Two-dimensional critical point configuration graphs
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 cou...
| Veröffentlicht in: | IEEE transactions on pattern analysis and machine intelligence. - 1979. - 6(1984), 4 vom: 01. Apr., Seite 442-50 |
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| 1. Verfasser: | |
| Format: | Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
1984
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| Zugriff auf das übergeordnete Werk: | IEEE transactions on pattern analysis and machine intelligence |
| Schlagworte: | Journal Article |
| 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 |
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| Beschreibung: | Date Completed 02.10.2012 Date Revised 12.11.2019 published: Print Citation Status PubMed-not-MEDLINE |
| ISSN: | 1939-3539 |