Conclusion and Future Work
5.2 Future work
ent regions in stage two. In addition, this two stage optimization framework is suitable for interactive use required by surface painting. For the optimization process, we de-rived the modified L2 metric denoted as L2s. The L2s metric takes signal stretch into account in the regions of signal variation and combines geometry stretch in the regions without signal variation.
5.2 Future work
Some potential future work are listed as follows:
• Better stroke sampling method
The stroke sampling method[2] based on graphics hardware is simple and fast for interactive use. However the result is bad when the resampling was done under either magnification or minification. Perhaps some filter on image space could alleviate this problem.
• Parameterization metric
In the proposed L2s stretch, geometry stretch is applied in the regions without sig-nal gradient to prevent the excessively undersampling in the un-painted regions.
The major issue is that the same value of geometry and signal stretch does not imply the equal significance. Therefore, a study on the weighted relationship be-tween geometry and signal stretch will enhance the theoretical background of our method. Though our L2s metric works well for a surface painting system, but it is a little heuristic in some measure. We look for a better metric, especially the one which is more sensitive for the anisotropical distribution of surface signal on parametric domain.
• Hierarchical optimization
5.2 Future work 59
Optimization based on adaptive sample points can be utilized to improve the per-formance. In our two-stage optimization framework, the sample points are uni-formly distributed on parametric domain at each step. To use the sample points more efficiently, we distribute more sample points on the regions of high signal gradient to accurately grab the signal variation. Less sample points are distributed on the regions of lower signal gradient, thus these regions will be converged more quickly. To achieve the goal, a hierarchy architecture of uniform grid is required to maintain the different resolution of grid points. For sampling, there are two major problems of the hierarchical method. The first one is the determination of high gradient region and lower gradient region. A two-pass method will be prac-tical to accomplish this. The second problem is that a theoreprac-tical and efficient method to propagate the L2s stretch from high resolution grid pints to lower reso-lution grid points is required. In addition to the problems of sampling, an efficient optimization algorithm for the hierarchical gird architecture is also required.
• Dynamic cutting
Topological surgery is used to transform the closed surface into an open-one.
Current method [9] only takes the geometric information into account. A signal sensitive topological surgery will be a novel and great contribution for current surface surface painting system. The main issue is the time complexity of the cutting algorithm.
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