一致性網格參數化技術與網格重建

Abstract

替多個網格模型建立對應關係的演算法在電腦圖學及幾何處理的領域裡十分有用。 然而，在建立對應關係的過程中，每一個網格模型上都需要大量的人為操作去指定出 一致性的切割方式以及許多特徵點的對應。 因此，我們提出一個新的方法叫做``一致性網格參數化技術''；在不需要大量人為設 定的前提之下，建立出多個網格模型之間的對應關係。 一致性網格參數化技術以幾何延展評量標準(geometric-stretch metric) 針對每個網格區塊做最佳化的處理。 同時，我們也應用無摺疊形變之演算法(foldover-free warping)去校正網格參數化的結果， 使得特徵點之間的對應關係能夠建立出來。 在得到網格參數化的結果之後，我們對原始網格模型的幾何資料做規則性或適應性的重新取樣， 產生``半正規網格''(semi-regular)表示法的物體。 接著，我們更可透過簡單的二維陣列結構去儲存重新取樣之幾何資料， 產生出幾何影像(geometry images)；這樣的二維陣列結構有益於多種不同的應用， 包括紋理貼圖、繪圖加速技術、多精細度模型(level-of-detail)、幾何壓縮、變形動畫(Morphing)。 我們以多個網格模型在三度空間中或是小波空間中計算而產生 變形動畫來當作本演算法的效果展示。

The correspondences establishment for a set of models is a versatile algorithm in computer graphics and geometry processing, which in general counts on a lot of specification by users to build a common dissection with a set of feature points between the input models. We propose a novel method to compute the consistent parametrizations for multiple models with a little user-input. Our consistent mesh parametrization scheme exploits mean value coordinates and geometric-stretch metric to optimize the parametrization of each patch. Moreover, we use a coarse-to-fine parametrization strategy to improve both the speed and the result of parametrization. Besides, the alignment of feature correspondences during the parametrization is performed using a foldover-free warping algorithm. Uniform or adaptive remeshing can be performed to yield a set of semi-regular meshes. Moveover, geometry images can be generated easily with the parametrizations to store the geometric information in a simple grid structure that benefits a number of applications, including normal mapping, texture mapping, rendering, level-of-detail, compression, and morphing. We also demonstrate the mesh morphing application between two or more objects in both spatial and wavelet domain based on the correspondence established by the proposed consistent mesh parametrizations.