The Camera : The Camera 15-463: Computational Photography
Alexei Efros, CMU, Fall 2008
How do we see the world? : How do we see the world? Let’s design a camera
Idea 1: put a piece of film in front of an object
Do we get a reasonable image? Slide by Steve Seitz
Pinhole camera : 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? Slide by Steve Seitz
Pinhole camera model : Pinhole camera model Pinhole model:
Captures pencil of rays – all rays through a single point
The point is called Center of Projection (COP)
The image is formed on the Image Plane
Effective focal length f is distance from COP to Image Plane Slide by Steve Seitz
Dimensionality Reduction Machine (3D to 2D) : Figures © Stephen E. Palmer, 2002 Dimensionality Reduction Machine (3D to 2D) 3D world 2D image What have we lost?
Angles
Distances (lengths)
Funny things happen… : Funny things happen…
Parallel lines aren’t… : Parallel lines aren’t… Figure by David Forsyth
Lengths can’t be trusted... : Lengths can’t be trusted... Figure by David Forsyth B’ C’ A’
…but humans adopt! : …but humans adopt! http://www.michaelbach.de/ot/sze_muelue/index.html Müller-Lyer Illusion We don’t make measurements in the image plane
Modeling projection : 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 Slide by Steve Seitz
Modeling projection : Modeling projection Projection equations
Compute intersection with PP of ray from (x,y,z) to COP
Derived using similar triangles (on board) Slide by Steve Seitz
Homogeneous coordinates : Homogeneous coordinates Is this a linear transformation? Trick: add one more coordinate: homogeneous image
coordinates homogeneous scene
coordinates Converting from homogeneous coordinates no—division by z is nonlinear Slide by Steve Seitz
Perspective Projection : Perspective Projection Projection is a matrix multiply using homogeneous coordinates: This is known as perspective projection
The matrix is the projection matrix
Can also formulate as a 4x4 Slide by Steve Seitz
Orthographic Projection : 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? Image World Slide by Steve Seitz
Spherical Projection : Spherical Projection What if PP is spherical with center at COP?
In spherical coordinates, projection is trivial:
(q,f) = (q,f,d)
Note: doesn’t depend on focal length d!
Building a real camera : Building a real camera
Camera Obscura : Camera Obscura The first camera
Known to Aristotle
Depth of the room is the effective focal length Camera Obscura, Gemma Frisius, 1558
Home-made pinhole camera : Home-made pinhole camera http://www.debevec.org/Pinhole/ Why so
blurry?
Shrinking the aperture : Shrinking the aperture Why not make the aperture as small as possible?
Less light gets through
Diffraction effects… Less light gets through Slide by Steve Seitz
Shrinking the aperture : Shrinking the aperture
The reason for lenses : The reason for lenses Slide by Steve Seitz
Focus : Focus
Focus and Defocus : Focus and Defocus 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 Slide by Steve Seitz
Thin lenses : 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 ) Slide by Steve Seitz
Varying Focus : Varying Focus Ren Ng
Depth Of Field : Depth Of Field
Depth of Field : Depth of Field http://www.cambridgeincolour.com/tutorials/depth-of-field.htm
Aperture controls Depth of Field : Aperture controls 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
But small aperture reduces amount of light – need to increase exposure
Varying the aperture : Varying the aperture Large apeture = small DOF Small apeture = large DOF
Nice Depth of Field effect : Nice Depth of Field effect
Field of View (Zoom) : Field of View (Zoom)
Field of View (Zoom) : Field of View (Zoom)
Field of View (Zoom) : Field of View (Zoom)
FOV depends of Focal Length : f FOV depends of Focal Length Smaller FOV = larger Focal Length f
Slide 35: From Zisserman & Hartley
Field of View / Focal Length : Field of View / Focal Length Large FOV, small f
Camera close to car Small FOV, large f
Camera far from the car
Fun with Focal Length (Jim Sherwood) : Fun with Focal Length (Jim Sherwood) http://www.hash.com/users/jsherwood/tutes/focal/Zoomin.mov
Lens Flaws : Lens Flaws
Lens Flaws: Chromatic Aberration : Lens Flaws: Chromatic Aberration Dispersion: wavelength-dependent refractive index
(enables prism to spread white light beam into rainbow)
Modifies ray-bending and lens focal length: f(?)
color fringes near edges of image
Corrections: add ‘doublet’ lens of flint glass, etc.
Chromatic Aberration : Chromatic Aberration Near Lens Center Near Lens Outer Edge
Radial Distortion (e.g. ‘Barrel’ and ‘pin-cushion’) : Radial Distortion (e.g. ‘Barrel’ and ‘pin-cushion’) straight lines curve around the image center
Radial Distortion : Radial Distortion Radial distortion of the image
Caused by imperfect lenses
Deviations are most noticeable for rays that pass through the edge of the lens No distortion Pin cushion Barrel
Radial Distortion : Radial Distortion