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The K-Ray Camera

Motivation

K-Ray Cameras

K-Ray Camera Construction

K-Ray Camera Model

K-Ray Camera Projection

3-Ray Camera

Continuity

Continuity

Continuity

Continuous 3-ray camera

Continuous 3-Ray Camera

Slide 13

6-Ray Camera

The K-Ray Camera

End of slide show, click to exit.

The K-Ray Camera

Motivation

Camera models are essential
infrastructure in computer vision, computer graphics, and visualization

Given a contiguous set of
coherent but non-concurrent rays, find a camera model that approximates the
set of rays well, yet provides efficient projection

K-Ray Cameras

A class of cameras

Rays are defined by
interpolating k given rays

k and the interpolation method
define the class members

K-Ray Camera Construction

Construction

Given k rays with origins oi
= (oxi, oyi, ozi), and  unit directions di = (dxi,
dyi, dzi)

Compute local 3D coordinate
system (O, x, y, z)

For each ray, compute
intersections (ui, vi), (si, ti)
with planes z = 0 and z = 1

Compute the coefficients of
expressions s(u, v) and t(u, v)

K-Ray Camera Model

K-Ray Camera Projection

Given point P(x, y, z), find
image plane point (u, v) whose ray passes through P

3-Ray Camera

Equivalent to General Linear
Camera (GLC) [Yu & McMillan 2004]

Camera model

s(u, v) = au + bv + c

t(u, v) = du + ev + f

Projection of P(x, y, z)

Continuity

Given two 3-ray cameras that
share an edge

Projection discontinuous across
shared edge

Side walls defined by shared
edge are not the same

Some points do not project
(cracks)

Some points project twice
(overlap)

Continuity

Continuity

Continuous 3-ray camera

Sweeping plane

not parallel to base plane

defined by equal segments on
construction rays

Projection equation becomes
cubic

Continuous 3-Ray Camera

Projection continuous across
shared edge

Same side wall, no cracks, no
overlap

Slide 13

6-Ray Camera

Most powerful camera with
closed form projection

Camera model

s(u, v) = a1u2
+ a2v2 + a3vu + a4u + a5v
+ a6

t(u, v) = b1u2
+ b2 v2 + b3vu + b4u + b5v
+ b6

Projection: quartic equation

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Second level

Third level

Fourth level

Fifth level

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Motivation

•

Camera models are essential infrastructure

in computer vision, computer graphics, and

visualization

•

Given a contiguous set of coherent but non-

concurrent rays, find a camera model that

approximates the set of rays well, yet

provides efficient projection