在三維模型的建構上，對應點的選取和改善佔有相當重要的地位。對應點的準確性影響整個建模的成效。本論文中我們提出了新的方法，透過極線轉換法(epipolar transfer)在多視角影像中做可見影像過濾和對應點改善。首先，我們以Furukawa所提出的方法，建構三維補綴面並加以做旋轉和位移，或是單純在二維影像移動對應點兩種方式選取初始對應點。然後再以本研究所提出的極線轉換法找到適當位置的對應點。接下來我們將每個三維點的可見影像(visible image)再次透過極線轉換法去檢查可見影像上的對應點位置是否適當，利用門檻值將不合適的對應點過濾掉。進一步針對對應點位置的改善和篩選，期望透過極線幾何法來找到位置最準確的對應點位置。最後比較實驗成果，觀察到以本研究所提出的方法做改善後，對應點準確度提高近百分之十五。 / In the construction of three-dimensional models, the selection and refinement of the correspondences plays a very important rule. The accuracy of the correspondences affects modeling results. In this paper, we proposed a new approach, that is filtering the visible images and improving the corresponding points in multi-view images by epipolar transfer method. First of all, we use Furukawa proposed method to construct three-dimensional patches and making rotation and displacement, or simply move the corresponding points in two-dimensional images are two ways to select the initial corresponding points. And then to use epipolar transfer method in this study to find the appropriate location of the corresponding points. Next we will check the corresponding points on the each 3D point’s visible image again through the polar transformation method , and we use the threshold value to filter out the corresponding points. Further the location of the corresponding points for the improvement and screening, hoped that through the epipolar geometry method to find the most accurate corresponding points’ location. Experimental results are compared to observe the improvements that the method proposed in this study, the corresponding point accuracy by nearly 15 percent.

近年來諸多學者專家致力於從多視角影像獲取精確的點雲資訊，並藉由點雲資訊進行三維模型重建等研究，然而透過多視角影像求取三維資訊的精確度仍然有待提升，其中萃取影像對應與重建三維資訊方法，是多視角影像重建三維資訊的關鍵核心，決定點雲資訊的形成方式與成效。 本論文中，我們提出了一套新的方法，由多視角影像之間的幾何關係出發，萃取多視角影像對應與重建三維點，可以有效地改善對應點與三維點的精確度。首先，在萃取多視角影像對應的部份，我們以相互支持轉換、動態高斯濾波法與綜合性相似度評估函數，改善補綴面為基礎的比對方法，提高相似度測量值的辨識力與可信度，可從多視角影像中獲得精確的對應點。其次，在重建三維點的部份，我們使用K均值分群演算法與線性內插法發掘潛在的三維點，讓求出的三維點更貼近三維空間真實物體表面，能在多視角影像中獲得更精確的三維點。 實驗結果顯示，採用本研究所提出的方法進行改善後，在對應點精確度的提升上有很好的成效，所獲得的點雲資訊存在數萬個精確的三維點，而且僅有少數的離群點。 / Recently, many researchers pay attentions in obtaining accurate point cloud data from multi-view images and use these data in 3D model reconstruction. However, this accuracy still needs to be improved. Among these researches, the methods in extracting the corresponding points as well as computing the 3D point information are the most critical ones. These methods practically affect the final results of the point cloud data and the 3D models so constructed. In this thesis, we propose new approaches, based on multi-view geometry, to improve the accuracy of corresponding points and 3D points. Mutual support transformation, dynamic Gaussian filtering, and similarity evaluation function were used to improve the patch-based matching methods in multi-view image correspondence. Using these mechanisms, the discrimination ability and reliability of the similarity function and, hence, the accuracy of the extracted corresponding points can be greatly improved. We also used K-mean algorithms and linear interpolations to find the better 3D point candidates. The 3D point so computed will be much closer to the surface of the actual 3D object. Thus, this mechanism will produce highly accurate 3D points. Experimental results show that our mechanism can improve the accuracy of corresponding points as well as the 3D point cloud data. We successfully generated accurate point cloud data that contains tens of thousands 3D points, and, moreover, only has a few outliers.

電腦視覺三維建模的精確度，仰賴影像中對應點的準確性。以前的研究大多採取兩張影像，透過極線轉換(epipolar transfer)取得影像間基礎矩陣(fundamental matrix)的關係，然後進行比對或過濾不良的對應點以求取精確的對應點。然極線轉換存在退化的問題，如何避免此退化問題以及降低兩張影像之間轉換錯誤的累積，成為求取精確三維建模中極待解決的課題。 本論文中，我們提出一套機制，透過三焦張量(trifocal tensor)的觀念來過濾影像間不良的對應點，提高整體對應點的準確度，從而能計算較精確的投影矩陣進行三維建模。我們由多視角影像出發，先透過Bundler求取對應點，然後採用三焦張量過濾Bundler產生的對應點，並輔以最小中值平方法(LMedS)提升選點之準確率，再透過權重以及重複過濾等機制來調節並過濾對應點，從而取得精確度較高的對應點組合，最後求取投影矩陣進行電腦視覺中的各項應用。 實作中，我們測詴了三組資料，包含一組以3ds Max自行建置的資料與兩組網路中取得的資料。我們先從三張影像驗證三焦張量的幾何特性與其過濾對應點的可行性，再將此方法延伸至多張影像，同樣也能證實透過三焦張量確實能提升對應點的準確度，甚至可以過濾出輸入資料中較不符合彼此間幾何性的影像。 / The accuracy of 3D model constructions in computer vision depends on the accuracy of the corresponding points extracted from the images. Previous studies in this area mostly use two images and compute the fundamental matrix through the use of the epipolar geometry and then proceed for corresponding point matching and filtering out the outliers in order to get accurate corresponding points. However, the epipoler transform suffers from the degenerate problems and, also, the accumulated conversion errors during the corresponding matches both will degrade the model accuracy. Solving these problems become crucial in reconstructing accurate 3D models from multiple images. In this thesis, we proposed a mechanism to obtain accurate corresponding points for 3D model reconstruction from multiple images. The concept of trifocal tensor is used to remove the outliers in order to improve the overall accuracy of the corresponding points. We first use Bundler to search the corresponding points in the feature points extracted from multiple view images. Then we use trifocal tensor to determine and remove the outliers in the corresponding points generated by Bundler. LMedS is used in these processes to improve the accuracy of the selected points. One can also improve the accuracy of the corresponding points through the use of weighting function as well as repeated filtering mechanism. With these high precision corresponding points, we can compute more accurate fundamental matrix in order to reconstruct the 3D models and other applications in computer vision. We have tested three sets of data, one of that is self-constructed data using the 3ds Max and the other two are downloaded from the internet. We started by demonstrating the geometric properties of trifocal tensor associated with three images and showed that it can be used to filter out the bad corresponding points. Then, we successfully extended this mechanism to more images and successfully improved the accuracy of the corresponding points among these images.