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http://courses.csail.mit.edu/6.869
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Administration
• Syllabus• Grading• Collaboration Policy• Project
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Course requirements
• Two take-home exams
• Five problem sets with lab exercises in Matlab
• No final exam
• Final project
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Grading
• Problem sets are graded check, check-plus, check-minus
• Contribution to grade:– 5 problem sets: 30 %– 2 take-home exams: 40%– final project: 30%
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Collaboration Policy
Problem sets may be discussed, but all written work and coding must be done individually. Take-home exams may not be discussed. Individuals found submitting duplicate or substantially similar materials due to inappropriate collaboration may get an F in this class and other sanctions.
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Project
The final project may be – An original implementation of a new or published idea
– A detailed empirical evaluation of an existing implementation of one or more methods
– A paper comparing three or more papers not covered in class, or surveying recent literature in a particular area
A project proposal not longer than two pages must be submitted and approved by April 1st. I can provide ideas or suggestions for projects.
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Problem Set 0• Out today, due 2/12• Matlab image exercises
– load, display images– pixel manipulation– RGB color interpolation– image warping / morphing with interp2
– simple background subtraction• All psets graded loosely: check, check-, 0.• (Outstanding solutions get extra credit.)
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Vision
• What does it mean, to see? “to know what is where by looking”.
• How to discover from images what is present in the world, where things are, what actions are taking place.
from Marr, 1982
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Vision
• What does it mean, to see? “to know what is where by looking”.
• How to discover from images what is present in the world, where things are, what actions are taking place.
from Marr, 1982
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Why study Computer Vision?• One can “predict the future” (and avoid bad
things…)!• Images and movies are everywhere; fast-growing
collection of useful applications– building representations of the 3D world from pictures– automated surveillance (who’s doing what)– movie post-processing– face finding
• Greater understanding of human vision• Various scientific questions
– how does object recognition work?
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What is object recognition?
• People draw distinctions between what is seen– This could mean “is this a fish or a bicycle?”– It could mean “is this George Washington?”– It could mean “is this poisonous or not?”– It could mean “is this slippery or not?”– It could mean “will this support my weight?”– Area of research:
• How to build programs that can draw useful distinctions based on image properties.
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The course, in broad categories
• Images and image formation• Low-level vision• High-level vision• Implementations and applications
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Computer vision class, fast-forward
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Images and image formation
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Cameras, lenses, and sensors
•Pinhole cameras•Lenses•Projection models•Geometric camera parameters
From Computer Vision, Forsyth and Ponce, Prentice-Hall, 2002.
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Radiometry…not covered (see 6.801)
Wolfgang Lucht
http://geography.bu.edu/brdf/brdfexpl.html
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From Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995
Color
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Low-level vision
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Image filtering• Review of linear systems, convolution• Bandpass filter-based image representations• Probabilistic models for images
ImageOriented, multi-scale representation
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SIFT (scale invariant feature transforms)
David Lowe,IJCV 2004
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viewer television display
IEEE Computer Graphics and Applications, 18, no. 3, 1998
template
image Normalized correlation
Non-linear filtering, and applications
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Models of texture
Non-parametric model
A. Efros and W. T Freeman, Image quilting for texture synthesis and transfer, SIGGRAPH 2001
A Parametric Texture Model based on Joint Statistics of Complex Wavelet Coefficients J. Portilla and E. Simoncelli, International Journal of Computer Vision 40(1): 49-71, October 2000.© Kluwer Academic Publishers.
Parametric model
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Learning and vision
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Bayesian framework for vision
Gahan Wilson’s Still Weird, Forge, 1994
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Bayesian framework for vision
http://www.cs.dartmouth.edu/whites/old_man.html
Coincidental appearance of face profile in rock?
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Bayesian framework for vision
http://bensguide.gpo.gov/3-5/symbols/print/mountrushmore.html
Coincidental appearance of faces in rock?
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Eigenfaces: linear bases for faces
Moghaddam, B.; Jebara, T.; Pentland, A., "Bayesian Face Recognition", Pattern Recognition, Vol 33, Issue 11, pps 1771-1782, November 2000
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Statistical classifiers
– MIT Media Lab face localization results.– Applications: database search, human machine interaction, video conferencing.
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Support vector machines and boosting
Large-margin classifier
www.support-vector.net/nello.html
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Support vector machines and boosting
“The kernel trick”
www.support-vector.net/nello.html
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Recent, now classic, paper on face detection:
Rapid Object Detection Using a Boosted Cascade of Simple Features
Paul Viola Michael J. JonesMitsubishi Electric Research Laboratories (MERL)
Cambridge, MA
Most of this work was done at Compaq CRL before the authors moved to MERL
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Face Detection Goal
Many Uses- User Interfaces- Interactive Agents- Security Systems- Video Compression- Image Database Analysis
Viola and Jones, Robust object detection using a boosted cascade of simple features, CVPR 2001
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Use of context for object detection
car pedestrian
Identical local image features!
Images by Antonio Torralba
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The world, to a face detector
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Structure from Motion
What is the shape of the scene?
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Segmentation (perceptual grouping)
How many ways can you segment six points?
(or curves)
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Segmentation
• Which image components “belong together”?
• Belong together=lie on the same object• Cues
– similar colour– similar texture– not separated by contour– form a suggestive shape when assembled
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Applications
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Tracking
Follow objects and estimate location..– radar / planes– pedestrians– cars– face features / expressions
Many ad-hoc approaches…General probabilistic formulation: model density
over time.
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Tracking
• Use a model to predict next position and refine using next image
• Model:– simple dynamic models (second order dynamics)– kinematic models– etc.
• Face tracking and eye tracking now work rather well
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Articulated Models
Find most likely model consistent with observations….(and previous configuration)
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Articulated tracking• Constrained
optimization• Coarse-to-fine
part iteration• Propagate joint
constraints through each limb
• Real-time on Ghz pentium…
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Video
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thisapplication
Computer vision applicationsas ocean-going vessels
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Game: Decathlete
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Optical-flow-based Decathlete figure motion analysis
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Decathlete 100m hurdles
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Decathlete javelin throw
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Companies and applications
• Cognex• Reactrix• Poseidon• Mobileye• Eyetoy• Identix• Roomba
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Motion magnification
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And…
• Visual Category Learning• Image Databases• Image-based Rendering• Medical Imaging
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Skills learned from this class
• Goal: You’ll be able to go to a computer vision conference and understand what’s going on in most of the presentations.
• You’ll have the skills and awareness of the literature to start building the vision systems you want.
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Cameras, lenses, and calibration
Today:• Camera models• Projection equations• Calibration methods
Images are projections of the 3-D world onto a 2-D plane…
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7-year old’s question
Why is there no image on a white piece of paper?
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Pinhole cameras
• Geometry
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Distant objects are smaller
Forsyth&Ponce
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Virtual image, perspective projection
• Abstract camera model - box with a small hole in it
Forsyth&Ponce
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Parallel lines meetCommon to draw film planein front of the focal point.Moving the film plane merelyscales the image.
Forsyth&Ponce
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The equation of projection
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The equation of projection
• Cartesian coordinates:– We have, by similar
triangles, that (x, y, z) -> (f x/z, f y/z, -f)
– Ignore the third coordinate, and get
(x,y, z)→ ( f xz
, f yz)
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Vanishing points
• We show this on the board…
• Each set of parallel lines (=direction) meets at a different point– The vanishing point for this
direction
• Sets of parallel lines on the same plane lead to collinear vanishing points. – The line is called the
horizon for that plane
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Geometric properties of projection
• Points go to points• Lines go to lines• Planes go to whole image
or half-planes.• Polygons go to polygons• Degenerate cases
– line through focal point to point
– plane through focal point to line
pointslinesthe whole imageor a half-plane
polygons
point
line
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What if you photograph a brick wall head-on?
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Wandell, Foundations of Vision, Sinauer, 1995
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Pinhole camera demonstrations
• Film camera, box, demo. Apertures, lens.
• The image is the convolution of the aperture with the scene.
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Wandell, Foundations of Vision, Sinauer, 1995
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Weak perspective
• Issue– perspective effects, but
not over the scale of individual objects
– collect points into a group at about the same depth, then divide each point by the depth of its group
– Adv: easy– Disadv: wrong
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Orthographic projection
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Example use of orthographic projection: inferring human body motion in 3-d
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Advantage of orthographic projection
Leventon and Freeman, Bayesian Estimation of Human Motion, MERL TR98-06
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Orthography can lead to analytic solutions
Prior probability
Likelihood function
Analytic solution for inferred 3-d motionLeventon and Freeman, Bayesian Estimation of Human Motion, MERL TR98-06
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Results
Leventon and Freeman, Bayesian Estimation of Human Motion, MERL TR98-06
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But, alas
“The results for the simplified problem appear promising. However serious questions arise because of the simplifying assumptions, which trivialize a number of the hard issues of the problem in the real world. Eg. scaling effects that arise from perpective projection are ignored, by assuming orthographic projection. …”
Reviewer’s comments
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The reason for lenses
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Water glass refraction
http://data.pg2k.hd.org/_exhibits/natural-
science/cat-black-and-white-domestic-short-
hair-DSH-with-nose-in-glass-of-water-on-bedside-
table-tweaked-mono-1-AJHD.jpg
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Snell’s law
)sin()sin( 2211 αα nn =
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Spherical lens
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Forsyth and Ponce
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First order optics
θθ ≈)sin(
f
D/2θ
fD 2/
≈θ
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Paraxial refraction equation
⎟⎟⎠
⎞⎜⎜⎝
⎛+≈+=
111
11dR
hβγα
⎟⎟⎠
⎞⎜⎜⎝
⎛−≈−=
222
11dR
hβγα
Rnn
dn
dnnn 12
2
2
1
12211
−=+⇔≈ αα
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The thin lens, first order optics
1z'
-1z
=1f )1(2 −
=nRf
Forsyth&Ponce
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US Navy Manual
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What camera projection model applies for a thin lens?
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Candle and laser pointer demo
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More accurate models of real lenses
• Finite lens thickness• Higher order approximation to• Chromatic aberration• Vignetting
)sin(θ
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Thick lens
Forsyth&Ponce
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Third order optics
6)sin(
3θθθ −≈
6
2/2/
3
⎟⎟⎠
⎞⎜⎜⎝
⎛
−≈f
D
fDθf
D/2θ
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Paraxial refraction equation, 3rd order optics
Forsyth&Ponce
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Spherical aberration (from 3rd
order optics
Tran
sver
se sp
heric
al a
berr
atio
n
Longitudinal spherical aberration Forsyth&Ponce
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Other 3rd order effects
• Coma, astigmatism, field curvature, distortion.
no distortionpincushion distortion
barrel distortion
Forsyth&Ponce
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Astigmatic distortion
Hardy & Perrin, The Principles of Optics, 1932
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Lens systems
Lens systems can be designed to correct for aberrations described by 3rd order optics
Forsyth&Ponce
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Vignetting
Forsyth&Ponce
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Chromatic aberration
(great for prisms, bad for lenses)
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Other (possibly annoying) phenomena
• Chromatic aberration– Light at different wavelengths follows different paths;
hence, some wavelengths are defocussed– Machines: coat the lens– Humans: live with it
• Scattering at the lens surface– Some light entering the lens system is reflected off each
surface it encounters (Fresnel’s law gives details)– Machines: coat the lens, interior– Humans: live with it (various scattering phenomena are
visible in the human eye)
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Summary
• Want to make images• Pinhole camera models the geometry of
perspective projection• Lenses make it work in practice• Models for lenses
– Thin lens, spherical surfaces, first order optics– Thick lens, higher-order optics, vignetting.
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Next
• how positions in the image relate to 3-d positions in the world.
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Translation⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛=
Z
Y
xB
BBB
P⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛=
Z
Y
xA
AAA
P
Ai
Ak
Aj
Bi
Bk
Bj
PxA
YAZA A
BOr
How does relate to ?PAPB
ABAB OPP +=
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Rotation⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛=
Z
Y
xB
BBB
P⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛=
Z
Y
xA
AAA
P
Ai
Ak
Aj
PxA
YAZA
How does relate to ?PAPB
PRP ABA
B =
![Page 120: Computer vision class, fast-forwardcourses.csail.mit.edu/6.869/lectnotes/lect1/lect1-slides.pdf · What camera projection model applies for a thin lens? Candle and laser pointer demo](https://reader036.vdocuments.us/reader036/viewer/2022071215/6044e90ed1287b127d1434b4/html5/thumbnails/120.jpg)
Find the rotation matrix
Project
onto the B frame’s coordinate axes.
( )⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛=
Z
Y
X
AAA
AAA
kjiOP ˆˆˆ Ai
Ak
Aj
PxA
YAZA
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
•••••••••
=⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
ZABYABXAB
ZABYABXAB
ZABYABXAB
Z
Y
X
AkkAjkAikAkjAjjAijAkiAjiAii
BBB
ˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆ
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
•••••••••
=⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
ZABYABXAB
ZABYABXAB
ZABYABXAB
Z
Y
X
AkkAjkAikAkjAjjAijAkiAjiAii
BBB
ˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆ
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
•••••••••
=⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
ZABYABXAB
ZABYABXAB
ZABYABXAB
Z
Y
X
AkkAjkAikAkjAjjAijAkiAjiAii
BBB
ˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆ
![Page 121: Computer vision class, fast-forwardcourses.csail.mit.edu/6.869/lectnotes/lect1/lect1-slides.pdf · What camera projection model applies for a thin lens? Candle and laser pointer demo](https://reader036.vdocuments.us/reader036/viewer/2022071215/6044e90ed1287b127d1434b4/html5/thumbnails/121.jpg)
Rotation matrix
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
•••••••••
=⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
ZABYABXAB
ZABYABXAB
ZABYABXAB
Z
Y
X
AkkAjkAikAkjAjjAijAkiAjiAii
BBB
ˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆthis
PRP ABA
B =implies
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
•••••••••
=
ABABAB
ABABAB
ABABABBA
kkjkikkjjjijkijiii
Rˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆˆ
where
![Page 122: Computer vision class, fast-forwardcourses.csail.mit.edu/6.869/lectnotes/lect1/lect1-slides.pdf · What camera projection model applies for a thin lens? Candle and laser pointer demo](https://reader036.vdocuments.us/reader036/viewer/2022071215/6044e90ed1287b127d1434b4/html5/thumbnails/122.jpg)
Translation and rotation
Let’s write
as a single matrix equation:
ABAB
AB OPRP +=
⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜
⎝
⎛
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
−−−−−−−−
=
⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜
⎝
⎛
11000|
|
1Z
Y
X
ABB
A
Z
Y
X
AAA
ORBBB