魚眼相機模型-相機畸變

 

魚眼鏡頭

魚眼相機鏡頭是由十幾個不同的透鏡組合而成，在成像的過程中，入射光線經過不同程度的折射，投影到尺寸有限的成像平面上，使得魚眼鏡頭擁有更大的視野范圍。下圖為魚眼相機的組成結構：

與針孔相機原理不同，魚眼鏡頭采用非相似成像，在成像過程中引入畸變，通過對直徑空間的壓縮，突破成像視角的局限，從而達到廣角成像。

所以魚眼鏡頭是一種極端 的廣角鏡頭，通常焦距小於等於16mm並且視角接近或等於180°（在工程上視角超過140°的鏡頭即統稱為魚眼鏡頭）。

相機畸變

魚眼鏡頭無論如何它的邊緣線條都是要彎曲的，即使90度的魚眼也是這樣，這種畸變我們在很多廣角鏡頭上都可以看到，而這就是明顯的桶形畸變。同樣的120度的魚眼看起來彎曲的更加厲害一些了，而且被容納進范圍的景物更多；150度同樣如此，而180度的魚眼則可以把鏡頭周圍180度范圍內的所有物體都拍攝進去。眾所周知，焦距越短，視角越大，因光學原理產生的變形也就越強烈。為了達到180度的超大視角，魚眼鏡頭不得不允許這種變形(桶形畸變)的合理存在。

針對原始圖像進行畸變校正后，帶有冗余邊界，需要做進一步截取。如下圖：

 

畸變模型和參數

 

魚眼相機投影模型有： 等距投影  正交投影  等立體角投影    體視投影 ；成像模型：先將三維點投影到單位球面，再將單位球面上的點投影到歸一化平面上。

（但這些，對於 不搞鏡頭研發，只搞 圖像處理的我們都不必關心，我們關心下面的opencv 模型）

 

opencv https://docs.opencv.org/3.4/db/d58/group__calib3d__fisheye.html

 

由 世界坐標點和圖像坐標點，標定得到相機 內參、外參、畸變參數

 

 

 

double cv::fisheye::calibrate    (
    InputArrayOfArrays     objectPoints,
        InputArrayOfArrays     imagePoints,
        const Size &     image_size, 
        InputOutputArray     K,
        InputOutputArray     D,
        OutputArrayOfArrays     rvecs,
        OutputArrayOfArrays     tvecs,
        int     flags = 0,
       TermCriteria     criteria = TermCriteria(TermCriteria::COUNT+TermCriteria::EPS, 100, DBL_EPSILON) 
)    

 

objectPoints    vector of vectors of calibration pattern points 
                in the calibration pattern coordinate space.
imagePoints        vector of vectors of the projections of calibration pattern points. 
                imagePoints.size() and objectPoints.size() and imagePoints[i].size() 
                must be equal to objectPoints[i].size() for each i.
image_size        Size of the image used only to initialize the camera intrinsic matrix.
K                Output 3x3 floating-point camera intrinsic matrix 
                If fisheye::CALIB_USE_INTRINSIC_GUESS is specified, 
                some or all of fx, fy, cx, cy must be initialized before calling the function.
D                Output vector of distortion coefficients (k1,k2,k3,k4).
rvecs            Output vector of rotation vectors (see Rodrigues ) estimated for each pattern view. 
                That is, each k-th rotation vector together with the corresponding k-th translation vector 
                (see the next output parameter description) brings the calibration pattern from the model 
                coordinate space (in which object points are specified) to the world coordinate space, 
                that is, a real position of the calibration pattern in the k-th pattern view (k=0.. M -1).
tvecs            Output vector of translation vectors estimated for each pattern view.
flags            Different flags that may be zero or a combination of the following values:
     fisheye::CALIB_USE_INTRINSIC_GUESS cameraMatrix contains valid initial values of fx, fy, cx, cy 
                          that are optimized further. Otherwise, (cx, cy) is initially set to the image center 
                          ( imageSize is used), and focal distances are computed in a least-squares fashion.
     fisheye::CALIB_RECOMPUTE_EXTRINSIC Extrinsic will be recomputed after each iteration of intrinsic optimization.
     fisheye::CALIB_CHECK_COND The functions will check validity of condition number.
     fisheye::CALIB_FIX_SKEW Skew coefficient (alpha) is set to zero and stay zero.
     fisheye::CALIB_FIX_K1,..., fisheye::CALIB_FIX_K4 Selected distortion coefficients are set to zeros and stay zero.
     fisheye::CALIB_FIX_PRINCIPAL_POINT The principal point is not changed during the global optimization. 
                      It stays at the center or at a different location specified when 
                      fisheye::CALIB_USE_INTRINSIC_GUESS is set too.

criteria    Termination criteria for the iterative optimization algorithm.