Let D be a digital manifold, J the subset of non-empty of D; and let A<sub>1</sub>, A<sub>2</sub>, …, A<sub>m</sub> be m real numbers with A<sub>1</sub>【A<sub>2&...Let D be a digital manifold, J the subset of non-empty of D; and let A<sub>1</sub>, A<sub>2</sub>, …, A<sub>m</sub> be m real numbers with A<sub>1</sub>【A<sub>2</sub>【…【A<sub>m</sub>. Supposing function f<sub>J</sub>: J → A<sub>1</sub>,…, A<sub>m</sub>, we want to find a function f<sub>D</sub>: D→{A<sub>1</sub>…, A<sub>m</sub>}, such that f<sub>D</sub> is gradual variation on D, having f<sub>D</sub>（x）=f<sub>J</sub>（x）, x∈J. Such f<sub>D</sub> is called the gradually varied extension or interpolation of f<sub>J</sub>.展开更多
Filling is an important part in pattern recognition and computer vision. In the discrete plane （grid of plane）∑<sub>2</sub>, fill means 'determination of the region D enclosed by the simple closed c...Filling is an important part in pattern recognition and computer vision. In the discrete plane （grid of plane）∑<sub>2</sub>, fill means 'determination of the region D enclosed by the simple closed curve J which is given beforehand'. In other words, if the valuation of the point on the contour J is 1, we want to do a valuation for ∑<sub>2</sub> to make the valuation of the point p be 1 iff point p belongs to D.展开更多
Whether or not the group isomorphism problem is tractable is still an important open problem. But for Abelian groups of order n, C. Savage has an algorithm of time complexity O(n^2) to determine whether they are isomo...Whether or not the group isomorphism problem is tractable is still an important open problem. But for Abelian groups of order n, C. Savage has an algorithm of time complexity O(n^2) to determine whether they are isomorphic, given their multiplication table as input. Notice that the length of the input is of order n^2, therefore this is a linear time algorithm.展开更多
基金Project supported by the Science Fund of the Chinese Academy of Sciences for Young Scientists.
文摘Let D be a digital manifold, J the subset of non-empty of D; and let A<sub>1</sub>, A<sub>2</sub>, …, A<sub>m</sub> be m real numbers with A<sub>1</sub>【A<sub>2</sub>【…【A<sub>m</sub>. Supposing function f<sub>J</sub>: J → A<sub>1</sub>,…, A<sub>m</sub>, we want to find a function f<sub>D</sub>: D→{A<sub>1</sub>…, A<sub>m</sub>}, such that f<sub>D</sub> is gradual variation on D, having f<sub>D</sub>（x）=f<sub>J</sub>（x）, x∈J. Such f<sub>D</sub> is called the gradually varied extension or interpolation of f<sub>J</sub>.
基金Project supported by the Science Fund of the Chinese Academy of Sciences for Young Scientists
文摘Filling is an important part in pattern recognition and computer vision. In the discrete plane （grid of plane）∑<sub>2</sub>, fill means 'determination of the region D enclosed by the simple closed curve J which is given beforehand'. In other words, if the valuation of the point on the contour J is 1, we want to do a valuation for ∑<sub>2</sub> to make the valuation of the point p be 1 iff point p belongs to D.
文摘Whether or not the group isomorphism problem is tractable is still an important open problem. But for Abelian groups of order n, C. Savage has an algorithm of time complexity O(n^2) to determine whether they are isomorphic, given their multiplication table as input. Notice that the length of the input is of order n^2, therefore this is a linear time algorithm.
