Knowledge

Grid cell topology

Source 📝

193: 234: 177: 156: 151:, by Reinhard Klette and Azriel Rosenfeld, Morgan Kaufmann Pub, May 2004, (The Morgan Kaufmann Series in Computer Graphics) 123:-dimensional grid cells and an intuitive definition for grid cell manifolds can be found in Chen, 2004. It is related to 227: 101: 253: 258: 25: 220: 91: 136: 173: 152: 29: 124: 21: 109: 204: 95: 247: 64: 170:
Discrete Surfaces and Manifolds: A Theory of Digital-Discrete Geometry and Topology
105: 164:
I, by Paul Alexandroff and Heinz Hopf, Springer, Berlin, 1935, xiii + 636 pp.
192: 200: 40: 94:(open sets are up-sets) with respect to this partial order. (See also 24:
as part of the theoretical basis for (low-level) algorithms in
149:
Digital Geometry: Geometric Methods for Digital Image Analysis
208: 108:first introduced the grid cell topology, for the 228: 8: 235: 221: 112:case, within an exercise in their text 7: 189: 187: 90:)). The grid cell topology is the 51:-dimensional grid cubes and their 14: 191: 119:A recursive method to obtain 1: 55:-dimensional faces ( for 0 ≤ 207:. You can help Knowledge by 63:−1); between these a 275: 186: 39:-dimensional grid cell 26:computer image analysis 35:The elements of the 92:Alexandrov topology 82:(and thus also dim( 137:Pixel connectivity 18:grid cell topology 216: 215: 168:Chen, L. (2004). 125:digital manifolds 30:computer graphics 266: 254:Digital topology 237: 230: 223: 201:topology-related 195: 188: 183: 172:. SP Computing. 22:digital topology 274: 273: 269: 268: 267: 265: 264: 263: 244: 243: 242: 241: 180: 167: 145: 133: 110:two-dimensional 78:is a subset of 12: 11: 5: 272: 270: 262: 261: 259:Topology stubs 256: 246: 245: 240: 239: 232: 225: 217: 214: 213: 196: 185: 184: 178: 165: 159: 144: 141: 140: 139: 132: 129: 96:poset topology 74:is defined if 20:is studied in 13: 10: 9: 6: 4: 3: 2: 271: 260: 257: 255: 252: 251: 249: 238: 233: 231: 226: 224: 219: 218: 212: 210: 206: 203:article is a 202: 197: 194: 190: 181: 179:0-9755122-1-8 175: 171: 166: 163: 160: 158: 157:1-55860-861-3 154: 150: 147: 146: 142: 138: 135: 134: 130: 128: 126: 122: 117: 115: 111: 107: 103: 99: 97: 93: 89: 85: 81: 77: 73: 69: 66: 65:partial order 62: 58: 54: 50: 47:≥ 1) are all 46: 42: 38: 33: 31: 27: 23: 19: 209:expanding it 198: 169: 161: 148: 120: 118: 113: 100: 87: 83: 79: 75: 71: 67: 60: 56: 52: 48: 44: 36: 34: 17: 15: 248:Categories 143:References 116:I (1935). 102:Alexandrov 162:Topologie 114:Topologie 131:See also 86:) ≤ dim( 41:topology 176:  155:  199:This 205:stub 174:ISBN 153:ISBN 106:Hopf 104:and 16:The 98:.) 32:. 28:or 250:: 127:. 70:≤ 59:≤ 236:e 229:t 222:v 211:. 182:. 121:n 88:B 84:A 80:B 76:A 72:B 68:A 61:n 57:k 53:k 49:n 45:n 43:( 37:n

Index

digital topology
computer image analysis
computer graphics
topology
partial order
Alexandrov topology
poset topology
Alexandrov
Hopf
two-dimensional
digital manifolds
Pixel connectivity
ISBN
1-55860-861-3
ISBN
0-9755122-1-8
Stub icon
topology-related
stub
expanding it
v
t
e
Categories
Digital topology
Topology stubs

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.