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系統識別號 U0026-1601201920122000
論文名稱(中文) 物品旋轉下的影像變形
論文名稱(英文) The image spacial transformation under object rotation
校院名稱 成功大學
系所名稱(中) 數學系應用數學碩博士班
系所名稱(英) Department of Mathematics
學年度 107
學期 1
出版年 108
研究生(中文) 翁立言
研究生(英文) Li-Yien Weng
學號 L16051077
學位類別 碩士
語文別 中文
論文頁數 51頁
口試委員 指導教授-沈士育
口試委員-王進猷
口試委員-廖炳松
中文關鍵字 影像變形  物品旋轉 
英文關鍵字 spacial transformation  object rotation 
學科別分類
中文摘要 在現代生活中經常靠影像得到許多資訊,例如車牌辨識就是從影像中得知車牌號碼,而本論文是透過兩張照片去探討被拍攝物品在空間中旋轉了幾度,但是翻轉的問題不在此討論中。
因為現在的相機成像原理跟針孔成像幾乎差不多,在這裡都是用針孔成像來討論,想要從不同角度所拍攝的物品中知道它旋轉了幾度,因此需要從兩張照片找到共軛對,而找到共軛對之前,得先找到特徵點,特徵點為容易辨認且明顯的點,而在論文中是以接近九十度的角落稱為特徵點,接著把共軛對進行最小二乘法之後可以從其中找到此物品旋轉了幾度。
為了知道數學模型是否正確,先是假設五個在空間的共軛對,並給予它們座標,用程式去模擬並且算出他們在空間中旋轉的角度,模擬實驗結果準確率很高,而且發現距離以及共軛點數多寡會影響誤差值。
在實際實驗中總共實驗了四個共軛對、五個共軛對和九個共軛對,因為是手持相機的關係誤差會比模擬實驗來的大,但是當共軛對數增加的時候,準確率卻有明顯的增加。
英文摘要 Because the current imaging principle of the camera is almost the same as that of the pinhole imaging, it is discussed here with pinhole imaging. It is known that it is rotated a few degrees from the items taken from different angles. Therefore, it is necessary to find the conjugate pair from the two photos. Before finding the conjugate pair, the feature points must be found first. The feature points are easily identifiable and obvious points. In the paper, the corners are close to ninety degrees. Then, after the conjugate pair is subjected to the least squares method, the item can be found rotated by a few degrees.
In order to know whether the mathematical model is correct, first assume five conjugate pairs in space, and give them coordinates, use the program to simulate and calculate the angle of their rotation in space, the simulation results are very accurate, and the distance and total points will affect the amount of conjugated error value.
In the actual experiment, a total of four conjugate pairs, five conjugate pairs and nine conjugate pairs were tested, because the relationship error of the handheld camera is larger than that of the simulation experiment, but when the conjugate logarithm increases, There is a significant increase in the rate of accuracy.
論文目次 中文摘要 --------------------------------------------I
英文延伸摘要 ----------------------------------------II
誌謝 ------------------------------------------------V
目錄 -----------------------------------------------VI
圖目錄 ------------------------------------------VIII
第一章- 緒論 ----------------------------------------1
1.1 前言 ---------------------------------------1
1.2 空間定位 -----------------------------------4
1.3 章節簡介 -----------------------------------6
第二章- 數學模型 ------------------------------------7
2.1相機模型 -----------------------------------------7
2.2 影像模型 ----------------------------------------9
2.3 線性化 -----------------------------------------13
2.4由A矩陣求得角度 ----------------------------------14
2.5最小二乘法在影像上之應用 --------------------------17
2.6 數值例ㄧ ----------------------------------------18
2.7 數值例二 ----------------------------------------22
2.8 數值例三 ----------------------------------------24
第三章-特徵點之取得方式和實驗 -------------------------27
3.1求共軛對問題 -------------------------------------27
3.2 拉普拉斯運算在影像上之應用 ------------------------28
3.3實驗ㄧ -------------------------------------------36
3.4實驗二 -------------------------------------------39
3.5多共軛對數之實驗ㄧ --------------------------------42
3.6多共軛對數之實驗二 --------------------------------45
第四章-實驗的討論和結論 ------------------------------48
4.1拍攝距離所造成的誤差變化 ---------------------------48
4.2實驗誤差的討論 ------------------------------------50
文獻參考 ---------------------------------------------51
參考文獻 [1]Rafael C.Gonzalez & Richard E.Woods”Digital Image Processing” Addison-Wesley Publishing Company 1992
[2] Alasdair McAndrew “An Introduction to Digital Image Processing with Matlab” School of Computer Science and Mathematics Victoria University of Technology 2004
[3] Azriel Rosenfeld and Avinash C. Kak. “Digital Picture Processing” Academic Press, second edition 1982
[4] Azriel Rosenfeld and Avinash C. Kak. Digital Picture Processing. Academic Press, second edition, 1982
[5] Jain, R., Kasturi, R. and Schunck, B.G. “Machine Vision” McGraw-Hill International Edition 1995
[6] Zhang, Z. “A Flexible New Technique for Camera Calibration.” IEEE Transactions on Pattern Analysis and Machine Intelligenc 2000
[7] George B. Thomas, Maurice D. Weir, Joel R. Hass” Thomas' Calculus 13/e in SI Unit” Pearson Education 2016
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