以物體外形幾何特性為基礎之表面重建與表面簡化研究

Surface Reconstruction and Simplification Based on Shape Geometric Properties

曾俊霖(Juin-Ling Tseng)

指導教授 ： 林聰武 ； 鍾斌賢

中原大學/工學院/電子工程研究所/博士(2006年)

https://doi.org/10.6840/cycu200600443

摘要

為了建構一個具有三角片資訊的3D模型，我們通常會利用表面重建的方法將原僅具有點資訊的模型建構出其所需之三角片。在表面重建演算法中，其困難點通常在於點密度的分布情形，當該模型具有充足的點資訊而且密度分佈較為均勻時，其可容易地重建出具有三角片資訊的極佳模型；相反地，當點密度相當不均勻時，其極有可重建出非預期三角片，甚至是非預期的洞。
點分布不均勻的區域通常是該模型的特徵區域，換句話說，在特徵區域進行表面重建，對表面重建來說，這是一個極大的挑戰。為了克服這樣的困難，我們通常會利用3D scanner來增加模型上的取樣點資訊，並選擇具有較多點資訊的模型來進行表面重建，以取得較佳的重建結果。然而，該模型上的點資訊越多，其所重建出的三角片數量則越多，如此雖可順利地重建出3D模型，但也隨之增加了描述3D模型的資料量，提高了因表面重建產生之時間成本，當然也增加了重建後對模型進行資料處理及顯象的時間成本。因此，適度地降低描述模型所需的點資訊以及三角片資訊是有其必要性的。表面簡化演算法可以有效地降低描述3D模型所需之點以及三角片的數量，然而，隨著模型上點資訊以及三角片資訊的減少，隨之而來的是簡化後所造成的誤差情形；換句話說，表面簡化的過程必須在儘可能減少誤差產生的情形下進行，而特徵區域的簡化是產生極大誤差的主要原因之一。也就是說，在進行表面簡化時，適度地保留模型上的特徵，有助於減少因表面簡化所造成的誤差。
特徵的萃取不但有助於表面重建的進行，而且在表面簡化時可以適度地保留模型特徵，減少表面簡化所造成的誤差，因此，在本論文中提出了一個針對表面重建以及表面簡化的特徵萃取方法。本論文所提出的方法是一個低時間成本的特徵萃取方法，其透過模型表面的幾何特性-外形運算子，來量測模型表面的變化情形，以提供表面重建以及表面簡化所需之特徵資訊。經過實驗證明，利用此特徵萃取方法所提出的表面重建演算法，可以有效地減少因點分布不均勻所產生的非預期三角片以及非預期的洞。而透過此特徵萃取法所提出的表面簡化演算法，則可在模型簡化時適度地保留模型特徵，降低因模型簡化所造成的誤差。而此特徵方法所需花費的時間成本僅佔表面重建以及表面簡化所需時間之ㄧ小部份。

關鍵字

外形運算子 ； 特徵萃取 ； 表面重建 ； 表面簡化

並列摘要

To construct a 3D triangular-mesh model, a surface reconstruction algorithm is usually used to reconstruct a point-cloud model. Point distribution was one of the most important impact factors of successful reconstruction. When the point distribution of a point-cloud model is sufficient and uniform, the point-cloud model can easily be reconstructed into a triangular-mesh model. On the contrary, if the point distribution of a point-cloud model is insufficient or non-uniform, the surface reconstruction of the point-cloud model would fail, and even some undesired triangles or holes would be created.
Unfortunately, these density-insufficient or non-uniform regions are usually feature surfaces on models. That is, reconstructing feature areas is difficult for surface reconstruction. To overcome this problem, the number of sampled points is increased using 3D scanner devices to improve the reconstruction results. However, the number of triangles created by surface reconstruction increases with the number of sampled points in point-cloud model. Therefore, although a point-cloud model can be successfully reconstructed by increasing the number of sampled points, this approach also increases the storage costs of reconstructed models. Undoubtedly, the computational costs involved in the processing step and rendering steps will also increase. Therefore, it is necessary to reduce the number of triangles. However, decreasing the number of triangles increases the errors caused by simplification. The surface simplification must be implemented under the condition of reducing errors. The simplification of feature surfaces is one of the most major factors of generating big errors. That is, in surface simplification, adaptively preserving model features can help reduce errors resulting from simplification.
Feature extraction can help to successfully reconstruct a surface, preserve the features of simplified models, and reduce the errors caused by simplification. Therefore, this study proposes a fast and economical feature extraction method for surface reconstruction and surface simplification. The proposed method exploited Discrete Shape Operator (DSO) to detect the surface variation of a 3D model. The DSO can provide surface variation information to help determine the sampling regions during surface reconstruction, and to retain object features when simplifying the model under low-resolution situations. The experimental results show that the proposed method can reduce undesired triangles and holes caused by irregular point distribution. During surface simplification, the DSO can provide surface variation to preserve the features of simplified models and reduce the errors caused by simplification. Additionally, there are minimal time costs involved in calculating DSO for surface reconstruction and surface simplification.

並列關鍵字

surface reconstruction ； surface simplification ； feature extraction ； shape operator

參考文獻

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