摘要
橢圓辨識之應用非常廣泛，除了數位影像辨識外，亦可應用於一般數值分析上。目前的橢圓辨識演算法大致上可分為幾何方法及數值方法，使用幾何方法雖然有較快的運算效能，但若考慮雜訊之影響，則根據幾何特性辨識出之結果可能產生較大之誤差，而使用數值方法如最小平方法，我們可求得誤差最小之解。因此本文由最小平方法為基礎的橢圓辨識演算法之推導過程，尋找影響演算法性能之關鍵點，經由浮點運算時間測試及誤差分析，找出演算法的最佳解法，將演算法作最佳化。並與B2AC法作比較，經由浮點運算時間測試及抗雜訊能力之測試，證明本文提出的演算法有較好的運算效能且易於實作，可實現於即時的機械視覺、影像辨識系統。
並列摘要
The application of ellipse fitting is very extensive. Not only the digit image recognition but also the numerical analysis. The methods of ellipse fitting algorithm can roughly class as geometric methods and numerical methods. Although the geometric method has better performance on computation but get larger error of estimation on calculation result with considering the noise affection. The numerical methods as the least square algorithms can minimize the numerical error. So the purpose of this text is to look for the key influence of the least square based ellipse fitting method from the algorithm deriving and verify it via FLOPS testings and error analysis. Find out the best solution of performing the algorithm and make it optimization. In order to prove the least square based ellipse fitting algorithm bas better efficiency and easy to implement, we compare with B2AC algorithm via FLOPS and noise testings. By way of these testing methods, we prove that the algorithm can realize on real-time mechanical vision and image recognition system.