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
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?
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.
• Camera Frame : coordinate system that uses the camera center as its origin (and the optic axis as the Z-axis) • Image or retinal plane : plane on which the image is formed, note that
Recall camera projection matrix: + Camera intrinsic parameter: metric space to pixel space
• Projection of 3D objects in camera coordinate frame to 2D image CSE 167, Winter 2018 5
Geometry of two views constrains where the corresponding pixel for some image point in the first view must occur in the second view. It must be on the line carved out by a plane connecting the world point and optical centers. Why is the epipolar constraint useful?
We will introduce different camera projection models that relate the location of an image point to the coordinates of the corresponding 3D points. The projection models include: full perspective projection model, weak perspective projection model, affine projection model, and orthographic projection model.
• Pinhole camera is a simple model to approximate imaging process, perspective projection. If we treat pinhole as a point, only one ray from any given point can enter the camera. All rays radiating from an object point converge to one point on a film plane.
• 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)
- Some results have been removed