How Do Users Map Points Between Dissimilar Shapes?

Michael Hecher, Paul Guerrero, Peter Wonka, Michael Wimmer
How Do Users Map Points Between Dissimilar Shapes?
IEEE Transactions on Visualization and Computer Graphics, accepted for publication, 2017.

Information

Abstract

Finding similar points in globally or locally similar shapes has been studied extensively through the use of various point descriptors or shape-matching methods. However, little work exists on finding similar points in dissimilar shapes. In this paper, we present the results of a study where users were given two dissimilar two-dimensional shapes and asked to map a given point in the first shape to the point in the second shape they consider most similar. We find that user mappings in this study correlate strongly with simple geometric relationships between points and shapes. To predict the probability distribution of user mappings between any pair of simple two-dimensional shapes, two distinct statistical models are defined using these relationships. We perform a thorough validation of the accuracy of these predictions and compare our models qualitatively and quantitatively to well-known shape-matching methods. Using our predictive models, we propose an approach to map objects or procedural content between different shapes in different design scenarios.

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BibTeX

@article{HECHER-2017-HDY,
  title =      "How Do Users Map Points Between Dissimilar Shapes?",
  author =     "Michael Hecher and Paul Guerrero and Peter Wonka and Michael
               Wimmer",
  year =       "2017",
  abstract =   "Finding similar points in globally or locally similar shapes
               has been studied extensively through the use of various
               point descriptors or shape-matching methods. However, little
               work exists on finding similar points in dissimilar shapes.
               In this paper, we present the results of a study where users
               were given two dissimilar two-dimensional shapes and asked
               to map a given point in the first shape to the point in the
               second shape they consider most similar. We find that user
               mappings in this study correlate strongly with simple
               geometric relationships between points and shapes. To
               predict the probability distribution of user mappings
               between any pair of simple two-dimensional shapes, two
               distinct statistical models are defined using these
               relationships. We perform a thorough validation of the
               accuracy of these predictions and compare our models
               qualitatively and quantitatively to well-known
               shape-matching methods. Using our predictive models, we
               propose an approach to map objects or procedural content
               between different shapes in different design scenarios.",
  issn =       "1077-2626",
  journal =    "IEEE Transactions on Visualization and Computer Graphics",
  volume =     "accepted for publication",
  keywords =   "shape matching, transformations, shape similarity",
  URL =        "https://www.cg.tuwien.ac.at/research/publications/2017/HECHER-2017-HDY/",
}