A Stochastic Multispectral Images Simulation Approach and Its Applications in Remote Sensing

多光譜衛星遙測影像已被廣泛應用於地表覆蓋分類的領域，其中監督式分類法是以選取訓練樣本(training data)作為特徵值分類之依據，以混淆矩陣(confusion matrix)計算而得的準確度(accuracy)評估分類結果。然而地表反射能力會隨著地表狀態的不同而改變，因此分類結果也會隨之改變，但利用有限的衛星影像無法表現其不確定性。此外，使用者準確度會受訓練樣本的類別比例影響，造成訓練樣本的分類準確度無法推估全影像的分類準確度。故本研究提出多光譜衛星遙測影像之序率模擬的方法，以多幅具有相同特性之模擬影像對分類結果之準確度進行探討。本研究採用日本ALOS衛星於台北市及其近郊拍攝所得之衛星影像作為原始影像。將多光譜衛星遙測影像視為隨機向量場域，各像元之灰階值代表特徵向量，故特徵向量具有來自不同波段間的特徵相關性，同時也具有因地物連續性造成的空間相關性。因此模擬影像時，首先利用非監督式分類法，將原始影像中具有相似光譜特性之特徵向量分群，不同群的特徵向量可視為來自不同參數之多變量分佈的樣本，並以多變量分佈之相關係數維持原始影像之特徵相關性。由於分群後的特徵向量之邊際分佈並非常態分佈，利用共變異數矩陣轉換演算法，將多變量常態分佈模擬之樣本轉換為相對應分佈之樣本。得到模擬樣本後，利用主成分分析之第一主成分的排序值所成之級值序列(rank series)，作為維持空間相關之依據，使模擬影像不喪失原始影像之地表樣貌。最後，以模擬影像評估分類結果之不確定性以及訓練像元之代表性。Multispectral remote sensing images are widely used in many environmental monitoring applications including landuse/landcover (LULC) classification and change detections. Remote sensing LULC classification can be conducted using various supervised or unsupervised classification techniques. Accuracies of classification results often are evaluated using the confusion matrix (or error matrix) derived from a set of training data which consists of training pixels of individual LULC classes. There are also applications that assessed classification accuracies based on the error matrix derived from an independent reference dataset. However, although widely accepted for classification accuracy assessment, uncertainties of the error matrix itself due to selection of training pixels (sampling uncertainties) have received little attention. In addition, the premise that training data are representative of the whole study area is not always valid. In this study, we aim to tackle both problems by a stochastic multispectral images simulation approach (SMISA). The SMISA considers multispectral images as a multivariate random field, or a random-vector field. Individual univariate random fields may be non-Gaussian and a covariance transformation algorithm was applied for transforming a non-Gaussian random-vector field to a corresponding Gaussian random-vector field. Cluster analysis was implemented to group all pixels into several clusters. All pixels of the same cluster are considered as a realization of a random-vector field. Principal component transformation was then applied to the Gaussian random-vector field and the resultant major principal components were evaluated. The major principal components were simulated independently and then scores of Gaussian random-vector were obtained through inversion of the principal components. By using rank series of the original multispectral remote sensing images, we were able to stochastically simulate a large number of multispectral images which preserve all the statistical properties of the original set of multispectral images. The proposed rank series based approach has been successfully tested using an AR(2) time series model. By decomposing a given AR(2) model into a rank series and an independent Gaussian distribution, we were able to simulate a large number of realizations which were identified are AR(2) time series with average parameters nearly identical to the parameters of the given AR(2) model. Finally, simulated images were used for assessing uncertainties of the error matrix