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Efficient Representations in Geometry: Hausdorff Distance and Polyline Measurement

Dive into Hausdorff distance and Polyline Distance Measure (PDM) for geometric sets with varied dimensions. Learn about skeletonization algorithms and border coordinates extraction. Understand the Euler number's significance and Door-In-Door-Out concepts in geometry.

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Efficient Representations in Geometry: Hausdorff Distance and Polyline Measurement

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  1. Chapter 11 Representation & Description Distância de Hausdorff The Hausdorff distance is a measure between two sets, not necessarily with the same dimensions. It measures how a subset of points of a set A is near from a subset of a distinct set B. Formally, given two point sets A and B, the Hausdorff distance between them is defined as:

  2. Chapter 11 Representation & Description Polyline Distance Mesure (PDM) Seja B1 e B2 duas bordas em coordenadas cartesianas. A medida PDM entre elas é definida como:

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  13. Chapter 11 Representation & Description Algoritmo para Esqueletização N(P1) é o número de vizinhos não zeros de p1; S(p1) é o número de transições 0-1 na seqüência ordenada p2, p3, ...., p8, p9, p2 (a) 2 ≤ N(p1) ≤ 6; (b) s(P1) = 1; (c) p1 . p4 . p6 = 0; (d) p4. p6. p8 = 0

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  22. Chapter 11 Representation & Description O número de Euler aqui é: E(A) = 0 e E(B) = -1

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  27. Chapter 11 Representation & Description Door-In-Door-Out Algoritmo para extrair coordenadas de Bordas

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