Two-Dimensional Critical Point Configuration Graphs

Medientyp: E-Artikel

Titel: Two-Dimensional Critical Point Configuration Graphs

Beteiligte: Lee, R. Nackman

Erschienen: IEEE, 1984

Sprache: Englisch

DOI: 10.1109/TPAMI.1984.4767549

ISSN: 0162-8828

Schlagwörter: Surface topography ; Constraint theory ; Earth ; Demography ; Organizing ; Spatial databases ; Differential equations ; Sea surface ; Calculus ; Shape ; Course line ; critical point ; critical point configuration graph ; ridge line ; slope district ; slope line ; surface decomposition ; surface description

Zusammenfassung: The configuration of the critical points of a smooth function of two variables is studied under the assumption that the function is Morse, that is, that all of its critical points are nondegenerate. A critical point configuration graph (CPCG) is derived from the critical points, ridge lines, and course lines of the function. Then a result from the theory of critical points of Morse functions is applied to obtain several constraints on the number and type of critical points that appear on cycles of a CPCG. These constraints yield a catalog of equivalent CPCG cycles containing four entries. The slope districts induced by a critical point configuration graph appear useful for describing the behavior of smooth functions of two variables, such as surfaces, images, and the radius function of three-dimensional symmetric axes.

Beschreibung: The configuration of the critical points of a smooth function of two variables is studied under the assumption that the function is Morse, that is, that all of its critical points are nondegenerate. A critical point configuration graph (CPCG) is derived from the critical points, ridge lines, and course lines of the function. Then a result from the theory of critical points of Morse functions is applied to obtain several constraints on the number and type of critical points that appear on cycles of a CPCG. These constraints yield a catalog of equivalent CPCG cycles containing four entries. The slope districts induced by a critical point configuration graph appear useful for describing the behavior of smooth functions of two variables, such as surfaces, images, and the radius function of three-dimensional symmetric axes.

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