在人臉辨識與人臉驗證的相關研究中，線性鑑別式分析(Linear Discriminant Analysis, LDA)是一種常見的線性轉換技術，透過LDA轉換後可以求出一組具有鑑別性的特徵參數。然而應用在線上的人臉辨識與人臉驗證系統上，必須因應資料的更新與刪除等情況，重新訓練LDA的轉換參數，LDA的轉換參數包括了散佈矩陣與轉換矩陣。傳統的LDA需花相當多的時間才能獲得更新後的轉換參數，在本篇論文中針對傳統LDA無法有效動態更新這些參數的缺點，提出了一個動態LDA演算法，利用代數的運算，不但能節省重新訓練的時間，在重新訓練時也只需要保留少數的相關參數，即能無誤差的獲得更新後的轉換參數。另外在人臉驗證的系統上，藉由 LDA與最佳相似度線性轉換(Maximum Likelihood Linear Transformation, MLLT)的結合獲得最佳的線性轉換矩陣，並且應用機率分布的概念對人臉驗證的問題作假設檢定(Hypothesis Testing)根據相似度比值(Likelihood Ratio, LR)為F分配，選擇不同的顯著水準進行假設檢定。本論文提出驗證的方法優於傳統人臉驗證的方法，主要是因為傳統方法採用相似度比值測試(Likelihood Ratio Test, LRT)，並用經驗法則手動的調整驗證的門檻值(threshold)，本方法可以依照不同的需要，選擇不同的顯著水準進行檢定。實驗中，我們將所提出來的方法應用在中研院人臉資料庫及本實驗室收集的汽車人臉資料庫皆有不錯的效果，我們也實現一套線上動態人臉辨識及驗證展示系統。

Linear Discriminant Analysis (LDA) is a popular linear transformation method for face recognition verification. Using LDA, we can extract the low-dimensional discriminative feature parameter for human faces. In the applications of face recognition and verification, it is usually necessary to enroll the system with new papers and templates. Also, we often need remove the out-of-date persons or templates from the system model. Namely, using the LDA model, the within and between class scatter matrices and the transformation matrices should be recomputed. However, such a recomputation is very time-consuming. To overcome this weakness, a dynamic LDA algorithm is proposed in this paper. Apply this algorithm, we cannot only save a huge amount of computation time but also obtain the updated new parameters with relatively small storage of model parameters. Moreover, in face verification system, we estimate the optimal matrix via by combining the theories of LDA and Maximum Likelihood Linear Transformation (MLLT). We also derive the distribution of likelihood ratio based on MLLT to be the F distribution. Then, the face verification system is carried out via hypothesis testing using different significant levels for F distribution. The advantage of new method is that the verification decision is done according to statistically meaning "significant levels". This superiority is attractive compared to the conventional method using empirical thresholds. In the experiments, we obtain desirable performance using IIS face database and CSIE/NCKU car face database. An online dynamic face recognition and verification demo system is implemented.

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