1	Announcements Mailing list (you should have received messages) Project 1 additional test sequences online
2	Projection Readings Nalwa 2.1
3	Müller-Lyer Illusion
4	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?
5	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?
6	Camera Obscura The first camera Known to Aristotle How does the aperture size affect the image?
7	Shrinking the aperture Why not make the aperture as small as possible?
8	Shrinking the aperture
9	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
10	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)
11	Thin 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? Thin lens applet: http://www.phy.ntnu.edu.tw/java/Lens/lens_e.html (by Fu-Kwun Hwang )
12	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
13	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”?
14	Digital camera A digital camera replaces film with a sensor array Each cell in the array is light-sensitive diode that converts photons to electrons Two common types Charge Coupled Device (CCD) CMOS http://electronics.howstuffworks.com/digital-camera.htm
15	Digital camera issues Some things that affect digital cameras blooming color issues noise interlace scanning
16	Blooming
17	Handling Color: 3-chip cameras
18	Mosaicing and Demosaicing
19	Noise Some factors affecting how noisy the image is CCD vs. CMOS size of sensor elements 5 to 10 μm; scientific up to 20 μm often hear 1/3’’, 1/2’’ inch chips (bigger is better) Fill factor (25% to 100%) What else?
20	Interlace vs. progressive scan
21	Progressive scan
22	Interlace
23	Progressive scan vs. intelaced sensors Most camcorders are interlaced several exceptions (check the specs before you buy!) some can be switched between progressive and interlaced Used to be true also for video cameras (interlaced) But now it’s becoming the opposite—many/most digital video cameras are progressive scan
24	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
25	Modeling projection Projection equations Compute intersection with PP of ray from (x,y,z) to COP Derived using similar triangles (on board)
26	Homogeneous coordinates Is this a linear transformation?
27	Perspective Projection Projection is a matrix multiply using homogeneous coordinates:
28	Perspective Projection How does scaling the projection matrix change the transformation?
29	Orthographic projection Special case of perspective projection Distance from the COP to the PP is infinite Also called “parallel projection”: (x, y, z) → (x, y) What’s the projection matrix?
30	Other types of projection Scaled orthographic Also called “weak perspective” Affine projection Also called “paraperspective”
31	Camera parameters
32	Distortion Radial distortion of the image Caused by imperfect lenses Deviations are most noticeable for rays that pass through the edge of the lens
33	Correcting radial distortion
34	Distortion
35	Modeling distortion To model lens distortion Use above projection operation instead of standard projection matrix multiplication