为什么3D点似乎在相机后面？

Question

我写了一个简单的脚本,将3D点投影到基于相机内在函数和extrintics的图像上.但是当我在原点指向z轴并且沿z轴进一步向下指向3D时,它看起来是在摄像机后面而不是在它前面.这是我的剧本,我已经多次检查过了.

import numpy as np

def project(point, P):
    Hp = P.dot(point)

    if Hp[-1] < 0:
        print 'Point is behind camera'

    Hp = Hp / Hp[-1]
    print Hp[0][0], 'x', Hp[1][0]
    return Hp[0][0], Hp[1][0]

if __name__ == '__main__':

    # Rc and C are the camera orientation and location in world coordinates
    # Camera posed at origin pointed down the negative z-axis
    Rc = np.eye(3)
    C  = np.array([0, 0, 0])

    # Camera extrinsics
    R = Rc.T
    t = -R.dot(C).reshape(3, 1)

    # The camera projection matrix is then:
    # P = K [ R | t] which projects 3D world points 
    # to 2D homogenous image coordinates.

    # Example intrinsics dont really matter ...

    K = np.array([
        [2000, 0,  2000],
        [0,  2000, 1500],
        [0,  0,  1],
    ])


    # Sample point in front of camera
    # i.e. further down the negative x-axis
    # should project into center of image
    point = np.array([[0, 0, -10, 1]]).T

    # Project point into the camera
    P = K.dot(np.hstack((R, t)))

    # But when projecting it appears to be behind the camera?
    project(point,P)

我唯一能想到的是识别旋转矩阵不对应于指向负z轴的相机,而向上矢量指向正y轴方向.但是我看不出这是不是这种情况,例如我从像gluLookAt这样的函数构造了Rc,并且在原点指向负z轴的相机,我会得到单位矩阵.

Answer 1

我认为困惑仅在于这一行：

if Hp[-1] < 0:
    print 'Point is behind camera'

因为这些公式假设正 Z 轴进入屏幕，所以实际上具有正 Z 值的点将位于相机后面：

if Hp[-1] > 0:
    print 'Point is behind camera'

我似乎记得这个选择是任意的，以使 3D 表示与我们的 2D 先入为主的效果很好地配合：如果你假设你的相机朝 -Z 方向看，那么当正 Y 指向上方时，负 X 将位于左侧。在这种情况下，只有负 Z 值的物体才会出现在相机前面。