臺灣博碩士論文加值系統

依據廣義相對論，光線的行進路徑會天受重力影響而彎曲。若遙遠的星體與地球之間有大質量的物質存在，在類似光線經過透鏡聚焦的情形下，我們會觀測到圓弧狀的天體或是雙重甚至多重影像。這種放大現象可以幫助我們更了解高紅移且微弱的星系。
目前大部份的天文學家用目視或基於星系團的稠密度來搜尋重力透鏡事件，而我們則利用星體形狀資訊進行物體的辨識。由於這種新的思維方法是基於形狀參數，理論上是可以偵測出由暗星系團或暗物質所造成的重力透鏡現象。
我們根據圖像的『第二階中心矩』守恆作出『橢圓形誤差』的形狀參數之定義，並使用它來篩選星體。接下是要對可疑的星體做線性和弧形回歸。最後根據以上兩種回歸的誤差來判別它是否是重力透鏡作用的現象。由於我們所使用的回歸法和形狀參數，與圖像的矩函數有關係，在資料有效的運用下使得整個運算過程很快。本方法除了可以挑出重力透鏡現象也可以篩選出交互作用星系，它們對了解宇宙論以及星系及星系團的演化都是非常重要的。

The scientific operations of space telescopes and ground-based facilities worldwide have produced a flood of astronomical data waiting to be analyzed. Thus the development of fast and efficient system is in urgent demand for the purpose of data mining.
The discovery of gravitational lensing events and interacting galaxies are very important in the study of cosmology. However, both types of structures are relatively rare and often hidden in the mountain of images. For these reasons, we have developed an automatic system to identify these objects from image archives by shape analysis.
First, candidates are selected with the shape parameter defined by our method and a line and an arc are then fitted to these potential candidates. From error analysis the best shape can be identified. The algorithm developed in this work has been tested on two of the gravitational lensing events found in the RCS and proved to be successful. Furthermore, it has also been applied to a portion of the RCS data set, which consists of 210 images and dozens of interacting galaxies have been found.

1 Introduction 1 1.1 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 The Basic of Gravitational Lensing . . . . . . . . . . . . . . . . . 3 1.2.1 Thin Lens Approximation . . . . . . . . . . . . . . . . . . 3
1.2.2 Lens Equation . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.3 The Critical Surface-Mass Density and Einstein Radius . 4
1.2.4 Image Magnifcations . . . . . . . . . . . . . . . . . . . . 5
1.2.5 Singular Isothermal Sphere . . . . . . . . . . . . . . . . . 6
1.2.6 Effective Lensing Potential . . . . . . . . . . . . . . . . . 7
1.2.7 The Fermat Principle . . . . . . . . . . . . . . . . . . . . 7
1.3 Gravitational Lensing as a Cosmological Probe . . . . . . . . . . 8

2 Methodology 11
2.1 Basic Idea - Recognition by Fitting Error . . . . . . . . . . . . . 11
2.2 Moment Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.2 Shape Representation Using Moments . . . . . . . . . . . 12
2.2.3 Invariant Moments . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Image Segmentation by Localized Thresholding . . . . . . . . . . 14
2.3.1 Estimation of Sky Background . . . . . . . . . . . . . . . 14
2.3.2 Local Thresholding . . . . . . . . . . . . . . . . . . . . . . 14
2.4 Shape Parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.4.1 Best-Fit Ellipse . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.2 Dissimilarity . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.5 Selection of Candidates by Using Dissimilarity and Eccentricity . 18
2.6 Estimation of the Circular Arc Center and Its Radius . . . . . . 19
2.6.1 Landau's Algorithm . . . . . . . . . . . . . . . . . . . . . 20
2.6.2 Thomas-Chan's Algorithm . . . . . . . . . . . . . . . . . . 22

3 Data Processing 24 3.1 The Red-Sequence Survey(RCS) . . . . . . . . . . . . . . . . . . 24
3.1.1 Incidence of Strong-Lensing in the RCS Survey . . . . . . 24
3.1.2 RCS 0224.5-0002 and RCS 1419.2+5326 . . . . . . . . . . 28
3.1.2.1 RCS 0224.5-0002 . . . . . . . . . . . . . . . . . . 29
3.1.2.2 RCS 1419.2+5326 . . . . . . . . . . . . . . . . . 30
3.2 Data Processing Pipeline . . . . . . . . . . . . . . . . . . . . . . . 30 3.3 Results of Test Images . . . . . . . . . . . . . . . . . . . . . . . . 33 3.3.1 Result of RCS 0224-0002 . . . . . . . . . . . . . . . . . . 33
3.3.2 Result of RCS 1419.2+5326 . . . . . . . . . . . . . . . . . 33
3.3.3 Parameter Spaces of The Detected Arcs . . . . . . . . . . 34
4 Results and Discussion 36 4.1 Results of 0920 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
A Principal Moments of Inertia 43
B Geometrical Moments of a General Ellipse 44
C Derivation of the Landau's Algorithm 45
D Derivation for the Thomas-Chan's Algorithm 47

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