Optimal N-view Reconstruction under Silhouette Constraint and Its Applications

給定一組影像，並假設其中的物體經過分割。在本文中考慮如何由這些影像中重建出能夠產生同樣的影像分割結果之三維結構。特別是我們提出一個方法，能夠在這些三維結構中尋找出一個使得最大影像比對誤差為最小的解。我們將闡明這樣的最佳解與1999年Kutulakos and Seitz於ICCV’ 99中所提出的「具影像一致性之三維結構」有高度的關連性。在我們的方法中使用了一組由寬鬆至嚴格的一致性準則來取代僅使用單一準則之方式，並由此定義出一個新的解 – MPH 。我們十是出一個可以成功求解MPH的演算法 – 「漸趨嚴格之空間雕刻法」。在本文的核心部份，我們將證明MPH是滿足以上所提之極小—極大之最佳化準則的一個解。同時我們的最佳化準則自然地將部份遮蔽的現象以合理的方式涵蓋在內，而非將之視為一個懲罰項。我們並成功地將本法所重建出的三維形狀應用於新視圖產生與三維合成的應用上。

Given a set of segmented images of an object as input, we consider the problem of reconstruction of a 3D shape that can generate the same silhouettes to those of the given images. In particular, among the solution shapes to this 3D reconstruction problem, we propose a systematic method to find an optimal solution in the sense that it allows the maximal measurement error associated with image correspondences to be the minimal. We will show that the solution shape to the above optimization problem is highly related to the theory of photo-consistent shape proposed by Kutulakos and Seitz in 1999. However, instead of using a single consistent criterion, a class of consistent criterions ordered from loose to strict is used in our work to define a unique shape called the minimal photo hull (MPH). We propose a provably-correct algorithm, the getting-stricter space carving, for finding the MPH. At the heart of our work is the observation to the fact that the MPH is a shape satisfying the min/max optimization criterion mentioned above. In essence, the optimization in our work is achieved by modeling the occlusion inherently, instead of penalizing it. The reconstructed 3D shapes were successfully applied for novel-view generation and 3D composition.