Camera Coords Film Coords Pixel Coords We now know how to transform 3D world coordinate points into camera coords, and then do perspective project to get 2D points in the film plane. Next time: pixel coordinates

Camera 3D world z Origin at world coordinate Camera Projection (Pure Rotation) X C 1 R W Coordinate transformation from world to camera: Camera World 3 C C W 3 == ªº «» «» «» ¬¼ X X R X r r r r 1: world x axis seen from the camera coord. r1r2 r 3 r 2: world y axis seen from the camera coord. K Camera projection of world point: r 3

Makes sense for projection of 3D world onto 2D. Do we get a reasonable image? How does this transform the image? How does the aperture size affect the image? possible? What’s the “film”? Put the image plane (Projection Plane) in front of the COP – Why? Is this a linear transformation?

What is the projection of the camera center in world coordinates? • The camera center is the null space of the projection matrix! Radial distortion – important in practice! − ... ... ... i.e., there exists a set of plane parameters = ( , , , ) such that = 0 for all ? ? ? (null . ? ? World to camera coord. Radial distortion – important in practice!

2023年2月27日 · Camera projection is used in a wide range of applications, including object tracking, augmented reality, and robotics. In this article, we’ll discuss the basics of camera projection, along...

Camera Rigid Motion Projection P=K[R|t] – Camera motion: alignment of 3D coordinate systems – Full extrinsic parameters beyond scope of this course, see “Multiple View Geometry” by Hartley and Zisserman

• Applications of camera model and projective geometry – Recovering the camera intrinsic and extrinsic parameters from an image – Recovering size in the world – Projecting from one plane to another (if time allows)

Goal: Introduce the basic concepts and mathematics for image projection. Given a 3D scene, how does it project to the image plane? (“Forward” model.) Given an image, what 3D scenes could project to it? (“Inverse” model.) Vision is all about guessing the scene and the story behind it. The latter is a (largely ignored) holy grail of computer vision.

Therefore, we will introduce a projection matrix camera class, ProjectiveCamera, and then define two camera models based on it. The first implements an orthographic projection, and the other implements a perspective projection—two classic and widely used projections.

camProjection = cameraProjection(intrinsics,tform) returns a 3-by-4 camera projection matrix camProjection. You can use camProjection to project a 3-D world point in homogeneous coordinates into an image according to the transformation tform.