藉由平面投射轉換執行影像嵌合及物體重建

Abstract

近年來，由未校正相機來重建物體的研究開始受到重視，相關應用也相繼問世。在本篇論文中，我們利用由手持相機任意擷取的影像，經由電腦視覺的幾何推導轉換，建立相機中所拍攝到的場景或物體。利用拍攝影像建立幾何模型(Geometry Model)並與影像結合。以真實的物體為藍本，建立更逼真的虛擬實境世界。其可以應用於網際網路上如電子商場場景瀏覽與虛擬實境場景導覽等。 我們希望使用者能簡便地僅以手拿相機方式，拍攝數張希望重建景物的影像，取得足夠的資訊後，初步能夠重建出其粗略的幾何物體來。因此，我們首先利用影像間存在的共同可視的物體平面，由初始不甚準確的點對應，經過Levenberg-Marquardt iterative nonlinear minimization algorithm[1][2]作最佳化的修正，得到二張影像平面上準確的影像點對應集合。經由求出的準確點對應，我們可以透過求取 fundamental matrix 和 epipolar geometry 等投影幾何資訊，計算出每一張影像，定義於同一projective space下的投影矩陣，利用該投影矩陣來進行場景的重建。在Projective Space下，物體間的長度，角度，比例，平行性會失真，但次序是不變的。再利用求得真實物體的Euclidean Space三維座標或epipolar geometry及物體剛體性（Rigidity）的等等限制（Constraints），將Projective Space下的物體座標轉換至真實場景的Euclidean座標系統下，完成物體的三度空間重建。 此外，對於影像中可能發生的遮蔽問題，我們亦有一個處理遮蔽的演算法，能夠自動解決影像中的遮蔽問題，使我們能得到完整的重建物材質影像，並能將重建出來的幾何模型加以貼圖，使最後重建結果能看起來更真實。

Recently, research on un-calibrated object reconstruction has received great attention. In this thesis, we take pictures with a hand-held digital camera. Through computer vision geometric transformation, we shall reconstruct the three-dimensional scenes and objects that are imaged. Combining geometric models with photo-realistic texture mapping, we'll try to rebuild the vivid virtual world. We can use this reconstruction in Internet-based applications such as e-commence on-line browsing or virtual reality. To obtain the precise point correspondence pairs on the object planar surface, we first make use of the common visible planar regions of the two images. We optimize the planar projective transformation using Levenberg-Marquardt iterative nonlinear minimization algorithm [1][2]. Through the precise point correspondence pairs between the two images, we can derive the geometric relation between two images through the fundamental matrix. Furthermore, we can acquire the projection matrix of each image in a projective space. After the projective reconstruction, we can proceed to obtain the real scene reconstruction. Moreover, we also develop an algorithm for removing the occluded parts of the planar object from multiple views. The application of texture mapping makes the reconstruction result look more realistic.