|Abstract: ||摘要:引起自然現象變化的因素通常都有很多個。不過，一般來說，都可以把這些因素歸納成最重要的、次要的、以及不重要的等三大類。譬如說，不論是什麼原因造成海面的波浪，使得它顯得非常紊亂複雜。一般來說，由於風是造成海面上波動最主要的因素，因此，一般藉著(傳統的)零上(下)切、頻譜分析、以及(較近代的)方向頻譜分等等方法，都可以找到一些–例如波高、主頻率(主波長)、主方向等–『特徵參數』來描繪某個時、空間點的海面。然而，這些傳統的量測方法只能量測某一個『點』的海況，不能顧及『面』。如果海面大致上合乎『均質性』或甚至『遍歷性』的假設，用點的量測結果來代表面，倒也還算合理。不過，如果想要同時獲得大量的面的訊息，就必須用遙測的方式了。 遙測所得到的初步結果是電壓的變化。一般為了方便觀看起見，大都把它們以影像的方式呈現。學者在處理這些影像時，通常都用頻譜分析的方式。如果是一張張衛星影像的話，就用波數譜；如果是連續的(船用、岸置)雷達影像的話，就藉著(三維)的波數–頻率譜，估算海面上波浪的主頻率、主方向等等。不過，筆者以為所謂的『主成份分析』應該也可以用來估算海象的特徵參數 『主成份分析』是多参數統計裡常用一種的方法。通常做這種分析的最主要目的就是希望能用(少數)幾個参數所構成的『正交函數』(orthogonal function)來代表(描述)紀錄裡的時、空的變化。擧個例來說，有許多判斷手紋的電腦程式就是利用這個方法。 簡單地說，主成份法所估算出來各個成份的大小與所謂的『變異』成正比。如果把海面上的變化看成是自由波的組合的話，那麼，利用這個方法所得到前面幾個最大的『成份』就似乎代表著波場裡幾個最主要、最常出現的波。一般船用雷達的影像序列大約是32或64張。根據採樣理論，最多只能得到16或32個頻率分量。筆者利用模擬的影像分析後發現，用14個『主成份』就可以涵蓋大約70 %波場的變異了(見計劃內容)。這似乎表示本計劃的構想是可行的。 本計劃的主要目的是要延續上一年的計劃，利用台北港的雷達影像，繼續探討利用『主成份分析』這個方法從影像中估算海象的可行性。|
abstract:Most of the natural phenomena are results of numerous factors interacting with each other. Generally speaking, these influencing factors can be divided into three categories: the major or most important ones, the less important ones, and those that can be treated as unimportant. On a confused sea surface, waves that were caused by numerous factors running from various origins to meet at a certain place at a certain time. Nonetheless, it is generally believed that wind is the major acting force for the existence of the surface waves. As a result, researchers have used various methods to extract characteristic parameters of an aroused sea. These include: the (now more or less traditional) zero-crossing, spectral analyses, and methods for the analyses of a directional wave field. All these methods are based on point measurements, i.e., instruments were deployed at a certain point for a certain period. It left without saying, that the basic underlying hypothesis for these kinds of measurements is that the flow field is homogeneous, and it satisfies the ergodic assumption. On the other hand, if the main objective is to obtain a large amount of information simultaneously, one has to rely on remote sensing techniques. To facilitate visualizations, the results of remote sensing are often displayed as images. The most common way to handle these images is through multi-dimensional spectral analysis. Wavenumber- or wavenumber-frequency spectra are obtained from Fourier transform techniques. Through analyzing these spectra, the resulting wave heights, dominant frequency/wavenumber, as well as the main traveling direction are obtained. However, the present author believes that the so-called principal component analysis can also be used to extract valuable information from radar images. Principal component analysis, often abbreviated as PCA, is often used in multivariate analysis. The main purpose is to extract a limited number of parameters that form the so-called orthogonal functions. With these few parameters, it is hoped that complicated phenomena can be (roughly) described. For example, algorithms based on PCA have been written to analyze fingerprints automatically. The magnitudes of the “components” are proportional to the variances. Now, wave fields are often treated as composed of numerous free waves propagating with their own speeds and directions, and the spectral density is proportional to variances of the wave fields. It seems natural to conjecture that, the first few large (principal) components seem to represent the most frequent waves that have the most energies of a wave field. In this way, the characteristics of a wave field can be obtained from principal component analysis. Quite often, image sequences gathered from marine radars are composed of 32 or 64 images. According to the sampling theorem, a maxima of 16 (32) frequency components can be obtained from spectral analyses. The present author has conducted experiments using simulated image sequences. It was found that with only 14 principal components, 70% of the variances in a wave field can be covered. The results seem promising for the objectives of the present proposed project. The main objective of this project is to use radar images from Taipei Harbour to study the feasibility of extracting the characteristics of wave fields using principal component analysis.