کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
414215 680827 2015 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Homological reconstruction and simplification in R3R3
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نظریه محاسباتی و ریاضیات
پیش نمایش صفحه اول مقاله
Homological reconstruction and simplification in R3R3
چکیده انگلیسی

We consider the problem of deciding whether the persistent homology group of a simplicial pair (K,L)(K,L) can be realized as the homology H⁎(X)H⁎(X) of some complex X   with L⊂X⊂KL⊂X⊂K. We show that this problem is NP-complete even if K   is embedded in R3R3.As a consequence, we show that it is NP-hard to simplify level and sublevel sets of scalar functions on S3S3 within a given tolerance constraint. This problem has relevance to the visualization of medical images by isosurfaces. We also show an implication to the theory of well groups of scalar functions: not every well group can be realized by some level set, and deciding whether a well group can be realized is NP-hard.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computational Geometry - Volume 48, Issue 8, September 2015, Pages 606–621
نویسندگان
, , , , ,