幾何失真廣泛地出現在影像擷取、遙測系統、顯示設備、醫學成像上，幾何失真將會造成影像結構的破壞，在複雜的成像系統中，幾何失真將會更進一步造成後續的假影、模糊以及亮度偏差。傳統方法對於固定的幾何失真將採取事前校正的方式，這些事前校正方式大多需要人為介入參與並無法全自動化，其使用範疇也多所侷限而無法應用於可變的幾何失真。
最基本的幾何失真校正為影像的幾何變換，然而本論文探討的幾何失真校正為泛指對於空間參數進行調整。透過影像特徵抽取與影像品質度量，我們對徑向變形校正、磁振造影移動補償與視差調適三個問題提出了不同以往的新演算法。 由於廣角及魚眼鏡頭的非線性特性，其將對影像產生空間變異的扭曲，我們採取了特徵轉換及度量的架構，首先使用邊緣特徵抽取並將影像特徵被轉移至特徵影像，再藉由特徵影像的品質評估達成變形參數估測與影像校正，利用此架構我們發展了全自動的徑像變形校正，並能應用於一般魚眼鏡頭和須即時校正的廣角內視鏡中。我們也進一步擴充該架構至含有不同校正樣式的影像上及含有可變幾何失真的可變焦鏡頭上。由於磁振造影擷取富利葉係數的特殊取像方式，造影中的移動將造成假影及模糊，對不同的相位編碼需給予不同的移動補償，傳統方法以貪婪完整式的搜索來最佳化一個影像品質函數，而忽略其他重要資訊，我們藉由在幅度上尋找重覆邊緣找出可能移動方向，並接著使用圖模形融合了個數種資訊(包含頻譜對稱、移動連續性以及影像品質函數)以求解。對雙眼視覺影像的視差調適也可以視為幾何失真修正，為了使得人眼能舒適的觀賞雙眼影像，我們需對左右眼影像進行不同幾何調整，最簡易而傳統的方式是將每一幀左右影像進行平移。然而單純平移在深度範圍極大的影像中，並不能發揮作用，因此我們採取了影像特徵進行影像切割，利用立體影像的品質度量估測決定每個區塊的幾何轉換參數並進行影像修正，進一步提升觀賞經驗。
本學位論文專注於探討在空間參數上進行調整的一般幾何失真修正，藉由影像特徵與影像品質度量，並對三種影像修正的問題提出新式演算法求解。

Geometric distortion is a very common problem in image capture, remote sensing, image display, and medical imaging. In a complicated imaging system, it can further induce ghosting, blurring, and intensity change. Traditional methods will adapt the approach of pre-calibration. These pre-calibration methods usually require some human intervention, thus their application scope is quite limited. In addition, they are not applicable in variable geometric distortion.
The basic geometric distortion correction is to apply appropriate geometric transformations for images. In this thesis, geometric distortion correction means a generalized one that adjusts spatial transformation parameters. By extracting image features and utilizing image quality measures, we propose three novel algorithms for three geometric distortion correction problems, i.e. radial distortion correction, motion compensation in Magnetic Resonance (MR) images, and disparity adjustment.
Due to the nonlinearity in radial distortion, it will result in spatially varying distortion for the image. We adapt the framework of utilizing feature transform and image measure to estimate the radial distortion parameters. First, we use edge extraction and transfer features into the feature map; and then assess the quality of feature map to estimate distortion parameters for the image correction. By using this framework, we develop fully automatic calibration and it can be applied in popular fisheye lenses and medical wide-angle endoscopes, which usually require real-time correction. In addition, we also extend the framework to different types of calibration patterns and zoom lenses with varying geometric distortion.
Because of the special capturing procedure of MR images in Fourier domain, the motion of subject during the imaging process will result in ghosting and blurring, and thus different motion compensations for different phase encoding lines have to be estimated. Traditional methods use greedy and exhausted search for optimizing an image quality measure, and ignore other important information. We search repeating edge for collecting candidate motion vectors and use graphical models to fuse different information (including symmetry of frequency, smoothness of motion, and an image quality measure) to solve the problem.
The disparity adjustment can be regarded as geometric distortion correction. In order to provide better viewing experience of stereoscopic images, we have to adjust the left and right images geometrically. The simplest method is to shift the left and right images to adjust the disparity range within a comfort zone. However, the shifting in stereoscopic images with large disparity range may not work. Hence, we take image feature for image segmentation and utilize a stereoscopic image quality measure to decide different geometric transformations for different segments for the image correction to improve the viewing experience.
In this thesis, we focus on a general geometric distortion correction over the domain of spatial parameters. By utilizing image features and image quality measures, we propose novel algorithms to resolve the three image correction problems described above.

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