentation performance as quantified using the effectiveness measure (a weighted product of precision and recall). Training sets were first developed using a lengthy iterative process. Thereafter, a novel cost function based on effectiveness is proposed for training that allows us to achieve dramatic improvements in segmentation performance, as well as faster, non-iterative selection of training examples. The classifications produced using this cost function were sufficiently good that the binary image produced by the MLP could be post-processed using an active contour model to provide an accurate segmentation of the lungs from the multiple slices in almost all cases, including unseen slices and subjects.

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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.

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