## Abstract

Often objects which are not convex in the mathematical sense are treated as 'perceptually convex'. We present an algorithm for recognition of the perceptual convexity of a 2-d contour. We start by reducing the notion of 'a contour is perceptually convex' to the notion of 'a contour is Y-convex'. The latter reflects an absence of large concavities in the OY direction of an XOY frame. Then we represent a contour by a G-graph and modify the slowest descent-the small leaf trimming procedure recently introduced for the estimation of shape similarity. We prove that executing the slowest descent down to a G-graph consisting of 3 vertices allows us to detect large concavities in the QY direction. This allows us to recognize the perceptual convexity of an input contour.

Original language | English |
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Pages (from-to) | 125-136 |

Number of pages | 12 |

Journal | Proceedings of SPIE - The International Society for Optical Engineering |

Volume | 2573 |

DOIs | |

State | Published - 11 Aug 1995 |

Event | Vision Geometry IV 1995 - San Diego, United States Duration: 9 Jul 1995 → 14 Jul 1995 |

## Keywords

- Contour
- G-graph
- Perceptual convexity
- Segmentation
- Slowest descent