本論文針對二維橢圓擬合問題，提出一種結合離心率約束與卡爾曼濾波器的遞迴擬合方法。橢圓擬合在工業檢測、虹膜追蹤與行為分析等應用中扮演關鍵角色。傳統方法如最小平方法在面對雜訊、離群點或資料缺漏時，常出現數值不穩定或擬合結果非橢圓（例如雙曲線）的情況，影響其可靠性。本文利用離心率約束確保擬合曲線保持幾何上的橢圓形狀，並引入卡爾曼濾波器，以遞迴方式利用每個點的測量數據逐步調整擬合參數，有效提升擬合精度及穩定性。透過模擬實驗與多種經典擬合算法比較，結果顯示所提方法在高雜訊與大量異常值環境中，依然能保持較低的均方誤差與視覺上優異的擬合效果，展現出數值上卓越的強健性與準確度。此外，本文也探討了不同算法在執行時間上的效能差異。研究成果不僅提供橢圓擬合的新途徑，也為未來三維橢球體擬合與即時視覺應用奠定基礎。

The thesis is concerned with the problem of two-dimensional ellipse fitting by proposing a novel recursive fitting method that integrates an eccentricity constraint with a Kalman filter. Ellipse fitting plays a critical role in applications such as industrial inspection, iris tracking, and behavior analysis. Traditional methods like the least squares approach often suffer from numerical instability or yield non-elliptical fits (e.g., hyperbolas) when confronted with noise, outliers, or incomplete data. We employ an eccentricity constraint to ensure that the fitted curve maintains the geometric properties of an ellipse, and incorporates a Kalman filter to iteratively refine the fitting parameters by measurement data, effectively enhancing fitting accuracy and stability. Through simulated experiments and comparisons with various classical fitting algorithms, the results demonstrate that one proposed method consistently achieve lower mean squared error and superior visual performance even under high noise and substantial outlier conditions, showcasing outstanding robustness and precision. In addition we also investigate the performance of these algorithms in terms of execution time. The research outcomes of the thesis not only offer a new approach to ellipse fitting, but also lay the foundation for future work on three-dimensional ellipsoid fitting and real-time vision applications.

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