利用加點策略提升局部密度之表面重建研究

Raising Local Density for Surface Reconstruction using Upsampling strategy

赫祥君(Hsiang-Chun Ho)

指導教授 ： 鍾斌賢

中原大學/工學院/資訊工程研究所/碩士(2005年)

https://doi.org/10.6840/cycu200500391

摘要

外貌重建(Surface Reconstruction)是將一群未組織的點集合（Unorginized Point Set），利用重建演算法建構出具有三角片資訊的物體外貌。而這些未組織的點集合，則是經由雷射掃描器在物體上取樣所得，因此隨著物體外表的變化程度越大，其掃描所得之取樣點，將越有可能產生取樣點密度分佈不均或不足的問題；而事實上，此一現象將嚴重影響到外貌重建後所呈現的效果，譬如，可能產生不屬於物體本身的洞。
為了克服這個問題，本論文提出一個增加密度的演算法，透過模型上取樣點之密度分佈，來判斷是否新增取樣點。事實上，本論文依物體外表的變化情形，將所有的取樣點分成非特徵點與特徵點兩個部分。在非特徵點方面，本論文利用第K個接近點的距離做為密度量測的標準，對整個僅具有點資訊的三度空間模型做密度值的判斷；而在特徵點方面，則利用外形運算子（Shape Operator）來進行特徵萃取。接著，對「所萃取出之特徵點」及「非特徵點密度不足」的點集合，以找最大半徑圓之圓心並投影至MLS曲面的加點演算法，來完成增加取樣點的動作。
經過實驗證明，本論文所提出的密度提升演算法，不僅能對模型中非特徵的部分，利用增加取樣點的策略來提升取樣點的密度；另外也能針對模型的特徵部分，達到相同的效果。事實上，我們所提出的演算法成功地改善了雷射掃點所導致取樣點分佈不足的問題，並且協助物體在外貌重建上，避免產生不屬於該物體的洞。

關鍵字

外貌重建 ； MLS ； 外形運算子

並列摘要

Surface reconstruction use reconstruction algorithms to construct the object surfaces from unorganized point clouds to triangulation information. However, these unorganized point clouds are obtained from laser scanning of objects, insufficient density and/or non-feature distribution of points might occur at surfaces with high curvature. In fact, the appearances of things affect the results of surface reconstruction seriously, for example it is likely to produces holes which not do belong to the objects.
To overcome these problems, this study presents an algorithm to raise the density of the point clouds, by adding new sample points according to the distribution of the points. Actually, the proposed algorithm divides a point cloud into feature points and non-feature points, depending on the characteristics of the model surfaces. For non-feature points, the distance of the k-nearest point is used as an estimate of the density of each point in a point cloud. For feature points, shape operators are used to process feature extraction.
To raise the density of the point cloud, at extracted feature points and non-feature points with low density, the circle center with maximum radius is found and projected onto the MLS surface.
Experiments show that not only does the proposed algorithm raises the density of non-feature points with low density, but it also raises the density of feature points. The proposed algorithm improves the problem of insufficient density produced by laser scanning. It successfully helps surface reconstruction algorithm by preventing the formation of small holes which does not original exist on the model.

並列關鍵字

MLS ； shape operator ； surface reconstruction

參考文獻

[1] H. Hoppe, T. DeRose, T. Duchamp, J. McDonald, and W. Stuetzle, “Surface reconstruction from unorganized points,” in Proceedings of ACM SIGGRAPH 92, 1992, pp.71-78.

[3] H. Edelsbrunner, and E. P. Mucke, “Three-dimensional alpha shapes,” ACM Transactions on Graphics, vol. 13(1), pp. 43-72, January 1994.

[4] J.-D. Boissonnat. “Geometric structures for three-dimensional shape representation,” ACM Transactions on Graphics, vol. 3(4), pp.266–286, October 1984.

[5] M. Gopi, and S. Krishnan. “A fast and efficient projection-based approach for surface reconstruction,” in 15th Brazilian Symposium on Computer Graphics and Image Processing, 2002, pp.179-186.

[8] M. Gopi, S. Krishnan, and C.T. Silva. “Surface reconstruction based on lower dimensional localized delaunay triangulation,” in Proceedings of EUROGRAPHICS 2000, 2000, pp.467-478.