• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.671-686
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• 1994

다양체 M은 매끈하고(smooth) 콤팩트(compact) n 차원 리만다양체이고, 실가함수 f는 M상에서 미분가능 함수임을 가정한다. Morse 함수는 임계점(critical point)들이 모두 비퇴화(non-degenerate)인 실가함수이다. 만약 함수 f가 Morse 함수이고, 임의의 점 $x \in M$에서 $\gamma_x$는 x를 통과하는 흐름(flow)이면 $$ (*) \frac{d\gamma_x(t)}{dt} + \bigtriangledown_{\gamma x(t)}(f) = 0 $$ 이다. 여기서 $\bigtriangledown(f)$는 함수 f에 의해서 정의되는 기울기 벡터장이고 초기조건 $\gamma_x(0) = x$ 이다.

• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.2
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• pp.206-211
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• 2008

Trainee can enhance his perception of and interaction with the real world by displayed virtual objects in simulation using image processing technology. Therefore, it is essential for realistic simulation to determine the occlusion areas of the virtual object produces after registering real image and virtual object exactly. In this paper, we proposed the new method to solve occlusions which happens during virtual target moves according to the simulated route on real image using improved object contour extraction by neighboring edge search and picking algorithm. After we acquire the detailed contour of complex objects by proposed contour extraction algorithm, we extract the three dimensional information of the position happening occlusion by using MER for performance improvement. In the experiment, we compared proposed method with existed method and preyed the effectiveness in the environment which a partial occlusions happens.