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CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
3-D Computer Vision3-D Computer VisionCSc 83029CSc 83029
StereoStereo
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
StereopsisStereopsis
Recovering 3D information (depth) from Recovering 3D information (depth) from two images.two images. The correspondence problem.The correspondence problem. The reconstruction problem.The reconstruction problem. Epipolar constraint.Epipolar constraint. The 8-point algorithm.The 8-point algorithm.
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
The 2 problems of StereoThe 2 problems of Stereo
Correspondence: Correspondence: Which parts of the left and Which parts of the left and right images are projections of the same scene right images are projections of the same scene element?element?
Reconstruction: Reconstruction: Given:Given: A number of corresponding points between the left A number of corresponding points between the left
and right image,and right image, Information on the geometry of the stereo system,Information on the geometry of the stereo system,
Find:Find:
3-D structure of observed objects3-D structure of observed objects..
The setting: Simultaneous acquisition of 2 images(left, right) of a static scene.
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Stereo VisionStereo Vision
depth map
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
A simple stereo systemA simple stereo system
f
T
Z
P
Ol Or
Left Camera Right Camera
X-axis
Z-axis
cl cr
FixationPoint:Infinity.Paralleloptical axes.
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
TriangulationTriangulation
f
T
Z
P
pl pr
Ol Or
Left Camera Right Camera
X-axis
Z-axis
cl cr
FixationPoint:Infinity.Paralleloptical axes.
Calibrated Cameras
TriangulationTriangulation
f
T
Z
P
pl pr
Ol Or
Left Camera Right Camera
X-axis
Z-axis
cl cr
FixationPoint:Infinity.Paralleloptical axes.
Calibrated Cameras
xl xr
rlrl xxd
d
TfZ
Z
T
fZ
xxT
,Similar triangles:
d:disparity (difference in retinal positions).T:baseline.Depth (Z) is inversely proportional to d (fixation at infinity)
TriangulationTriangulation
f
T
Z
P
pl pr
Ol Or
Left Camera Right Camera
X-axis
Z-axis
cl cr
FixationPoint:Infinity.Paralleloptical axes.
Calibrated Cameras
xl xr
rlrl xxd
d
TfZ
Z
T
fZ
xxT
,Similar triangles:
d:disparity (difference in retinal positions).T:baseline.Baseline T: accuracy/robustness of depth calculation.
TriangulationTriangulation
f
T
Z
P
pl pr
Ol Or
Left Camera Right Camera
X-axis
Z-axis
cl cr
FixationPoint:Infinity.Paralleloptical axes.
Calibrated Cameras
xl xr
rlrl xxd
d
TfZ
Z
T
fZ
xxT
,Similar triangles:
d:disparity (difference in retinal positions).T:baseline.Small baselines: less accurate measurements.
TriangulationTriangulation
f
T
Z
P
pl pr
Ol Or
Left Camera Right Camera
X-axis
Z-axis
cl cr
FixationPoint:Infinity.Paralleloptical axes.
Calibrated Cameras
xl xr
rlrl xxd
d
TfZ
Z
T
fZ
xxT
,Similar triangles:
d:disparity (difference in retinal positions).T:baseline.Large baselines: occlusions/foreshortening.
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Parameters of Stereo SystemParameters of Stereo System
f
T
Z
P
pl pr
Ol Or
Left Camera Right Camera
X-axis
Z-axis
cl cr
FixationPoint:Infinity.Paralleloptical axes.
1) Intrinsic parameters (i.e. f, cl, cr)2) Extrinsic parameters: relative position and orientation of the 2 cameras.
xl xr
STEREO CALIBRATION PROBLEM
• Difficulties – ambiguities, large changes of appearance, due to changeOf viewpoint, non-uniquess
Stereo – Photometric ConstraintStereo – Photometric Constraint• Same world point has same intensity in both images.
• Lambertian fronto-parallel• Issues (noise, specularities, foreshortening) From Jana Kosecka
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Correspondence Is DifficultCorrespondence Is Difficult
Ambiguity: there may be many possible 3D reconstructions.
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Correspondence Is DifficultCorrespondence Is Difficult
No texture: difficult to find a unique match.
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Correspondence Is DifficultCorrespondence Is Difficult
Foreshortening: the projection in each image is different.
Correspondence Is DifficultCorrespondence Is Difficult
Occlusions: there may not be a correspondence.
Assumptions: 1) Most scene points are visible from both views. 2) Corresponding image regions are similar.
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Correspondence Is DifficultCorrespondence Is Difficult
Curved surfaces: triangulation produces incorrect position.
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Correspondence is difficult: The Correspondence is difficult: The Ordering ConstraintOrdering Constraint
But it is not always the case ...
Points appear in the same order
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
More Correspondence ProblemsMore Correspondence Problems Regions without textureRegions without texture Highly Specular surfacesHighly Specular surfaces Translucent objectsTranslucent objects
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Methods For CorrespondenceMethods For Correspondence
Correlation based (dense correspondences).Correlation based (dense correspondences). Feature based (such as edges/lines/corners).Feature based (such as edges/lines/corners).
Correlation-Based MethodsCorrelation-Based Methods
pl
R(pl )
Left Image Right Image
1) For each pixel pl in the left image search in a region R(pl) in the right image for corresponding pixel pr.2) Use image windows of size (2W+1)x(2W+1).3) Select the pixel pr that maximizes a correlation function.
HAVE TO SPECIFY: Region R, size W, and correlation function ψ.
Correlation-Based MethodsCorrelation-Based Methods
pl
R(pl )
Left Image Right ImageFor each pixel pl=[i,j] in the left image
For each displacement d=[d1,d2] in R(pl)Compute
The disparity of pl is the d that maximizes c(d)
)),(),,(()( 21
W
Wk
W
Wll dljdkiIrljkiIc d
HAVE TO SPECIFY: Region R, size W, and correlation function ψ.
Correlation-Based MethodsCorrelation-Based Methods
pl
R(pl )
Left Image Right Image
2)(),(
),(
vuvu
uvvu
SUM OF SQUARED DIFFERENCESSSD
CROSS-CORRELATION
SSD is usually preferred: handles different intensity scales.
Normalized cross-correlation is better (but is more expensive).
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Correspondence Is DifficultCorrespondence Is Difficult
Intensities in window may differ.
Normalized cross-correlation may help.
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Image NormalizationImage Normalization Even when the cameras are identical models, there Even when the cameras are identical models, there
can be differences in gain and sensitivity.can be differences in gain and sensitivity. The cameras do not see exactly the same surfaces, The cameras do not see exactly the same surfaces,
so their overall light levels can differ.so their overall light levels can differ. For these reasons and more, it is a good idea to For these reasons and more, it is a good idea to
normalize the pixels in each window:normalize the pixels in each window:
pixel Normalized ),(
),(ˆ
magnitude Window )],([
pixel Average ),(
),(
),(),(
2
),(
),(),(),(
1
yxW
yxWvuyxW
yxWvuyxW
m
mm
m
m
II
IyxIyxI
vuII
vuII
From Sebastian Thrun/Jana Kosecka
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
It is closely related to the SSD:It is closely related to the SSD:
Maximize Cross correlation
Minimize Sum of Squared Differences
Comparing Windows:Comparing Windows:
From Jana Kosecka
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
• Sum of squared differences
• Normalize cross-correlation
• Sum of absolute differences
Region based Similarity MetricsRegion based Similarity Metrics
From Jana Kosecka
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
NCC score for two widely NCC score for two widely separated viewsseparated views
NCC score
From Jana Kosecka
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Window sizeWindow size
W = 3 W = 20
Better results with adaptive window• T. Kanade and M. Okutomi,
A Stereo Matching Algorithm with an Adaptive Window: Theory and Experiment,, Proc. International Conference on Robotics and Automation, 1991.
• D. Scharstein and R. Szeliski. Stereo matching with nonlinear diffusion. International Journal of Computer Vision, 28(2):155-174, July 1998
Effect of window sizeEffect of window size
(S. Seitz)
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Stereo resultsStereo results
Ground truthScene
Data from University of TsukubaData from University of Tsukuba
(Seitz)
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Results with window correlationResults with window correlation
Window-based matching(best window size)
Ground truth
(Seitz)
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Results with better methodResults with better method
Boykov et al., Fast Approximate Energy Minimization via Graph Cuts, International Conference on Computer Vision, September
1999.(Seitz)
Ground truthState of the art
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Feature-Based MethodsFeature-Based Methods
Left Image Right Image
Match sparse sets of extracted features.A feature descriptor for a line could contain:
length l, orientation o, midpoint (x,y), average contrast c
An example similarity measure (w’s are weights):
23
22
2211
20 )()()()(
1
rlrlrl ccwmmwwllwS
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Correspondence Using Correspondence Using CorrelationCorrelation
Left Disparity Map
Images courtesy of Point Grey Research
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
LEFT IMAGE
corner line
structure
Correspondence By FeaturesCorrespondence By Features
From Sebastian Thrun/Jana Kosecka
Correspondence By FeaturesCorrespondence By FeaturesRIGHT IMAGE
corner line
structure
Search in the right image… the disparity (dx, dy) is the displacement when the similarity measure is Search in the right image… the disparity (dx, dy) is the displacement when the similarity measure is maximummaximum
From Sebastian Thrun/Jana Kosecka
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Comparison of Matching MethodsComparison of Matching Methods
Dense depth maps.Dense depth maps. Need textured imagesNeed textured images Sensitive to Sensitive to
foreshorening/illumination foreshorening/illumination changeschanges
Need close viewsNeed close views
Sparse depth maps.Sparse depth maps. Insensitive to Insensitive to
illumination changes.illumination changes.
A-priori info used.A-priori info used. Faster.Faster.
Problems: occlusions/spurious matches:=>Introduce constraints in matching (i.e. left-right consistency constraint)
Correlation-Based Feature-Based
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Epipolar Constraint (Geometry)Epipolar Constraint (Geometry)
Center of projection
Image planeπl
Scene point
Center of projection
Epipoles
Ol Or
P
Pl Pr
plpr
EPIPOLARPLANE
el er
Image planeπr
EPIPOLARLINE EPIPOLAR
LINE
Epipolar ConstraintEpipolar Constraint
Center of projection
Image planeπl
Scene point
Center of projection
Epipoles
Ol Or
P
Pl Pr
plpr
EPIPOLARPLANE
el er
Image planeπr
EPIPOLARLINE EPIPOLAR
LINE
Extrinsic parameters: Left/Right Camera Frames: Pr=R(Pl-T), T=Or-Ol (1)
Epipolar ConstraintEpipolar Constraint
Center of projection
Image planeπl
Scene point
Center of projection
Epipoles
Ol Or
P
Pl Pr
plpr
EPIPOLARPLANE
el er
Image planeπr
EPIPOLARLINE EPIPOLAR
LINE
Given pl, pr is constrained to lie on the Epipolar Line (E.L.).For each left pixel pl, find the corresponding right E.L.Searching for pr reduces to a 1-D problem.
Ol, Or, pl =>Enough to define right E.L.
Epipolar ConstraintEpipolar Constraint
Center of projection
Image plane
Scene points
Center of projection
Epipoles
All E.L.s go through epipoles.Parallel image planes => epipoles at infinity.
el er
Essential MatrixEssential Matrix
T
lPTPP lr
coplanar are and T-TPP ll ,
0)( lT
rT PTPR
0 lT
r PTRP
Estimate the epipolar geometry: correspondencebetween points and E.L.s.
0)( lT
l PTTP
(1)
0
0
0
XY
XZ
YZ
ll
TT
TT
TT
S
SPPT
0)( lT
r PRSP0lT
r EPP
Link bw/ epipolar constraint and extrinsic parameters of stereo system.
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Essential MatrixEssential Matrix
T
lPrP
lprp
lu
ru
00
0
0
lTT
TT
TTT
r pRpxy
xz
yz
E
rT
l
lr
pEu
Epu
Epipolar lines are found by
Essential matrixRank 2
0lT
r EPPPerspectiveProjection
0lT
r Epp
scoordinate camera in points are and rl pp
erel
Perspective: pl=[xl,yl,fl]T, pr=[xr,yr,zr]T
pl= fl/Zl Pl, pr=fr/Zr Pr
Camera Models (linear versions)Camera Models (linear versions)
World Point(Xw, Yw,Zw)
Measured Pixel(xim, yim)
Elegant decomposition.No distortion!
?
HomogeneousCoordinates
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Fundamental MatrixFundamental Matrix
rrr
lll
pMp
pMp
Camera to pixel coordinates:
01 ll
Tr
Tr pEMMp
Essential matrix equation becomes:
F
rT
l
lr
pFu
pFu
Epipolar lines:
T
lPrP
lprp
lu
ru
F: pixel coordinates !E: camera coordinates !
erel
Ml (Mr) matrix of intrinsic parameters for left (right) camera.
Fundamental matrix
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
ConclusionsConclusions
Encodes information on Encodes information on extrinsic parametersextrinsic parameters..
Has rank 2.Has rank 2. Its 2 non-zero singular Its 2 non-zero singular
values are equal.values are equal.
Encodes information on Encodes information on both the both the extrinsicextrinsic and and intrinsicintrinsic parameters. parameters.
Has rank 2.Has rank 2.
Essential Matrix Fundamental Matrix
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Estimating the epipolar geometryEstimating the epipolar geometry
el erel er
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Estimating the epipolar geometryEstimating the epipolar geometry
Problem: Find the fundamental matrix from a set of image correspondences
0 liT
ri pFp
ir
il pp ,
el erel er
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Estimating the epipolar geometryEstimating the epipolar geometry
2 min liT
ri
iF
pFpWith the respect to the constraint: Rank(F) = 2.
el er
The 8-point algorithmThe 8-point algorithm
0 liT
ri pFp 0vA
n>=8 correspondences
v: the 9 elements of F.A: n x 9 measurement matrix.Solve using SVD (solution up to a scale factor).Enforce rank(F)=2 =>SVD on the computed F.Be careful: numerical instabilities.
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Epipolar Lines – ExampleEpipolar Lines – Example
ExampleExampleTwo views
Point Feature Matching
From Jana Kosecka
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
ExampleExampleEpipolar Geometry
Camera Pose and
Sparse Structure Recovery
From Jana Kosecka
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Locating the Epipoles from E & FLocating the Epipoles from E & F
el er
F => el, er in pixel coordinates.E => el, er in camera coordinates.
Fact: All epipolar lines pass through epipoles.
Accurate epipole localization:1) Refining epipolar lines.2) Checking for consistency.3) Uncalibrated stereo.
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Image rectificationImage rectification
Given general displacement how to warp the viewsGiven general displacement how to warp the views Such that epipolar lines are parallel to each other Such that epipolar lines are parallel to each other How to warp it back to canonical configurationHow to warp it back to canonical configuration (more details later)(more details later)
(Seitz)
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Epipolar rectificationEpipolar rectification
• Rectified Image Pair • Corresponding epipolar lines are aligned with the scan-lines• Search for dense correspondence is a 1D search
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Epipolar rectificationEpipolar rectification
Rectified Image Pair
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Rectification (Trucco, Ch. 7)Rectification (Trucco, Ch. 7)
Rotate left camera so that epipole goes to Rotate left camera so that epipole goes to infinity (known R, known epipoles)infinity (known R, known epipoles)
Apply same rotation to right cameraApply same rotation to right camera Rotate right camera by RRotate right camera by R Adjust scale in both camera reference framesAdjust scale in both camera reference frames
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
RectificationRectification
Problem: Epipolar lines not parallel to scan Problem: Epipolar lines not parallel to scan lineslines
plp
r
P
Ol Orel er
Pl Pr
Epipolar Plane
Epipolar Lines
Epipoles
From Sebastian Thrun/Jana Kosecka
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
RectificationRectification
Problem: Epipolar lines not parallel to scan Problem: Epipolar lines not parallel to scan lineslines
plp
r
P
Ol Or
Pl Pr
Epipolar Plane
Epipolar Lines
Epipoles at infinity
Rectified Images
From Sebastian Thrun/Jana Kosecka
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
3-D Reconstruction3-D Reconstruction
Reprinted from “Stereo by Intra- and Intet-Scanline Search,” by Y. Ohta and T. Kanade, IEEE Trans. on Pattern Analysis and MachineIntelligence, 7(2):139-154 (1985). 1985 IEEE.
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
3-D Reconstruction3-D Reconstruction
Intrinsic and extrinsicIntrinsic and extrinsic Intrinsic onlyIntrinsic only No informationNo information
Unambiguous (triangulation)Unambiguous (triangulation) Up to unknown scaling factorUp to unknown scaling factor Up to unknown projective Up to unknown projective
transformationtransformation
A Priori Knowledge 3-D Reconstruction from two views
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Projective ReconstructionProjective Reconstruction
Euclidean reconstruction Projective reconstruction
From Sebastian Thrun/Jana Kosecka
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Euclidean vs Projective Euclidean vs Projective reconstructionreconstruction
Euclidean reconstructionEuclidean reconstruction – true metric properties of objects – true metric properties of objects lenghts (distances), angles, parallelism are preserved lenghts (distances), angles, parallelism are preserved
Unchanged under rigid body transformationsUnchanged under rigid body transformations => Euclidean Geometry – properties of rigid bodies under => Euclidean Geometry – properties of rigid bodies under
rigid body transformations, similarity transformationrigid body transformations, similarity transformation
Projective reconstructionProjective reconstruction – lengths, angles, parallelism are – lengths, angles, parallelism are NOT NOT preserved – we get distorted images of objects – their preserved – we get distorted images of objects – their distorted 3D counterparts --> 3D projective reconstructiondistorted 3D counterparts --> 3D projective reconstruction
=> Projective Geometry => Projective Geometry
From Sebastian Thrun/Jana Kosecka
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Check this out!Check this out!
http://www.well.com/user/jimg/stereo/stereo_list.html
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
How can We Improve Stereo?How can We Improve Stereo?
Space-time stereo scanneruses unstructured light to aidin correspondence
Result: Dense 3D mesh (noisy)
From Sebastian Thrun/Jana Kosecka
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Active Stereo: Adding Texture to SceneActive Stereo: Adding Texture to Scene
By James Davis, By James Davis, Honda Research,Honda Research,
Now UCSCNow UCSC
From Sebastian Thrun/Jana Kosecka
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
rect
ified
Active Stereo (Structured Light)Active Stereo (Structured Light)
From Sebastian Thrun/Jana Kosecka
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Range Images (depth images, depth Range Images (depth images, depth maps, surface profiles, 2.5-D images)maps, surface profiles, 2.5-D images)
•Sensors that produce depth directly.•Pixel of a range image is the distance between a known reference frame and a visible point in the scene.•Representations:
•Cloud of Points (x,y,z)•Rij form (spatial information is explicit)
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Active Range SensorsActive Range Sensors
Project energy or control sensor’s parameters.Project energy or control sensor’s parameters. Laser, Radars (accurate)/Sonars(inaccurate).Laser, Radars (accurate)/Sonars(inaccurate). Active Focusing/Defocusing.Active Focusing/Defocusing.
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
TriangulationTriangulation
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
TriangulationTriangulation
Xc
YcZc
Image
Light Stripe System.
Light Plane:AX+BY+CZ+D=0 (in camera frame)Image Point:x=f X/Z, y=f Y/Z (perspective)
Triangulation: Z=-D f/(A x + B y + C f)
Move light stripe or object.
CSc83029 3-D Computer Vision / Ioannis StamosCSc83029 3-D Computer Vision / Ioannis Stamos
Time of FlightTime of Flight