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Two-Dimensional Critical Point Configuration Graphs
April 1984 (vol. 6 no. 4)
pp. 442-450
| ASCII Text | x | ||
| R. Nackman Lee, "Two-Dimensional Critical Point Configuration Graphs," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 6, no. 4, pp. 442-450, April, 1984. | |||
| BibTex | x | ||
| @article{ 10.1109/TPAMI.1984.4767549, author = {R. Nackman Lee}, title = {Two-Dimensional Critical Point Configuration Graphs}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {6}, number = {4}, issn = {0162-8828}, year = {1984}, pages = {442-450}, doi = {http://doi.ieeecomputersociety.org/10.1109/TPAMI.1984.4767549}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - JOUR JO - IEEE Transactions on Pattern Analysis and Machine Intelligence TI - Two-Dimensional Critical Point Configuration Graphs IS - 4 SN - 0162-8828 SP442 EP450 EPD - 442-450 A1 - R. Nackman Lee, PY - 1984 VL - 6 JA - IEEE Transactions on Pattern Analysis and Machine Intelligence ER - | |||
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.
Citation:
R. Nackman Lee, "Two-Dimensional Critical Point Configuration Graphs," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 6, no. 4, pp. 442-450, April 1984, doi:10.1109/TPAMI.1984.4767549
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