List of Algorithms
2D borders, boundaries, or frontiers
• border tracing, 142
• boundary approximation (“marching squares”), 146
• frontier tracing (frontier grid, incidence grid), 187
3D boundaries or frontiers
• frontier tracing (FILL algorithm), 191
• frontier tracing (Artzy-Herman algorithm), 300–301
• boundary approximation (marching cubes), 301–302
adjacency and connectedness
• FILL for component labeling (adjacency grid), 53
• Rosenfeld-Pfaltz component labeling, 54
• local adjacency (incidence grid), 182
• ordered adjacency procedure (multilevel pictures), 183
• switch adjacency (multilevel pictures), 39, 249
2D convex hulls
• Graham scan (set of points), 25
• Sklansky algorithm (“visible” simple polygon), 430
• simple polygon, 429
• set of grid points, 428
minimum-length polygons
• 2D MLP calculation, 344–345
• approximating-sausage algorithm, 351
• 3D MLP approximation (rubber-band algorithm), 385–390
2D curve representation and analysis
• directional encoding, 71
• vertex chain code, 72–75
• local and global length estimation, 302–304
• tangent-based length estimation, 346, 352–353
• corner detection, 363–364
• curvature estimation, 364–366
3D curve analysis
• local and global length estimation, 409–413
• estimation of curvature and torsion, 413
diagrams
• 2D Delaunay (Voronoi) diagrams, 440–443
• watersheds, 449–450
distance
• Hausdorff metric, 86
• two-pass distance transform (chamfer metric), 94–95
• Danielsson distance transform (Euclidean metric), 109
DSS generation and recognition
• Bresenham’s algorithm (DSS generation), 63
• 8-DSS based on syntactic characterization (CHW1982a), 329–331
• 4-DSS for frontier in incidence grid (K1990), 334–336
• 3D DSS recognition, 379
• 8-DSS based on arithmetic geometry (DR1995), 378
DPS recognition
• incremental algorithm (KS2001), 402–404
• convex-hull based algorithm, 407
graphs
• FILL (connected components), 120
• Dijkstra algorithm (shortest path), 128
• border cycle in an oriented adjacency graph, 142
region analysis (2D)
• medial axis transform, 111–112, 495–496
• discrete integration (area of isothetic polygon), 279–280
• circumscribing rectangle of smallest area, 428–429
region analysis (3D)
• local surface area estimation, 414
• surface area estimation based on normal integration, 418–419
• surface area estimation based on DPS recognition, 421
• mean curvature estimation (HK2003a), 423–424
geometric transformations
• value interpolation, 466–477
• magnification, 58, 468, 470–471
• demagnification, 471, 473–474
morphologic operations
• dilation, 481–483
• erosion, 483–485
• opening and closing, 486
• hit-and-miss transforms, 485–486
• fusing of clusters, 492–493
• detection of (intrinsically) elongated object parts, 493–494
• distance transforms and medial axes, 495–496
deformations
• shrinking, 506–509
• thinning (skeletonization), 509–513
• deformation of curves, 532–534
• thinning of multivalued pictures, 533
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