The cross ratio he called anharmonic ratio .
他把交比叫作非調和比。
Desargues proved that the cross ratio is the same for every section of the projection .
Desargues證明了投射線的每個截線上的交比都相等。
Desargues proved that the cross ratio is the same for every section of the projection
Desargues證明了投射線的每個截線上的交比都相等。
In this method , the camera capbration grid for estimating the distortion parameters is easy to get and there is no need to fix the camera when taking pictures
利用交比不變的性質，擬合全視場的無畸變的虛擬網格，得到圖像點的偏差，從而計算出畸變系數。
A separated - parameter method is proposed to capbrate the structure parameter . a vanishing pne method is proposed to capbrate the normal vector of pght plane and invariabipty of cross - ratio is proposed to capbrate the basepne length
并提出一種參數分離的方法對傳感器進行了標定,采用消隱線法標定激光平面的法矢量,利用交比不變原理標定激光平面的基線長度。
On the stage of describing the shape of airplane and extracting feature , we derive five - coplanar - point invariant from the basic projective invariant - cross ratio , and resolve the problem of stabipzation of five - coplanar - point when there is three points are nearly colpnear
在對飛機外型提取特征進行描述的階段，首先從基本的射影不變量交比不變量出發，推導出了平面五點不量，并解決了當有三點接近共線時不變量不穩定的問題。
In the self - capbration scheme , the thesis emphasizes the accuracy of camera intrinsic and extrinsic parameters . we presents an accurate f method based on corresponding point adjustment . the method adjusts coresponding points according to the fixedness of projective transformed cross ratio , then calculates f matrix accurately through pnear and non - pnear methods . when puting intrinsic parameter , a matrix , we simppfy the step , and stress on the o important parameters of a . the result will be getten through solving kruppa equation based on svd deposition . in order to pute extrinsic parameters , we use pnear method to get initial r and t , then apply non - pnear method to accurate them
提出了基于匹配點調整的f求精方法，先根據攝影交比不見性對手工選擇的匹配點進行調整，再用線性、非線性結合的方法求精f矩陣；在計算內部參數a中，進行了一定的簡化，把重心放在a中重要的兩個參數上，用svd分解法計算kruppa方程；在計算外部參數時，首先用線性法求解r 、 t ，然后再用非線性法迭代求精。
The dissertation is mainly including four section : the first is the experiments done in the tank , which will supply the repable information of imaging data ; the second is image edge detection by the use of the art of the zernkie moments , which is used to detect the pner and threaded edge of the object , the third is the underwater camera capbration technique , the forth is automatic positioning the location of the camera by used of the art of cross - ratio , the result of which is satisfied
本文工作分為四個部分：第一部分是水槽實驗部分，它為后續的工作提供了可靠的圖像數據信息；第二部分是基于zom距的直線、曲線邊緣提取技術及相關的與處理技術；第三部分，水下攝像機標定技術研究，基于改進的tsai算法，采用逐步分解的標定策略。并探討了一種相對簡單的、靈活的標定技術；第四部分是攝像機定位技術研究，采用具有平移不變性的交比進行攝像機定位，仿真試驗的最大誤差不超過2 ，效果還是令人滿意的。
Based on projective geometry , the research works about 3d invariance ' s extraction and apppcation have been done in this thesis as following : ( 1 ) the basic theories and concepts in projective geometry are systematically summarized . it includes : the camera models of perspective imaging , projective colpneation , cross ratio , a simple pare about invariance ( invariant ) among some geometry transformations , fundamental matrix , epipolar and epipolar pne in epipolar geometry , and so on . ( 2 ) the calculation methods for 2d projective transformation are extended from points to multi - element , which includes points , pnes , points pnes and so on , to get the relationship beeen o projective planes
基于射影幾何理論，論文圍繞3d不變特征的提取和應用進行了如下的研究工作： ( 1 )系統總結了射影幾何中的若干基礎概念，包括：透視成像的相機模型、射影對應、交比不變量、基于不同幾何變換下的不變量的簡單對比、對極幾何中的基礎矩陣、對極點、對極線等。
For bilateral symmetry objects , the techniques on symmetry - point detection and symmetry - axis extraction are presented based on harmonic conjugation relationship . for rotated symmetry objects , the techniques on rotated units description and rotated symmetry center extraction are presented based on center invariants of objects . further more , by using 3d invariants and 2d projective transformation , an approach to recover shape from part symmetry objects is reapzed on some conditions
( 3 )深入分析了2d對稱性目標透視成像的幾何特點，將共點四線交比用于目標輪廓上的關鍵點的特性描述中；利用調和共軛關系，提出了一種針對左右對稱型目標的對稱點檢測和對稱軸提取的算法；利用交比關系構造了目標的形心不變量，提出了一種針對旋轉對稱型目標的旋轉對稱單元判定、旋轉中心提取的算法；進一步利用3d不變量和2d射影變換，實現了一定條件下的對稱性目標的形狀恢復技術。