利用影格特徵及主成份分析壓縮3D動畫

3D Animation Compression Using Frame Features and Principle Component Analysis

郭育嘉(Yu-Chia Kuo)

指導教授 ： 林聰武 ； 鍾斌賢

中原大學/工學院/資訊工程研究所/碩士(2006年)

https://doi.org/10.6840/cycu200600358

摘要

在計算機圖學的領域中，3D動畫已經是一個主要的研究課題。一個動畫可以分為時間與空間兩大部分來做探討。依時間性，我們可以清楚知道動畫是由多個不同時間的檔案所組成，每一個檔案我們稱之為影格。而每一個影格表現出3D模型在空間中不同的變化。在3D動畫中，每個影格包含了3D模型的點座標位置與三角片組成的相鄰資訊，其中只有模型的點位置會依時間性改變，其三角片的相鄰關係並不會隨時間而有所改變。因此我們希望能降低3D動畫所需的資料量，也就是希望能維持住相同的相鄰關係，並且針對模型的點資訊進行壓縮，使得能利用較低的資料量但能表現出誤差在可容許範圍內的動畫模型。

使用主成份分析對一般的3D動畫模型均可以獲得不錯的簡化結果，理由是主成份分析能將多個有相關性的變數簡化成少數幾個沒有相關的主成份，而且經由線性組合可還原出近似原始動畫。但其較適合使用在原地進行運動模擬的動畫模型，若將原始動畫加入剛體運動，諸如:平移、旋轉、縮放，則對使用相同基底的主成份分析將會造成龐大的失真情形。

本論文使用仿射矩陣與主成份分析來壓縮3D動畫。仿射矩陣可以將幾何轉換所造成的位移變化利用4*4矩陣來記錄，轉換過後的模型可去除幾何轉換的影響，並將動畫模型正規化至侷限空間內；之後使用主成份分析將可以更正確的計算出最適當的基底(變異數)。使用主成份分析線性組合的動畫可以經由仿射矩陣得到最後的近似動畫。實驗證明經由仿射矩陣與主成份分析壓縮的3D動畫誤差相對於只進行主成份分析的誤差小，而且近似於原始模型未加入剛體運動的誤差值。

關鍵字

主成份分析 ； 仿射矩陣

並列摘要

In recent years, the research on the compression of 3D animation sequence has become more important in computer graphics . Animation can be discussed in two parts, temporal and spatial parts .Depend on temporal domain, animation sequences was combined with several single static meshes over time , which was called frames. In each frame, a single 3D mesh has different variation in spatial domain. However, a single 3D static model requires large storage space for vertex information and adjacency relationship of triangles. For life-like soft body animations of the 3D data, because the vertex positions change over time, the storage space and the amount of calculation required would be even more voluminous, but the connectivity of adjacency triangles are the same in each frames. Hence, the reduction concept emerges in the hope of reducing the required storage space and keeps within an acceptable error range.

This paper concerns with the use of the affine transformation matrix in working with Principal Component Analysis (PCA) to compress the data of 3D animation models. Satisfactory results were achieved for the common 3D models by PCA because it can simplify several related variables to a few independent main factors in addition to make the animation identical to the original by linear combination. However, it is more suitable for animation models for original semi-movement. If the original animation is integrated with the transformation movements such as translation, rotation, and scaling, the animation model for transformation movement will have a greater distortion in the case of the same base vector as compared with the original animation model for semi-movement.

In this paper , the first is to extract the model movement characteristics using the affine transformation matrix and then to compress 3D animation by PCA. The affine transformation matrix can record the changes in geometric transformation by using 4 * 4 matrixes. The transformed model can eliminate the influences of geometric transformation with the animation model normalized to limited space. Then, by using PCA, the most suitable base vector (variance) can be selected more precisely.

並列關鍵字

Principle Component Analysis ； affine transformation matrix

參考文獻

[3]. B. Hamann, “A Data Reduction Scheme for Triangulated Surfaces,” Computer Aided Geometric Design, Vol.11, pp. 197--214, 1994.

[7]. D. Zhang1, Z. Zhou, “2-Directional 2-Dimensional PCA for Efficient Face Representation and Recognition,” Neurocomputing, Vol. 69(1-3), pp. 224-231, 2005.

[10]. H. Hotelling, “Analysis of a Complex of Statistical Variables into Principal Components,” Journal of Educ. Psychol., Vol. 24, pp. 417-441, 498-520, 1933.

[11]. I. Guskov, A. Khodakovsky, “Wavelet Compression of Parametrically Coherent Mesh Sequences”, ACM SIGGRAPH Symposiumon Computer Animation, pp. 183-192, Grenoble, France, 2004

[13]. J. E. Lengyel. “Compression of time-dependent geometry,” In ACM Symposium on Interactive 3D Graphics, pp. 89--96, 1999.