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Midterm out today |
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Project 1 demos |
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Today’s Readings |
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Nalwa 2.1 (handout) |
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Let’s design a camera |
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Idea 1:
put a piece of film in front of an object |
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Do we get a reasonable image? |
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Add a barrier to block off most of the rays |
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This reduces blurring |
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The opening known as the aperture |
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How does this transform the image? |
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The first camera |
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Known to Aristotle |
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How does the aperture size affect the image? |
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Why not make the aperture as small as possible? |
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A lens focuses light onto the film |
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There is a specific distance at which objects
are “in focus” |
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other points project to a “circle of confusion”
in the image |
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Changing the shape of the lens changes this
distance |
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A lens focuses parallel rays onto a single focal
point |
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focal point at a distance f beyond the plane of
the lens |
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f is a function of the shape and index of
refraction of the lens |
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Aperture of diameter D restricts the range of
rays |
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aperture may be on either side of the lens |
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Lenses are typically spherical (easier to
produce) |
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Thin lens equation |
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Any object point satisfying this equation is in
focus |
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What is the shape of the focus region? |
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How can we change the focus region? |
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Changing the aperture size affects depth of
field |
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A smaller aperture increases the range in which
the object is approximately in focus |
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The human eye is a camera |
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Iris - colored annulus with radial muscles |
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Pupil - the hole (aperture) whose size is
controlled by the iris |
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What’s the “film”? |
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A digital camera replaces film with a sensor
array |
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Each cell in the array is a Charge Coupled Device |
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light-sensitive diode that converts photons to
electrons |
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http://www.howstuffworks.com/digital-camera2.htm |
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The coordinate system |
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We will use the pin-hole model as an
approximation |
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Put the optical center (Center Of Projection) at
the origin |
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Put the image plane (Projection Plane) in front
of the COP |
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Why? |
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The camera looks down the negative z axis |
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we need this if we want right-handed-coordinates |
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Projection equations |
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Compute intersection with PP of ray from (x,y,z)
to COP |
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Derived using similar triangles (on board) |
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Is this a linear transformation? |
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Projection is a matrix multiply using
homogeneous coordinates: |
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How does multiplying the projection matrix
change the transformation? |
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Special case of perspective projection |
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Distance from the COP to the PP is infinite |
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Also called “parallel projection” |
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What’s the projection matrix? |
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Scaled orthographic |
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Also called “weak perspective” |
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Affine projection |
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Also called “paraperspective” |
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