## Discrete Representation of Spatial Objects in Computer VisionOne of the most natural representations for modelling spatial objects in computers is discrete representations in the form of a 2D square raster and a 3D cubic grid, since these are naturally obtained by segmenting sensor images. However, the main difficulty is that discrete representations are only approximations of the original objects, and can only be as accurate as the cell size allows. If digitisation is done by real sensor devices, then there is the additional difficulty of sensor distortion. To overcome this, digital shape features must be used that abstract from the inaccuracies of digital representation. In order to ensure the correspondence of continuous and digital features, it is necessary to relate shape features of the underlying continuous objects and to determine the necessary resolution of the digital representation. This volume gives an overview and a classification of the actual approaches to describe the relation between continuous and discrete shape features that are based on digital geometric concepts of discrete structures. Audience: This book will be of interest to researchers and graduate students whose work involves computer vision, image processing, knowledge representation or representation of spatial objects. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

II | 1 |

III | 8 |

IV | 12 |

V | 15 |

VI | 17 |

VII | 22 |

VIII | 24 |

IX | 33 |

XXXVIII | 105 |

XXXIX | 107 |

XL | 108 |

XLI | 109 |

XLII | 112 |

XLIII | 117 |

XLIV | 118 |

XLV | 119 |

X | 37 |

XI | 41 |

XII | 45 |

XIII | 46 |

XIV | 49 |

XV | 50 |

XVI | 55 |

XVII | 57 |

XVIII | 59 |

XIX | 66 |

XX | 67 |

XXI | 73 |

XXIII | 75 |

XXIV | 77 |

XXV | 80 |

XXVI | 81 |

XXVII | 83 |

XXVIII | 85 |

XXIX | 86 |

XXX | 89 |

XXXI | 90 |

XXXII | 93 |

XXXIV | 96 |

XXXV | 101 |

XXXVI | 102 |

XXXVII | 104 |

### Other editions - View all

Discrete Representation of Spatial Objects in Computer Vision L.J. Latecki No preview available - 2010 |

Discrete Representation of Spatial Objects in Computer Vision L.J. Latecki No preview available - 2014 |

### Common terms and phrases

adjacency algorithm allows angle applied approach area(s2 assume ball black points boundary bounded called camera Chapter characterize color components concept configuration connected connectedness Consequently consider contained continuous analog convex set corner cubes defined definition deleted denote described determined digital image digital picture digital set direct distance edge endpoints equivalent exactly example exists faces fact Figure finite function geometric given graph grid half-plane Hence homeomorphic implies intersection least Lemma line segment locally mapping neighborhood neighbors Note object obtain occur par(r)-regular parallel patterns plane possible preserves projection Proof properties property CP3 Proposition prove real objects relation representations represented respect Rosenfeld rotations satisfies shown in Figure side simple closed curve space spatial square straight line structure subarc subset supported surface Theorem thinning topology turn vector well-composed well-composed sets

### Popular passages

Page 212 - A Comparison of Line Thinning Algorithms from Digital Geometry Viewpoint,