在這篇論文中，我們提出了一個利用人臉特徵的統計資料對於廣角鏡頭拍攝的團體照進行扭曲補償的系統，我們更進一步將人臉特徵運用於自適應的圓柱投影，減少校正影像邊緣的透視變形。不同於傳統的校正方法，我們的方法有幾個優點:不需事前的校正物體(例如:棋盤格樣板、校正方塊、建築物等場景中的直線萃取)，此外，我們的校正結果相較於傳統的校正方法，較無人臉的嚴重透視變形。此系統可分為四個部分：事前的人臉特徵模型統計過程、扭曲人臉的特徵點萃取、影像扭曲參數的估測、扭曲補償及自適應圓柱投影。
估測扭曲參數的部分，我們將事先統計好的人臉特徵資料，運用PCA取出特徵資料裡最主要的幾個特徵向量。設定扭曲參數的搜尋範圍，利用分層的搜尋方式。在選擇最佳扭曲參數時，我們利用最小平方法，找到最佳臉部特徵的線性組合，能使不同形變參數下校正的臉部特徵與事前統計好的人臉特徵資料彼此之間的差異最小。
在實驗結果當中，對於扭曲的影像，套用我們估測出的最佳參數進行校正，我們也實作其他不同方法並且產生出最終校正影像，可以看出我們的校正影像中，人臉具有視覺上相較合理的結果。同時也對校正後具有透視變形的影像，進行自適應圓柱投影的調整。

In this thesis, we propose a new technique for compensating radial distortion of photos acquired with wide-angle lens by using facial features extracted from images. Our method utilizes a statistical facial feature model to recover radial distortion and the facial features are further used for adaptive cylindrical projection which will reduce perspective distortion near the image boundary. Our method has several advantages over the traditional methods. First, traditional calibration patterns, like man-made straight buildings, chessboards, or calibration cubes, are not required in our method. Secondly, the faces in the corrected photos by using the proposed method are better corrected than those by using the traditional methods. In addition, the proposed method produces photos with less perspective distortion compared to the traditional methods because our method includes an adaptive cylindrical projection. Our distortion correction system is composed of four components: offline training of the statistical face feature model, feature point extraction from distorted faces, estimation of radial distortion parameters and distortion compensation, and adaptive cylindrical projection.
In order to estimate the distortion parameters, we propose an energy considering the fitness between the undistorted coordinates of the facial feature points extracted from the input image and the learned statistical facial feature model. Given the distortion parameters, the fitness is calculated by solving a linear least squares system. The distortion parameters that minimize the fitness function are searched in a hierarchical manner. Experimental results are shown to demonstrate the distortion reduction in the corrected images by using the proposed method.

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