This is one of a series of reports on the digital geometry of three-dimensional images, such as those produced by computed tomography. In this report we define simple surface points and simple closed surfaces, and show that any connected collection of simple surface points form a simple closed surface, thus proving a three-dimensional analog of the two-dimensional Jordan curve theorem. We also show that the converse is not a theorem (in contrast to the two-dimensional case) and discuss more complex surface types. The support of the U.S. Air Force Office of Scientific Research under Grant AFOSR-77-3271 and of Pfizer Medical Systems, Inc., is gratefully acknowledged, as is the help of Kathryn Riley in preparing this paper. AIR FORCE OFFICE OF SCIENTIFIC RESEARCH (AFSC) 7)TICE OF T7''""TT,, TO DDC revie',ed ai.d is ,. .... k" 190-12 (7b). \. D. 8L&technical Inforn ition Offioer READ INSTRUCTIONS Oct EPOT DOUMETA~rON AGEBEFORE COMPLETING FORM + EPRT ""WR :2. GOVT ACCESSION NO. 3. RECIPIENT'S CATALOG NUMBER 5. TYPE OF REPORT 6 PERIOD COVERED SURACE IN EE-EE4IMENSI n6 eq 7. ATHORa) S CONTRACT OR GRANT NUMBER(&) *Azrie])Roserifeld (F0114-27 9. RGANIZATION NAME AND ADDRESS I0. PROGRAM ELEMENT. PROJECT TASK i ..%kVR UNIT NU.sftilt-Computer Science Center College Park, IMd. 20742 6110 2 A2 I I. CONTROLLING OFFICE NAME AND ADDRESS lI...
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