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Finally, I used fsolve() from scipy using equations I got from initUndistortRectify() source code. I only get first 2 angles so one may needs to rotate the image.

``` def _find_angles(self, u, v): """ Finds 'alpha' and 'beta' Rodrigues' angles so that the output undistorted image is centered on a specific input pixel from the fisheye image.

    :param u: x-coordinate of the pixel to center.
    :param v: y-coordinate of the pixel to center.
    :return: 'alpha' and 'beta' Euler angles
    """
    tic = timeit.default_timer()

    def _equations(ab, *args):
        alpha, beta = ab
        u, v, = args
        w = self.dims[0]
        h = self.dims[1]

        f = [self.K[0, 0], self.K[1, 1]]
        c = [self.K[0, 2], self.K[1, 2]]

        P = self.K.copy()
        P[0, 0] *= self.zoom
        P[1, 1] *= self.zoom

        R = cv2.Rodrigues(np.array([alpha, beta, 0.]))[0]

        iR = np.linalg.inv(np.dot(P, R))

        _x = h/2 * iR[0, 0] + w/2 * iR[0, 1] + iR[0, 2]
        _y = h/2 * iR[1, 0] + w/2 * iR[1, 1] + iR[1, 2]
        _w = h/2 * iR[2, 0] + w/2 * iR[2, 1] + iR[2, 2]

        x = _x / _w
        y = _y / _w
        r = np.sqrt(x**2 + y**2)

        theta = np.arctan(r)
        theta_d = theta * (1 + self.D[0]*theta**2 + self.D[1]*theta**4 + self.D[2]*theta**6 + self.D[3]*theta**8)
        scale = (r == 0) * 1.0 + (1 - (r == 0)) * theta_d / r
        return f[0]*x*scale + c[0] - u, f[1]*y*scale + c[1] - v

    alpha, beta = fsolve(_equations, (0., 0.), args=(u, v))
    print(alpha, beta)
    print("Computation time :", timeit.default_timer() - tic)
    return alpha, beta

```

Finally, I used fsolve() from scipy using equations I got from initUndistortRectify() source code. I only get first 2 angles so one may needs to rotate the image.

``` ```

def _find_angles(self, u, v):
     """
     Finds 'alpha' and 'beta' Rodrigues' angles so that the output undistorted image is centered on a specific input
     pixel from the fisheye image.
 
image.

    :param u: x-coordinate of the pixel to center.
    :param v: y-coordinate of the pixel to center.
    :return: 'alpha' and 'beta' Euler angles
    """
    tic = timeit.default_timer()

    def _equations(ab, *args):
        alpha, beta = ab
        u, v, = args
        w = self.dims[0]
        h = self.dims[1]

        f = [self.K[0, 0], self.K[1, 1]]
        c = [self.K[0, 2], self.K[1, 2]]

        P = self.K.copy()
        P[0, 0] *= self.zoom
        P[1, 1] *= self.zoom

        R = cv2.Rodrigues(np.array([alpha, beta, 0.]))[0]

        iR = np.linalg.inv(np.dot(P, R))

        _x = h/2 * iR[0, 0] + w/2 * iR[0, 1] + iR[0, 2]
        _y = h/2 * iR[1, 0] + w/2 * iR[1, 1] + iR[1, 2]
        _w = h/2 * iR[2, 0] + w/2 * iR[2, 1] + iR[2, 2]

        x = _x / _w
        y = _y / _w
        r = np.sqrt(x**2 + y**2)

        theta = np.arctan(r)
        theta_d = theta * (1 + self.D[0]*theta**2 + self.D[1]*theta**4 + self.D[2]*theta**6 + self.D[3]*theta**8)
        scale = (r == 0) * 1.0 + (1 - (r == 0)) * theta_d / r
        return f[0]*x*scale + c[0] - u, f[1]*y*scale + c[1] - v

    alpha, beta = fsolve(_equations, (0., 0.), args=(u, v))
    print(alpha, beta)
    print("Computation time :", timeit.default_timer() - tic)
    return alpha, beta
 
```