Abstract
In this paper, we investigated the effect of adding more small curves to the initial condition which determines the required number of iterations of a fast level set (LS) evolution. As a result, we discovered two new theorems and developed a proof on the worst case of the required number of iterations. Furthermore, we found that these kinds of initial conditions fit well to many-core architectures. To show this, we have included two case studies which are presented on different platforms. One runs on a graphical processing unit (GPU) and the other is executed on a cellular nonlinear network universal machine (CNN-UM). With the new initial conditions, the steady-state solutions of the LS are reached in less than eight iterations depending on the granularity of the initial condition. These dense iterations can be calculated very quickly on many-core platforms according to the two case studies. In the case of the proposed dense initial condition on GPU, there is a significant speedup compared to the sparse initial condition in all cases since our dense initial condition together with the algorithm utilizes the properties of the underlying architecture. Therefore, greater performance gain can be achieved (up to 18 times speedup compared to the sparse initial condition on GPU). Additionally, we have validated our concept against numerically approximated LS evolution of standard flows (mean curvature, Chan-Vese, geodesic active regions). The dice indexes between the fast LS evolutions and the evolutions of the numerically approximated partial differential equations are in the range of 0.99±0.003.
Highlights
The use of level-set (LS)-based curve evolution has become an interesting research topic due to its versatility and accuracy
In the case of the dense initial condition on graphical processing unit (GPU), there is a significant speedup compared to the sparse initial condition in all cases since our proposed dense initial condition together with the algorithm utilizes the properties of the underlying architecture
To automatically detect segment object on an image or on a region of it, the LS-based algorithms are feasible tools. It was shown theoretically and experimentally through two case studies that the initial condition plays an essential role in decreasing the execution time
Summary
The use of level-set (LS)-based curve evolution has become an interesting research topic due to its versatility and accuracy. These flows are widely used in various fields like computational geometry, fluid mechanics, image processing, computer vision, and materials science [1]. We do not form any operator or speedfield (F) for driving the evolution of the LSs. two theoretical worst-case bounds of the required number of iterations are proposed to reach the steady state for a well-defined class of LS-based evolution. Two theoretical worst-case bounds of the required number of iterations are proposed to reach the steady state for a well-defined class of LS-based evolution
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