1	Projection Readings Nalwa 2.1
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 a Charge Coupled Device light-sensitive diode that converts photons to electrons other variants exist: CMOS is becoming more popular http://electronics.howstuffworks.com/digital-camera.htm
15	Issues with digital cameras Noise big difference between consumer vs. SLR-style cameras low light is where you most notice noise Compression creates artifacts except in uncompressed formats (tiff, raw) Color color fringing artifacts from Bayer patterns Blooming charge overflowing into neighboring pixels In-camera processing oversharpening can produce halos Interlaced vs. progressive scan video even/odd rows from different exposures Are more megapixels better? requires higher quality lens noise issues Stabilization compensate for camera shake (mechanical vs. electronic)
16	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
17	Modeling projection Projection equations Compute intersection with PP of ray from (x,y,z) to COP Derived using similar triangles (on board)
18	Homogeneous coordinates Is this a linear transformation?
19	Perspective Projection Projection is a matrix multiply using homogeneous coordinates:
20	Perspective Projection How does scaling the projection matrix change the transformation?
21	Orthographic projection Special case of perspective projection Distance from the COP to the PP is infinite Good approximation for telephoto optics Also called “parallel projection”: (x, y, z) → (x, y) What’s the projection matrix?
22	Other types of projection Scaled orthographic Also called “weak perspective” Affine projection Also called “paraperspective”
23	Camera parameters
24	Distortion Radial distortion of the image Caused by imperfect lenses Deviations are most noticeable for rays that pass through the edge of the lens
25	Correcting radial distortion
26	Distortion
27	Modeling distortion To model lens distortion Use above projection operation instead of standard projection matrix multiplication
28	Other types of lenses