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Related Experiment Videos

Dynamic shape.

J J Koenderink, A J van Doorn

    Biological Cybernetics
    |January 1, 1986
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a novel morphogenetic framework for shape analysis, enabling unique shape embedding via resolution-based sequences. This approach defines natural part boundaries and characterizes singularities, offering new insights into shape perception and geometric theories.

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    Area of Science:

    • Computational geometry
    • Shape theory
    • Mathematical morphology

    Background:

    • Existing geometric shape theories lack methods for partial order and similarity of shapes with different connectivity.
    • Current theories prioritize topological type over other geometric features for categorization.
    • Psychologically valid shape descriptions often involve notions not captured by standard geometric models.

    Purpose of the Study:

    • To develop a shape theory incorporating morphogenesis to address limitations in existing geometric and psychological models.
    • To present a measurement theory for defining surfaces and curves at multiple resolutions.
    • To establish a framework for unique embedding of shapes in morphogenetic sequences.

    Main Methods:

    • Embedding objects uniquely in a morphogenetic sequence parameterized by resolution.

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  • Developing a theory of measurement for multi-resolution surfaces and curves.
  • Utilizing a partial differential equation to govern the evolutionary embedding process.
  • Defining canonical projections from high to low resolution versions of shapes.

    • Main Results:

    • The theory allows for unique embedding of any object in a morphogenetic sequence.
    • Natural part boundaries are generated by the bifurcation set of canonical projections.
    • Singularities in the evolution are characterized as emergence, accretion, and versification processes, including topological changes.
    • Inflection generation and modification are described through specific singularity processes.

    Conclusions:

    • Morphogenetic shape theories provide a logical framework for relations not captured by traditional geometry.
    • The proposed theory offers a unified approach to shape analysis across different resolutions.
    • This framework has potential applications in robotics, artificial intelligence, and psychophysics by bridging geometric and perceptual aspects of shape.