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Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Computer Vision
Arrangement: A Spatial Relation Comparing Part Embeddings and its Use in Medical Image Comparisons
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Medical tomographic images are formed by the intersection of the image plane and an object. As the image plane changes, different parts of the object come in view or drop out of view. However, for small changes of the image plane, most parts continue to remain visible and their qualitative embedding in the image remains similar. Therefore, similarity of part embeddings can be used to infer similarity of image planes. Part embeddings are useful features for other vision applications as well.In view of this, a spatial relation called 驴arrangement驴 is proposed to describe part embeddings. The relation describes how each part is surrounded by its neighbors. Further, a metric for arrangements is formulated by expressing arrangements in terms of the Voronoi diagram of the parts.Arrangements and their metric are used to retrieve images by image plane similarity in a cardiac magnetic resonance image database. Experiments with the database are reported whichvalidate the observation that similarity of image planes can be inferred from similarity of part embeddings, andcompare the performance of arrangement based image retrieval with that of expert radiologists.