在電腦視覺領域中，主成份分析一直是常被應用至與資料分析或子空間學習等相關問題上的統計方法。而在某些情況下，主成份分析的輸入資料會不可避免地含有一些不正確的離群值，即所謂的outlier，此時，我們可利用強固計算方法來偵測outlier，並將之剔除。在這篇論文中，我們提出了以隨機抽樣來達成此目的之強固主成份分析演算法。
總體來說，本演算法包含了以下幾個步驟。首先，在全部資料中隨機選取幾筆資料來計算一個主成份模型，接著，以其他未被選取之資料來評估此模型，而如果該模型不夠好的話，則不斷重複此抽樣評估的程序，直到找到一個好的模型為止。為了處理不同種類的outlier，我們使用不同的抽樣策略。對於sample outlier，我們採取一維抽樣，而對intra-sample outlier，則採取二維抽樣。此外，針對傳統隨機抽樣方法所遇到的問題，即誤差規模估計及停止條件設定，我們則以extended MSSE (Modified Selective Statistical Estimator) 機制來解決。
為了瞭解本演算法在不同情況下的表現，我們在模擬資料及真實資料上均進行了實驗。實驗結果證明，相較於標準主成份分析，以及採用M-估計之強固主成份分析方法，本隨機抽樣演算法擁有較為準確的結果，且對於含有高達百分之八十sample outlier的資料，或是含有百分之三十隨機分佈之intra-sample outlier的資料，本演算法都可以計算出與正確值相當接近之主成份模型與重建資料。

In this thesis, we propose RANSAC [6] (RANdom SAmple Consensus) based approaches to achieve robust PCA [1] (Principal Component Analysis) for data containing outliers. This problem is related to a variety of vision applications that require data analysis or subspace learning, especially for the case that outliers are unavoidable.
Overall, our algorithms consist of the following steps. We randomly select a subset of data to compute a PCA model, evaluate the model by other unselected data, and repeat the hypothesize-and-test procedure until a good model is found. To deal with different types of outliers, we apply different sampling strategies, one-dimensional sampling for sample outliers, and two-dimensional sampling for intra-sample outliers. In addition, problems resulted from traditional RANSAC, i.e. a prior error scale and the stopping criteria, are solved by the developed extended MSSE [2] (Modified Selective Statistical Estimator) framework.
Experiments on simulated and real data demonstrate superior performance of the proposed RANSAC-like algorithms compared to standard PCA and the robust PCA technique [5] based on M-estimation. The results also verify that the proposed algorithms are robust against up to 80% sample outliers or 30% randomly distributed intra-sample outliers.

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