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Accurate Stereophotogrammetry

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Accurate Stereophotogrammetry John Morris Electrical and Computer Engineering/ Computer Science, The University of Auckland Iolanthe on the Hauraki Gulf – PowerPoint PPT presentation

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Title: Accurate Stereophotogrammetry


1
Accurate Stereophotogrammetry
  • John Morris
  • Electrical and Computer Engineering/ Computer
    Science, The University of Auckland

Iolanthe on the Hauraki Gulf
2
What is Stereo PhotogrammetryF?
Pairs of images giving different views of the
scene
can be used to compute a depth (disparity) map ?
3
Depth Maps
4
Motivation
  • Stereophotogrammetry started with a focus on
    accuracy
  • Used to produce accurate maps from aerial
    photography
  • Relied on
  • Large, expensive, mechanical machines to align
    images and measure disparities
  • High resolution photographic film in precise
    cameras

5
Motivation
  • Large, expensive, mechanical machines to align
    images and measure disparities
  • High resolution photographic film in precise
    cameras

Wild A10
Santoni Model III
6
Motivation
  • then .. Along came digital cameras and computers
  • Low resolution toy applications became the
    focus!
  • Web cameras
  • cheap and
  • stream low resolution images into a machine
  • Potential for
  • tracking objects
  • limited accuracy real-time environment mapping
  • All you need is
  • a piece of wood,
  • 2 webcams and
  • some of Cliffs time to interface two cameras to
    a single PC

7
Stereophotogrammetry
  • Total cost
  • Webcams 2 x 100
  • Wood 2
  • Cliffs time priceless
  • Total 202
  • but
  • What can you really do with such a
    system? (Except pass COMPSCI 773 ?) ?
  • In reality,
  • not much
  • Resolution and accuracy too low!
  • Lenses distort images also
  • Not much stereophotogrammetry

Choose some expensive ones! Already done,
incremental cost 0
8
Stereophotogrammetry
  • But Im a CS graduate
  • Software can do anything!
  • Correct for lens distortion
  • Interpolate
  • Sub-pixel accuracy
  • but
  • Accuracy is related to the quality of the input
    data!
  • Correction factors have limited accuracy
  • Theyre derived from low accuracy images!
  • In reality,
  • Theres a limited amount you can do with poor
    input!

True signal enhancement usually relies on
multiple samples of the same signal! In image
processing, multiple samples from the same image
? lower resolution
9
Need for accuracy
  • Self-evident!
  • One example
  • Application Collision avoidance (or navigating
    through any dynamic environment)
  • Critical measurement
  • Relative velocity
  • Obtained from two scene measurements
  • z a ? 10
  • Then v ? Dz/Dt (z(t2) z(t1)) / (t2 t1 )
  • Error(v) ? Error(z(t1)) Error(z(t2))
    Error(t1) Error(t2) 10 10
    (negligible, lt0.1) 20
  • Would you sit in an autonomous vehicle at 100km/h
    which measured its distance to other vehicles
    with this accuracy?

10 error in z? High? Check the stereo test
images in the Middlebury database! Maximum
disparities 20 If dmeasured 10, error is 10
10
Photogrammetry Lab
Canon Digital SLR 50mm fixed focus
lens Measured distortion 1 pixel max in 3000 ?
2000 pixel image (subject to confirmation!)
  • High resolution cameras
  • Stable platforms / precise alignment
  • Error reduction at source
  • Rectification of images
  • Introduced errors

High quality, fixed focal length lens
Precise alignment
Precise, stable base
Verging optics
11
Stereo Camera Configuration
Points along these lines have the same L?R
displacement (disparity)
  • Standard Case Two cameras with parallel optical
    axes
  • Rays are drawn through each pixel in the image
  • Ray intersections represent points imaged onto
    the centre of each pixel
  • but
  • An object must fit into the Common Field of
    View

12
Depth Accuracy Parallel Camera Axes
  • Given an object of an extent, a, theres an
    optimum position for it!
  • Assuming baseline, b, can be varied
  • Common fallacy just increase b to increase
    accuracy

13
Stereo Camera Configuration
Points along these lines have the same L?R
displacement (disparity)
  • This result is easily understood if you consider
    an object of extent, a
  • To be completely measured, it must lie in the
    Common Field of View
  • but
  • place it as close to the camera as you can so
    that you can obtain the best accuracy, say at D
  • Now increase b to increase the accuracy at D
  • But you must increase D so that the object stays
    within the CFoV!
  • Detailed analysis leads to the previous curve and
    an optimum value of b ? a

a
D
b
14
Stereophotogrammetry vs Collision Avoidance
  • This result is more relevant for stereo
    photogrammetry
  • You are trying to accurately determine the
    geometry of some object
  • Its fragile, dangerous, and you must use
    non-contact measurement
  • For collision avoidance, you are more concerned
    with measuring the closest approach of an object
    (ie any point on the object!)
  • you can increase the baseline so that the
    critical point stays within the CFoV

Dcritical
15
Parallel Camera Axis Configuration
  • Accuracy depends on d - or the difference in
    image position in L and R images and in a digital
    system, on the number of pixels in d
  • Measurable regions also must lie in the CFoV
  • This configuration is rather wasteful
  • Observe how much of the image planes of the two
    cameras is wasted!

Dcritical
16
Evolution
  • Human eyes verge on an object to estimate its
    distance, ie the eyes fix on the object in the
    field of view

Configuration commonly used in stereo systems
Configuration discovered by evolution millions of
years ago
Note immediately that the CFoV is much larger!
17
Nothing is free!
  • Since the CFoV is much larger, more sensor pixels
    are being used and depth accuracy should increase
  • but
  • Geometry is much more complicated!
  • Position on the image planes of a point at (x,z)
    in the scene
  • Does the increased accuracy warrant the
    additional computational complexity?

xL f/p tan( arctan((b2x)/2z) - f )
f vergence angle
yL f/p tan( arctan((b-2x)/2z) - f )
18
Depth Accuracy
OK - better but its not exactly
spectacular! Is it worth the additional
computational load?
19
A minor improvement?
  • What happened?
  • As the cameras turn in, Dmin gets smaller!
  • If Dmin is the critical distance, D lt Dmin isnt
    useful!

This area is now wasted!
20
Depth Accuracy - Verging axes, increased f
Small vergence angle ? significantly better
depth accuracy
Note that at large f, the CFoV does not
extend very far!
21
Increased focal length
  • Lenses with large f
  • Thinner
  • Fewer aberrations
  • Better images
  • Cheaper?
  • Alternatively, lower pixel resolution can be used
    to achieve better depth accuracy ...

22
Zero disparity matching
  • With verging axes, at the fixation point, scene
    points appear with zero disparity (in the same
    place on both L and R images)
  • If the fixation point is set at some sub-critical
    distance (eg an early warning point), then
    matching algorithms can focus on a small range of
    disparities about 0
  • With verging axes, both ve and -ve disparities
    appear
  • Potential for fast, high performance matching
    focussing on this region

23
Non-parallel axis geometry
Locus for d -1
Locus for d 0
Locus for d 1
  • Points with the same disparity lie on circles now
  • For parallel axes, they lie on straight lines

24
Verging axis geometry
  • Points with the same disparity lie on
    Veith-Muller circles with the baseline as a chord

25
Zero disparity matching (ZDM)
  • Using a fixation point in some critical
    region introduces the possibility of faster
    matching
  • It can alleviate the statistical factor reducing
    matching quality
  • You search over a restricted disparity range
  • Several pyramidal matching techniques have been
    proposed (and success claimed!) for conventional
    parallel geometries
  • These techniques could be adapted to ZDM
  • Care
  • It has no effect on the other three factors!

26
Correspondence
  • OK .. now we have an optimum geometry ..
  • We just match up the images and
  • Sit back and enjoy the ride as our car weaves its
    way through the traffic!
  • Unfortunately, digital computers arent as good
    as human operators!
  • eg the ones who produce maps from aerial photos!

27
Stereo Photogrammetry
Pairs of images giving different views of the
scene
can be used to compute a depth (disparity) map ?
28
Sources of noise in automated
stereophotogrammetry
  • Signal noise
  • Electromagnetic interference (eg cross-talk)
  • Quantum behaviour of electronic devices (eg
    resistor shot-noise)
  • Quantization digitization of real-valued signals
  • Geometric sources
  • Discrete pixel sensors with finite area
  • Occlusions
  • Perspective distortion
  • Electronic sources
  • Intensity sensitivity variations between
    cameras (eg different optical or electronic gain
    settings)
  • Different dark noise levels
  • Optical sources
  • Non-uniform scattering (non-Lambertian sources)
  • Reflections and specular highlights
  • Angle dependent colour scattering (grating
    effects)
  • Lighting variation due to differing view angles
  • Next stage
  • 3D streaming video with custom processor support

29
Discrete Pixels
  • CMOS image sensors
  • Usually matrix of sensors with coloured dye mask
    arranged in BGRG arrangement
  • Values for each colour at each pixel position
    derived by interpolation
  • Weve already lost some accuracy in this process!
  • Cameras aim to produce pleasing pictures the
    interpolation process is not visible
  • Some cameras provide RAW output more suitable
    for photogrammetry ?

30
Rectification
  • Given all these sources of noise, its important
    to eliminate as many as possible at source!

Clearly, the smaller you can make the needed
corrections, the better the input to the matching
algorithms will be
This is what your camera gives you
Real lens distortion
This is what it should look like in image plane
coordinates
Calculate fractions of neighbouring pixel
intensities
This is what youd like to input to your stereo
matching program
31
Discrete Pixels
  • Pixelization noise
  • Assume a uniform green object on a red background
  • Pixels in the body of the objects projection
    will be saturated green
  • Pixels in the edge will have some RG ratio
  • Pixels in the same edge in the other image will
    generally have a different ratio
  • No possible match! (if youre trying for a
    perfect match)

32
Noise model
  • Each correction introduces some additional
    uncertainty (or noise)
  • Matching algorithms should work in the context of
    a noise model
  • Most matching algorithms assume ideal systems
  • Ideal has many connotations here!!
  • Concurrent Stereo Matching
  • Work in progress (Liu, Gimelfarb, Delmas,
    Morris)
  • Initially accepts all possible matches
  • Given a model of the noise (including all
    sources)
  • Ask Jiang to talk about it!

33
Tsukuba Stereo Test Image
  • Real image 384 ? 240
  • Hand generated disparity map
  • Very low resolution
  • Dmax 14

34
CSM Processing the Tsukuba Image Set
Step 1 Identify possible matches
d 5
d 14
d 8
d 6
Step 2 Form surfaces from local data
propagate back into scene
35
Competing techniques
  • Structure from motion
  • Motion is equivalent to baseline of stereo system
  • If accuracy of motion ? accuracy of baseline
  • Accuracy similar to parallel axis stereo
  • Generally relies on small movements to make
    matching problem tractable
  • Much smaller distance resolution

36
Competing techniques
  • Structured light
  • Requires two devices (camera and projector) of
    comparable resolution
  • Slower
  • Unique labeling of pixels requires O(log n)
    images
  • Projector is a real optical device too (with a
    real lens)
  • Pattern edges are only sharp over a limited depth
    of field
  • Efficient pixel labeling over a small depth range
    only
  • Closing lens aperture to increase depth of field
    not an option
  • Structured light ideas combined with stereo
    cameras
  • Most effective combination?

37
Competing techniques
  • Laser Range Finder
  • Produces depths directly from time of flight or
    phase difference measurements
  • Single device
  • High precision scanning optics required
  • Limits portability and robustness
  • Slow
  • One point at a time
  • Very high potential accuracy
  • Interferometer (l/n) accuracy possible
  • Time of flight systems limited by pulse length
  • High accuracy still possible!
  • Affected by reflectivity of targets
  • Sparse point clouds
  • Doesnt need texture in the scene!

38
Future work
  • Real-time environment maps
  • Very large numbers of trivial computations!
  • High degree of parallelism (esp CSM algorithm)!
  • Ideal application for custom hardware
  • Limited accuracy system is feasible on 2005 FPGA
    hardware
  • Current work
  • Efficient parallel algorithms
  • Concurrent Stereo Matching (EMMCVPR, Florida,
    Sept 2005)
  • Custom hardware implementation
  • Goal Depth maps at 30 fps video rates (3D
    movies!)
  • Efficient optical systems
  • Manufacturable
  • Robust
  • Next stage
  • 3D streaming video with custom processor support
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