Duanxx image processing learning: perspective transformation (III)

Our common coordinate system is the Cartesian coordinate system, that is, the world coordinate system mentioned in duanxx image processing learning: perspective transformation (I.

From the perspective of observation, it is the camera coordinate system mentioned in duanxx image processing learning: perspective transformation (I.

In the observer coordinate system (camera coordinate system), we generally use the observer (or viewpoint) as the origin of the observer coordinate system, and the orientation of the observation point to the object is the Z axis, the orientation toward the left and perpendicular to the Z axis is the X axis, and the vertical direction toward the X axis and Y axis is the Y axis to form the observer coordinate system.

All the operations in this article are based on the Conversion principle in duanxx image processing learning: 3D image transformation and homogeneous coordinate representation. Therefore, this article only introduces the relevant concepts, refer to the above for the main principles.

Conversion

In general, point P (x, y, z) in the world coordinate system is transformed into point Q (x *, y *, z *) in the observed coordinate system *) the process is called "visual transformation ".

The visual transformation is the first operation in camera projection. It mainly converts the world coordinate system, that is, the image information of our real world, to the camera coordinate system, then the projection can be completed in the camera coordinate system.

Forward Translation

If the origin of the camera coordinate system is not the same as that of the world coordinate system, the first step is to make a translation and put the origin of the two coordinate systems together.

For example, in the following coordinate system model, the origin of the camera coordinate system is (x0, y0, z0)

We can use duanxx's image processing and learning: image transformation 3D transformation and its homogeneous coordinate representation to move the camera coordinate system first to the world coordinate system.

Forward rotation

Here is an example of rotating an angle around the Y axis.

From duanxx's image processing and learning: 3D image transformation and homogeneous coordinate representation, we can easily know that the transformation matrix here is the following matrix, and others can be like this.

Duanxx image processing learning: perspective transformation (III)