由於電腦科技的快速發展，虛擬實境在近幾年來吸引了許多人的眼光及注意。對虛擬實境而言，建構三度空間(three-dimensional, 3D)的虛擬環境是非常重要的一環。樹木是自然界中非常常見的物體，因此樹木的3D立體模型建構對於自然環境的3D虛擬重現佔有非常重要的角色。事實上，建構逼真的虛擬樹木在過去幾年來一直是電腦圖學中非常重要的一項研究領域，並已有所多的方法發表於研究文獻上。這些方法大都是利用一些數學演算法合併植物生長的規則產生出樹木的3D幾何結構。通常這些方法在樹木的產生過程中會加入一些隨機的變化以避免所產生的樹木具有高度的自我相似性。然而，雖然這些方法可以模擬出非常逼真的樹木3D立體模型，但這些方法所產生的樹木與我們週遭環境的樹木並不相同，亦即這些樹木是由演算法所自行生長而不是根據真實世界的樹木所建構。欲模擬出與真實世界相類似的樹木，我們必須從真實樹木的影像著手。在此篇論文中，我們發展了一個從未校正的影像串列(uncalibrated image sequence)建構逼真的樹木3D立體模型的方法。我們首先利用樹幹在不同影像間位置的不同推測出其在三度空間中的位置並以此建構出樹幹的3D立體模型，隨後再依據所建構的樹幹生長樹葉。由於樹幹是依照影像所建構，因此此方式所建構的樹幹與真實樹木的樹幹非常地相似，而只要樹葉能夠依據所建構的樹幹適當地生長，則整棵樹的整體外觀與真實樹木亦會相當地接近。然而，欲達到上述的目的，有幾個課題必須審慎地考量。這些課題包含了對應點的找尋(correspondences searching)、相機的自我校正(camera self-calibration)以及樹木影像的分割(tree segmentation)。在本篇論文中我們也針對這些課題進行詳細的研究及探討。
為了從未校正的影像串列中取得樹幹的3D資訊，相機的自我校正是必要的一環。然而，為了要校正相機，我們必須先取得物體在不同影像間的對應點。對應點的找尋是電腦視覺領域中一極為基礎但卻困難的問題。幸而對於影像串列而言，光流場的計算(optical flow computation)提供了一個估測影像移動或者對應點找尋的絕佳方式。因此在本論文中我們首先針對光流場的估測做進一步的探討，我們提出了一個在非均勻亮度變化下仍可精確估算出光流場的演算法。隨後我們即利用所取得的對應點進行相機的自我校正。在本論文我們也提出了一個極為彈性的相機自我校正演算法，此方法可根據實際情況的不同設定不同的相機限制以取得更精確的校正結果。同時，在本論文中，我們也提出了一個分割影像中樹幹及樹葉區域的演算法，此分割出來的樹幹區域對於隨後樹幹3D模型的建構有極大的幫助。我們先從分割出來的樹幹區域擷取出其平面骨架，之後再利用已校正的相機以及樹幹的對應點計算出樹幹各個部位的三度空間位置，從而將此平面骨架延伸為樹幹的三度空間骨架。當取得樹幹的三度空間骨架之後，我們即可環繞此三度空間骨架建構許多相連的圓柱體已達成樹幹的3D模型建立。由於相機已適當地校正，故樹幹的紋理(texture)可藉由將此樹幹3D模型重新投影到影像平面而取得，此樹幹紋理的產生可大幅增加樹幹3D模型的真實度。最後，我們再將樹葉適當地生長於此樹幹3D模型上即可完成一逼真的樹木3D立體模型。目前我們已進行多項的實驗，由實驗結果可證明我們的系統確實能夠從未校正的影像串列建構出非常逼真的樹木3D立體模型。

Because of the rapid development of computer technology, virtual reality has received much attention in recent years. For virtual reality, constructing a realistic three-dimensional (3D) virtual environment is of particular importance. Tree is very a common object in natural environment, thus its 3D model construction plays a quite important role for natural scene 3D reconstruction. In fact, modeling realistic trees has been a topic in computer graphics for many years and many approaches have been published in the literature. In computer graphics, trees are typically synthesized by some mathematical algorithms in conjunction with some botanic knowledge to generate the geometrical structures of the trees. Often some random variations are also imposed in the modeling process to avoid auto-similarity. Although these graphical methods can model quite realistic trees, the generated trees are, however, different from the real ones in our surrounding environment, i.e., they are grown themselves without any reference to the real trees in the nature. To create a 3D tree model similar to a real tree in the nature, we must model the tree according to the images of this tree. In this dissertation, a complete framework for constructing a realistic 3D tree model from uncalibrated image sequence (i.e., the images are captured with unknown camera internal and external parameters) is developed. We first construct the 3D trunk model via structure from motion technique, and then generate leaves on the created 3D trunk model. This manner can produce quite similar 3D trunk model since the 3D information of the trunk is directly computed from the images. Meanwhile, the generated tree crown will be also similar to the real tree as long as the leaves are appropriately generated. However, to achieve this goal several issues should be addressed. These issues, including correspondences searching, camera self-calibration, and tree segmentation, are also deeply investigated in this dissertation.
To acquire the 3D information of the trunk from uncalibrated image sequence, camera self-calibration (i.e., calibrating the camera directly from the captured images) is a necessary step. However, to calibrate the camera, image correspondences should be identified first. Searching image correspondences is an elementary but ill-posed problem in computer vision. Nevertheless, it is convinced that optical flow can provide quite accurate image motion estimation, and hence image correspondences from an image sequence. In this dissertation, an accurate algorithm for computing optical flow under non-uniform brightness variations is first developed. Following this, the issue of camera self-calibration is deeply discussed. A camera self-calibration algorithm suitable for variant camera constraints is proposed. An algorithm for segmenting trunk and leaf regions from a single image is also discussed. The extracted trunk region is quite useful for the subsequent 3D trunk model construction. The skeleton of the segmented trunk region is first extracted to represent the 2D trunk structure of the tree. Subsequently, the 2D trunk skeleton is extended to 3D trunk skeleton by exploiting the calibrated camera and the trunk correspondences. After recovering the 3D trunk skeleton, a set of generalized cylinders is generated around the recovered 3D trunk skeleton to model the 3D trunk. Since the camera has been calibrated, trunk texture can be easily obtained by reprojecting the 3D trunk model onto the image plane. Mapping trunk texture can greatly improve the realism of 3D trunk model. Finally, the leaves are generated on the created 3D trunk model to produce a more realistic 3D tree model. Some experiments were conducted and the results demonstrate the feasibility of proposed system for creating a realistic 3D tree model from uncalibrated image sequence.

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