1	Announcements
2	Projection Today’s Readings Nalwa 2.1
3	Image formation Let’s design a camera Idea 1: put a piece of film in front of an object Do we get a reasonable image?
4	Pinhole camera Add a barrier to block off most of the rays This reduces blurring The opening known as the aperture How does this transform the image?
5	Camera Obscura The first camera Known to Aristotle How does the aperture size affect the image?
6	Shrinking the aperture Why not make the aperture as small as possible?
7	Shrinking the aperture
8	Adding a lens A lens focuses light onto the film There is a specific distance at which objects are “in focus” other points project to a “circle of confusion” in the image Changing the shape of the lens changes this distance
9	Lenses A lens focuses parallel rays onto a single focal point focal point at a distance f beyond the plane of the lens f is a function of the shape and index of refraction of the lens Aperture of diameter D restricts the range of rays aperture may be on either side of the lens Lenses are typically spherical (easier to produce)
10	Lenses Thin lens equation Any object point satisfying this equation is in focus What is the shape of the focus region? How can we change the focus region?
11	Depth of field Changing the aperture size affects depth of field A smaller aperture increases the range in which the object is approximately in focus
12	The eye The human eye is a camera Iris - colored annulus with radial muscles Pupil - the hole (aperture) whose size is controlled by the iris What’s the “film”?
13	Digital camera A digital camera replaces film with a sensor array Each cell in the array is a Charge Coupled Device light-sensitive diode that converts photons to electrons http://www.howstuffworks.com/digital-camera2.htm
14	Modeling projection The coordinate system We will use the pin-hole model as an approximation Put the optical center (Center Of Projection) at the origin Put the image plane (Projection Plane) in front of the COP Why? The camera looks down the negative z axis we need this if we want right-handed-coordinates
15	Modeling projection Projection equations Compute intersection with PP of ray from (x,y,z) to COP Derived using similar triangles (on board)
16	Homogeneous coordinates Is this a linear transformation?
17	Perspective Projection Projection is a matrix multiply using homogeneous coordinates:
18	Perspective Projection How does multiplying the projection matrix change the transformation?
19	Orthographic projection Special case of perspective projection Distance from the COP to the PP is infinite Also called “parallel projection” What’s the projection matrix?
20	Other types of projection Scaled orthographic Also called “weak perspective” Affine projection Also called “paraperspective”
21	Camera parameters
22	Summary Things to take away from this lecture Properties of a pinhole camera effects of aperture size Properties of lens-based cameras focal point, optical center, aperture thin lens equation depth of field circle of confusion Modeling projection homogeneous coordinates projection matrix and its elements orthographic, weak perspective, affine models Camera parameters intrinsics, extrinsics
23	Distortion Radial distortion of the image Caused by imperfect lenses Deviations are most noticeable for rays that pass through the edge of the lens
24	Distortion
25	Modeling distortion To model lens distortion Use above projection operation instead of standard projection matrix multiplication