Camera Models I July 27, 1999 Motivational Film Card Trick July - - PowerPoint PPT Presentation

Camera Models I

July 27, 1999

July 27, 1999

Motivational Film

✔Card Trick

July 27, 1999

Logistics

✔Paper summaries on Camera Models I

– Any takers?

✔Projects

– Still slots open for presentation

July 27, 1999

Photography and Light

pho•tog•ra•phy, n., the process or art of producing images of objects by the action of light on a sensitized surface, esp, a film in a camera.

Light…Light…Light….Light...

July 27, 1999

Computer Graphics as Virtual Photography

camera (captures light) synthetic image camera model (focuses simulated lighting)

processing

photo processing tone reproduction real scene 3D models Photography: Computer Graphics: Photographic print

July 27, 1999

Cameras -- What they do

✔In photography, cameras collect light

from a scene and focuses it onto a plane (film)

✔Two aspects to consider

– Geometry – Radiometry

July 27, 1999

Cameras -- What they do

✔Geometry

– Mapping of position of light rays in scene to position of light on film plane

✔Radiometry

– Determination of how much light reaches the image plane

July 27, 1999

Today’s Class

✔Camera Models -- Geometry

– Projections / Pinhole Camera – Aperture Model

• Thin Lens Model
• Thick Lens Model

– Geometrical Model

July 27, 1999

Projection

✔In CG, projects 3D world onto a 2D

plane

– Projection from 3D to 2D. – From world to image. – Basis for camera models

July 27, 1999

Projection

✔Projection of a 3D object on a 2D

projection plane is defined by straight rays (projectors) emanating from a single point (center of projection) to each point on the 3D object. The projection is the intersection of these rays with the projection plane.

July 27, 1999

Projection

July 27, 1999

Projection

✔ Perspective ✔ Parallel

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Projection

✔View Plane Coordinate System

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Projection

✔Viewing Frustrum

July 27, 1999

Projection

✔ View coordinate system may not coincide

with world coordinate system.

✔ Must transform point in world (x,y,z) to a point

in coordinate system of view (u,v,n)

            =             1 1 z y x M n v u

July 27, 1999

Projection

            − − − = 1

z z y x y z y x x z y x

• n

n n

• v

v v

• u

u u M

✔ (ux,uy,uz) are

coordinates of unit u vector w.r.t. world space

✔ Similar for v, n,

✔ (ox, oy, oz) is the origin

• f view space w.r.t

world space

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Projection

✔ Now that you’re in u,v,n space, you still need

to perform the perspective projection.

July 27, 1999

Projection

d p p d p

n u u

+ = ′ d p p d p

n v v

+ = ′ 1 + = ′ d p p p

n u u

1 + = ′ d p p p

n v v

July 27, 1999

Projection

✔Recall homogeneous coordinates

– (X,Y,Z,W) where x = X/W, y = Y/W, z = Z/W

W p d p p p

u n u u

= + = ′ 1 W p d p p p

v n v v

= + = ′ 1

1 + = d p W

n

July 27, 1999

Projection

✔In Matrix form:

            =                         =             1 1 1 1 1 1 1 n v u P n v u d W P P P

n v u

July 27, 1999

Projection

✔Combine with your coordinate system

transform

            =             1

z y x n v u

p p p PM w P P P

July 27, 1999

Projection

✔And this is how it’s done in computer

graphics

✔Use homogeneous coordinates to

include perspective transformation in matrix transform chain.

✔So how does all this relate to cameras...

July 27, 1999

The Pinhole Camera

✔CG uses the pinhole camera model

July 27, 1999

The Pinhole Camera

✔However

– Real cameras have real openings (apertures) -- depth of field – Shutter speed is not instantaneous -- motion blur

July 27, 1999

The Aperture Model

✔First attempt to model real camera

• ptics

– lens opening is no longer a pinhole – can move the lens away from or toward the film plane to achieve “focussing” – Uses thin lens model

July 27, 1999

The Aperture Model

✔Focal length

July 27, 1999

The Aperture Model

✔The aperture

– circular region in which light can pass through. – Contains a lens that focuses the light – F-Stop = focal length / diameter of opening

July 27, 1999

The Aperture Model

✔Thin lens geometry - focus

f s s 1 1 1 = ′ +

July 27, 1999

The Aperture Model

✔Depth of Field

– Depth range at which the scene will appear in focus in the resulting image. – Points outside this range will appear as blurry circles on the image (circle of confusion)

July 27, 1999

The Aperture Model

✔Depth of field -- example

July 27, 1999

The Aperture Model

✔Circle of confusion

July 27, 1999

The Aperture Model

✔Simulating Depth of field effects

– [Potmesil81] – Postprocess the image to simulate additional light resulting from circle of confusion. – Filter based on the physics of lens optics

July 27, 1999

The Aperture Model

July 27, 1999

The Aperture Model

✔Note on depth of field

– In reality, most image point are circles of confusion – Points outside of depth of field are perceived as blurry – Depth of field effects are a result of human thresholds for perceived acuity and will depend upon image viewing conditions.

July 27, 1999

The Aperture Model

✔Another way to look at depth of field

July 27, 1999

The Aperture Model

✔This is the approach used in distributed

ray tracing.

July 27, 1999

The Aperture Model

✔Motion blur

– Blurring due to motion of objects occurring while camera shutter is open. – Simple approach: add blurring as post- process based on motion of objects

July 27, 1999

The Aperture Model

✔Motion blur

– The Distributed Ray Tracing Approach

• Sample scene in time by using “jittered” time

steps.

• Use same ray set in each sampling
• Final image is created by averaging sample

scenes

• Has native support in Renderman spec

July 27, 1999

The Aperture Model

✔Motion blur

July 27, 1999

The Aperture Model

✔Thick Lens Model

– Thin lens model assume that lens is infintesimally narrow – In reality, lens system have some thickness

July 27, 1999

The Aperture Model

✔ Thick lens model

f s s 1 1 1 = ′ +

July 27, 1999

The Aperture Model

✔Thick lens model - Perspective matrix:

            =                         ′ ′ + =             1 1 1 1 1 1 1 n v u P n v u f d f d W P P P

n v u

July 27, 1999

The Aperture Model

✔Ray Tracing Using the thick lens model

July 27, 1999

The Aperture Model

✔Summary

– Extension of the basic pinhole model (perspective projection) – Finite Aperture – Focus Capability (depth of field) – Non-instantaneous (motion blur) – Models

• Thick lens / Thin Lens

July 27, 1999

Geometric Model

✔Aperture model lacks in that it is still

based on perspective projection

– Produces perfectly undistorted (geometrically) images – In reality, all lenses do introduce distortion, sometimes intentionally (e.g. fish eye lens)

July 27, 1999

Geometric Model

✔Geometric model

– Accurately accounts for geometry of the elements in a lens system – Thick and thin lens models are approximations of effects due to actual lens geometries.

July 27, 1999

Geometric Model

✔A typical lens system (from Lens

handbook)

July 27, 1999

Geometric Model

✔For each element:

– radius of curvature – thickness – index of refraction – change of index of refraction – diameter

✔This spec can be used to trace rays

through the system.

July 27, 1999

Geometric Model

✔Kolb model [Kolb95]

– brute force ray tracing solution using lens spec – Accurately calculates geometry and radiometry – Framework also allows for thin and thick model approximations

July 27, 1999

Geometric Model

✔Kolb Model - Ray tracing

– ray direction modified using

• curvature of lens surface
• refraction using Snell’s Law

– Rays are cast towards exit pupil and not aperture opening – supersampling - Multiple rays cast per pixel.

July 27, 1999

Geometric Model

✔Exit pupil vs aperture opening

July 27, 1999

Geometric Model

✔Kolb model

– Pixel values are determined relative to accurately calculated irradiance on surface. – Note that depth of field effects come for free since we’re accurately modeling lens effect. – Now we’re getting close to real photography!

July 27, 1999

Geometric Model

✔Kolb model -- examples

Thin lens Thick lens Geometry

July 27, 1999

Geometric Model

✔Kolb Model - examples

16mm fisheye 200mm telephoto 50mm double-Gauss 35mm wide-angle

July 27, 1999

Camera Models - geometry

✔Summary

– Looked at the geometry of camera models – Pinhole model (basic perspective projection) – Aperture Model (depth of field/motion blur) – Geometric model (for full geometric effects)

July 27, 1999

Next Class

✔Camera Models

– Radiometry – A different perspective (no pun intended)

• Lumigraph / Light field model

July 27, 1999

Remember

✔Class Web Site:

– http://www.cs.rit.edu/~jmg/virtualPhoto