由二維影像序列建構三維物體幾何模型

Abstract

本論文提出四個利用二維影像序列建構三維物體幾何模型的方法。首先，我們透過物體輪廓線及相機成像中心的連線，產生不同視角的成像空間。透過成像空間的交集，我們可以產生物體的八分樹表示式。因為有限的時間及空間資源限制，傳統上使用者透過指定最大八分樹細分階層來控制八分樹建構程序終止於資源殆盡之前。此方式之缺點在於使用者無法由所設定之參數推估建構出的模型和實際物體的差異。再者，八分樹節點無論投影誤差大小，皆須細分到指定的最大八分樹細分階層。在此論文中，我們提出一個投影誤差上限的概念。在前兩個方法，透過投影誤差的計算及比較，我們分別定義新的灰色八分樹節點。利用此新定義的灰色八分樹節點，我們提出兩個投影誤差控制的快速八分樹建構程序。不只是以實驗證明，在相同的建構模型品質下，我們所提出的方法在空間需求及運算時間上皆優於傳統的八分樹建構方法，我們亦在理論上得到相同的驗證。 在第三個方法中，我們提出一個最佳八分樹遊走演算法。我們利用八分樹節點投影誤差做排序，如此在建構八分樹模型時，可以最大誤差之節點為最優先處理之節點。實驗及理論上均證明所提出之方法在每單位八分樹節點的處理之誤差改進效能上皆能比傳統利用深度優先或橫向優先有較佳之表現。 在第四個方法中，我們提出一個未校正相機的平面物體模型建構方法。相較於前三種方法需要獲知相機內外部參數方可建構物體三維模型，在此方法中，我們提出一個不需事先校正相機參數的物體模型建構方法。並且，針對平面物體的建構，我們捨棄利用易受影像雜訊干擾之傳統點特徵的程序。我們透過平面轉換矩陣，直接推導相當的投影矩陣。進而推導出物體組成平面的平面方程式。最後再利用平面轉換矩陣及平面方程式將不同的建構結果統合在同一個座標系統中。大量的實驗及雜訊影響分析證明我們的方法是有效且強健的。

Constructing 3D object models from image sequences has gained tremendous attraction in computer vision for the past few decades. The constructed object geometric model finds many applications including robotic system, computer aided design, virtual reality, digital entertainment and target recognition. There are many methods for constructing the object geometric model. Two types of approaches will be addressed in this dissertation: shape from silhouettes and shape fitting with planes. The shape-from-silhouette method is one of the popular techniques used to construct the object shape model from a sequence of object silhouette images. The object silhouette provides important clues of the object shape for human visual system. From the object silhouette and its corresponding viewing position, one can generate a viewing volume encapsulating the object in the particular view. By intersecting the viewing volumes obtained from all viewing directions, a volumetric representation for the object can be generated. However, it often requires a huge memory space to store the 3D object volume even using a hierarchical data structure like octree. Besides, a long computer time is taken to intersect all the viewing volumes to generate the final octree. Another type of construction methods is to fit the 3D object surface with planes. The feature correspondence and robust estimation of the 3D shape of the object are two of the main problems in this type of approaches.

In this dissertation, four different methods for constructing the 3D model of a real object from image sequences are proposed. In the first method, a new octree-based subdivision strategy of two novel types of “grey” octants is proposed to speed up the octant subdivision process under a construction quality control. To further expedite the construction process a fast way for computing the 3D-to-2D projection of octant vertices using the information of vanishing point and cross ratio is proposed. In the second method, the octant whose image touches the silhouette is further classified into three types of grey octants: grey-grey, grey-black and grey-white. Then those octants having little intersection with object silhouettes will not be subdivided. This method has a great improvement on the computer processing time and memory storage space for a given construction quality specification. In the third method, a progressive mode instead of a recursive mode is proposed for the octree construction. The octree generation will be implemented using a best-first tree traversal scheme instead of a conventional depth first or breadth first tree traversal scheme. The precedence of octants for the arrangement of subdivision is ranked according to the XOR error between the projected octant image and the object silhouette. The progressive octree construction method generally gives the better visual quality rate of the object rendering effect, compared to the conventional recursive construction method.

The fourth construction method is to fit the object surface with planes. The 3D object model construction usually requires camera calibration beforehand. However, it is not easy for a user to calibrate the camera in circumstances, in particular, in the case of a hand-held camera. The fourth method for constructing the object from an uncalibrated image sequence is proposed. Instead of using the point based feature to construct the 3D information, the planar homography defined over an object planar surface is used to derive the projective geometric model of the object. All of the four construction methods are tested on real and synthetic images. The performance of the methods is evaluated in terms of visual projection error, memory space and processing time. Analytical analysis on each method is also given. The four methods offer the user more choice in constructing the object geometric model to meet the different application requirements.