1279740 九、發明說明： 【發明所屬之技術領域】 本發明係_-賴影齡數校正方法 心引力影響騎_體之校正方法。兀純於又到地 【先前技術】 正Ϊ彻料鍊觸影—微狀間所存在 的理_上不會鶴_係參數值 峰職拍翻校正物的圖 參紐可分為内在參數和外在參數。攝 係，_二ΐΐ要為有關攝影機座標與影像座標間的關 可==角度與位置。所以，透過 -二摄不同攝衫機座標間的轉換，因此可由 “t彡^彡=過外在參數烟另—台攝影機 筘所方式犧在參數和外在參數的關 的任意點m表示式為：㈣,vf ;而3D的空間 表1表示式為：叫，若冠以〜符號代 月〇里，為原向量增加一個元素1貝Γ· 且 焦距等包括成像中咖、攝影機 亦摊〃 ’數則表不該攝影機在世界座標與攝影機 1279740 Μ 點之間的]關：可胤上的M點與影像座標上的m ^ = A[R|T]M, With A： a r u〇 〇 β v0 0 0 1 ⑴ m的比例係數(scaie fa伽）；[r|t]為外在參數.r y ; 在參數；（y。）為攝影機 =在影像上垂直投影的座標；《和分別為影像上uf 2比例係數；γ絲示兩條影像上的軸的歪斜。如此’ 方衫⑴雜體在世界絲和攝影機 換。以下，以A—來表示(A-lf或卜卞。 Ή乍轉 假设攝影機拍攝到校正物，其在世界座標中= X β· y 1 = Atri r2 r3 t Y 0 = Atri r2 t X' Y 丄 1 1 (2) 接著可再推導成： *ym=HM, withH = A[r1 r2 t]. ⑶ 這其中，fi為μ的平面鄉觀矩陣(h_ matnx)’可表示_之間的對應關係。 由於% /g，因此方程式⑶可為： [h, h2 h3]=M[ri r2 t] (4) &為單位正切(〇rth〇_ai)㈣ ===⑷可得兩個内在參數矩_件限 1279740 W = H + JhfA-AXA-A' (5) η . r2 = 0 |hf A~rA_1h2 = 0 (6) 令 B = A rA 1 B\i B2l B3l B\2 B22 B32 •B\3 B23 B33 丄 —_r_ v0y-u0js a2 α2β α2β __Ύ_ Y1 1 Λν〇7-^〇β) ν〇 α2β α2β2 β2 α2β2 β21279740 IX. Description of the invention: [Technical field to which the invention pertains] The present invention is a method for correcting the riding body.兀 pure to the ground [previous technique] Ϊ Ϊ Ϊ Ϊ — — — — — — — — Ϊ 微 微 微 微 微 微 微 微 微 微 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ External parameters. The camera system, _2 ΐΐ should be related to the camera coordinates and image coordinates can be == angle and position. Therefore, through the two-camera conversion between the coordinates of the different camera, it can be sacrificed at any point m of the parameter and the external parameter by "t彡^彡=over-external parameter smoke----------- For: (4), vf; and 3D space table 1 expression is: call, if the crown is replaced by the ~ symbol, add an element to the original vector 1 and the focal length, including the image of the coffee, the camera is also spread 'The number indicates that the camera is between the world coordinates and the camera 1279740 ] point: the M point on the 胤 and the m ^ = A[R|T]M on the image coordinates, With A: aru〇〇β V0 0 0 1 (1) The scale factor of m (scaie fa gamma); [r|t] is the extrinsic parameter .ry ; in the parameter; (y.) is the coordinate of the camera = vertical projection on the image; The uf 2 scale factor; γ silk shows the skew of the axis on the two images. So the 'square shirt (1) hybrid is exchanged in the world silk and the camera. Below, it is represented by A- (A-lf or divination. Suppose the camera captures the calibrator, which is in the world coordinates = X β· y 1 = Atri r2 r3 t Y 0 = Atri r2 t X' Y 丄1 1 (2) It can be deduced as follows: *ym=HM, withH = A[r1 r2 t]. (3) Among them, the plane of the plane of view (h_ matnx) where fi is μ can represent the correspondence between _. Because % /g, Therefore, equation (3) can be: [h, h2 h3]=M[ri r2 t] (4) & is unit tangent (〇rth〇_ai) (four) ===(4) can obtain two intrinsic parameter moments _ parts limit 1279740 W = H + JhfA-AXA-A' (5) η . r2 = 0 |hf A~rA_1h2 = 0 (6) Let B = A rA 1 B\i B2l B3l B\2 B22 B32 •B\3 B23 B33丄—_r_ v0y-u0js a2 α2β α2β __Ύ_ Y1 1 Λν〇7-^〇β) ν〇α2β α2β2 β2 α2β2 β2
^r-u〇p riyQY-u0p) ν〇 {y〇r-uQp)2 ν〇 ⑺ ~ΊΓβ άψy α2β2 y 由於Β為對稱矩陣，因此可用6D的向量來表示： b = [5U Bu B22 Bl3 B23 B33 ] (8) 令第i行的丑為^[/^〜W，則： h[B/z.-yJb (9) v々=Ά2+ά〗Ά2 ，Wltn h；3hfj3] 由條件限制式可得 >nX)r b = 0 (10) 因為b有6個未知數且b的值為比例係數相關，所以當取 像張數n>3，可求b的maximum likelihood解，即使以下 的式子結果為最小 zSlm" -ώ(Α，υ/，Μ7】Ι i=\ >=1 (11) 1279740 求得b之後，則可求得内在參數，如下 v〇 - (b12bu -bub2^)i{bub22 ~-δ122] ^ = ^33 ' [α23 + ν〇(ΒηΒη - ΒηΒ23)]/Βη «=λ/Ιλ^7(12) Τ^-Βηα2β/λ 11^22 - Α22) :^0/β-Β13α2/χ 内ΐί數'之後’再用Church方法與Arun方法則 =求件不同攝影機彼此間座標系轉換的外在參數R與τ。 校正時’需要讓多台攝影機同 正物’ *傳驗正綠的缺點是校正物為一侧 以方Γ遺意放大，或是當校正物太大時，娜 【發明内容】 t發？主要目的在提供—種攝影機參數校正方法，藉著 j叉到地d丨力影響的物物體，*對攝影機進行校正。 t明為-麵影機參數校正綠，主妓基於受到地心 引力影響的運動物體對攝影機進行校正。此方法首先使 ，物體沿著其所受到的地㈣力影響觸_運動路徑而 在世界座標上進機動、錄影機哺定驗n速度，對 在運動路財運躺運動物體連續_ 複^ru〇p riyQY-u0p) ν〇{y〇r-uQp)2 ν〇(7) ~ΊΓβ άψy α2β2 y Since Β is a symmetric matrix, it can be represented by a 6D vector: b = [5U Bu B22 Bl3 B23 B33 ] (8) Let the ugly line of the i-th line be ^[/^~W, then: h[B/z.-yJb (9) v々=Ά2+ά〗 Ά2, Wltn h; 3hfj3] >nX)rb = 0 (10) Since b has 6 unknowns and the value of b is proportional to the proportional coefficient, when taking the number of images n>3, the maximum likelihood solution of b can be obtained, even if the following expression is The minimum zSlm" -ώ(Α,υ/,Μ7]Ι i=\ >=1 (11) 1279740 After obtaining b, the intrinsic parameters can be obtained, as follows v〇- (b12bu -bub2^)i{bub22 ~-δ122] ^ = ^33 ' [α23 + ν〇(ΒηΒη - ΒηΒ23)]/Βη «=λ/Ιλ^7(12) Τ^-Βηα2β/λ 11^22 - Α22) :^0/β- Β13α2/χ ΐ 数 数 'after' using the Church method and the Arun method = the external parameters R and τ of the coordinate system conversion between the cameras. When correcting, 'multiple cameras need to be the same thing'. * The shortcoming of passing the test green is that the calibration object is enlarged by one side, or when the correction object is too large, Na [invention] t hair? The main purpose is to provide a camera parameter correction method, which corrects the camera by j-to-ground object affected by the ground force. t Ming is - the camera parameters are corrected green, and the main frame is corrected based on the moving object affected by gravity. This method first makes the object move along the earth (four) force it receives to influence the _ motion path, and the maneuver on the world coordinates, the video machine feeds the n speed, and the moving object in the sports road continually _ complex
定拍攝_和在影像座標上㈣定xy位㈣校 及依據透視投職何絲4 ’❿胁縣物财影像座掉 的位置和拍攝時間來求出攝影機的内部參數和 I 平面投影轉換矩陣。 8 ⑧ 1279740 最佳可能解(maximum likelihood estimation)來求得較適 當的Η’。由於基於/r而求出内在參數和外在參數屬於習= 方法，因此，底下將簡略說明如何進一步求出内在參數和1 外在參數。 又fee 〜則方程式⑸和⑹可將η推成以以央 表示 ^ (^yA-A-々)=h【™2 (16) φ ΚΤ^~ΤΑ~\ =0 令弟i行的/τ為[1: =¾ /4 ；2;3]r，方程式（9)則成： (17) ，wi th v) 一 卜為1 Ά + Ά 厶:2厶;2 hi3hjX + hnhj3 hnhj2 + hfi2hj3 ] 再由方程式（16)可得： ^=0 (18) b有6個未知數，不過b的值為比例係數相關，因此必須 修使^動物體1 〇被重新拋出至少5次並獲得相對數量的複數 個校正影像，而每拋一次球，我們可得到一π，則可得到 一個對應的〜。因此當拋球次數us，可得到足夠的式子（18) 來解b，並藉此採用習知的方程式進一步獲得内部參數。 =過，有時會有測量誤差產生，所以若拋球取像愈多次所 求得的值會愈精確。可用最佳可能解的方法，透過使方程 式(^)為最小來求得較精確的結果。 f求得内在參數A後’則每次拋球的水平速度V，可由方程 5(16)求得。求得v之後，則χ，γ均為已知，因此可以推 估出球運動時的拋物線式子，接著可再由得到的拋物線式 12 ⑧The camera's internal parameters and the I-plane projection conversion matrix are determined by taking the shot _ and the image coordinates (4) the xy position (4) and the position and shooting time of the Hesi 4' 8 8 1279740 The maximum likelihood estimation is used to find the appropriate Η'. Since the intrinsic parameters and extrinsic parameters are obtained based on /r, they are abbreviated as follows. Therefore, how to further find the intrinsic parameters and the 1 extrinsic parameters will be briefly explained. Also fee ~ then equations (5) and (6) can be used to push η to represent ^ (^yA-A-々)=h[TM2 (16) φ ΚΤ^~ΤΑ~\ =0 For [1: =3⁄4 /4 ;2;3]r, equation (9) is: (17) , wi th v) 1 为 + Ά 厶: 2厶; 2 hi3hjX + hnhj3 hnhj2 + hfi2hj3 ] From equation (16), we can get: ^=0 (18) b has 6 unknowns, but the value of b is proportional to the coefficient, so we must repair the animal 1 〇 to be re-thrown at least 5 times and get the relative amount. A plurality of corrected images, and each time we throw a ball, we can get a π, then we can get a corresponding ~. Therefore, when the number of throws is us, a sufficient formula (18) can be obtained to solve b, and thereby the internal parameters are further obtained by using a conventional equation. = too, sometimes there will be measurement errors, so the more the value obtained by the ball is, the more accurate the value will be. The best possible solution can be used to find a more accurate result by making the equation (^) minimum. f After obtaining the intrinsic parameter A, then the horizontal velocity V of each throwing ball can be obtained by Equation 5(16). After v is obtained, then γ, γ is known, so the parabolic equation for the ball motion can be estimated, and then the parabola can be obtained.