pinhole camera model

Catalog

1、 How to record the world with a camera ？

2、 pinhole video camera

3、 Pinhole camera model

4、 Pinhole camera problem

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1、 How to record the world with a camera ？

         idea ： Place the film directly in front of the object .

         As can be seen from the figure above , The film is placed in front of the object , The image cannot be formed when there is no obstruction between the object and the film . A point on the film receives information from multiple points on the object , From such an image , You can't see anything , It looks like a blur , You can't tell what this image actually records .

2、 pinhole video camera

         idea ： Add barriers , Reduce blurring .

         One of the simplest imaging methods , There is an intersection between this object and this imaging plane , Add a partition between them , A small hole in the middle of the diaphragm . Through this small hole, you can see that there is a one-to-one relationship between the light of the object and its image point . This image is a very simple basic principle of pinhole imaging .

3、 Pinhole camera model

         There are several concepts , It's in this picture , There is a partition in the middle . The whole box can be considered as a camera , On the far right is a three-dimensional object （ A candle ）. There is a concept called The phase plane , It is the projection of three objects onto the image surface . You can see that the three-dimensional object becomes an opposite image in the image plane . The center of this camera , Also known as aperture perhaps pinhole , perhaps Camera Center .

         This hole in the camera , aperture o This distance to the imaging plane is called The focal length . The object is in the opposite direction to the imaging result , There will be a minus sign when we calculate this . We don't usually study this plane like thing , We study a project called Virtual phase plane . Virtual image plane and real image plane , If the focal length is not F Words , There is only an overall magnification , The concept of shrinking , So we often study the virtual phase plane , Our coordinates are all in the same direction. It is convenient to study them . So when we talk about this mapping relationship later , Although it is drawn on this image , But in fact, we study the virtual image plane , There is no sign relationship , At least in this direction . This is a pinhole camera model .

         The following is a data-based description , The mapping process from 3D points to 2D points . Camera coordinate system ： In the center of the camera （ aperture ） Origin , Build a 3D coordinate system as shown in the following figure . The imaging process is to take the camera coordinate system P The point is mapped to... In the phase plane coordinate system P` spot .

        P Point to P` The mapping relationship of points is shown in the following figure , about o-j-k The projection relation on the plane can be obtained ：

         Empathy , You can get Three dimensional points in the camera coordinate system P To Two dimensional phase plane coordinate system Coordinate mapping relationship under ：

4、 Pinhole camera problem

         When the aperture is too large , The same point on the film may receive information about the positions of different objects in the real world , Create an illusion ; As the aperture decreases , The imaging effect becomes clearer and clearer 、 It's getting darker .

         To see clearly , And the image should be bright enough . How to deal with the decrease of light reaching the film ？ The answer is ： Add lens .