COMPUTER VISION

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COMPUTER VISION

• Visually Guided Autonomous Robot Navigation
• By
• Punarjay Chakravarty (AUSCC 2003)

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(No Transcript)
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GOAL Autonomous Detection of Objects in
Cyclops Field of View
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Vision

• Problem Convert real world 3-D information into
  one that computer can understand.
• Spectra
• Visible
• IR
• Ultrasound
• Laser Ranging
• Concentrate on visible.

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Converting 3-D object to 2-D info

• Colour image of object formed on cameras focal
  plane.
• Convert colour image to grayscale.
• Convert grayscale image to binary (ones and
  zeros).
• 3-D object described by 2-D array much easier
  to handle perform Mathematical operations on
  it.

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Binary Images

• How to convert grayscale image to binary image?
• Use Edge Detection
• Basic Idea Region of sharp increase in
  intensity of grayscale image is an edge.

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Edge Detection

• Gradient has large peak centred around edge.
• Detect edge wherever gradient exceeds
  pre-definded threshold.

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Colour -gt Grayscale -gt Binary
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Binary Correlation

• Mathematical process for identifying region in
  image that looks most like given reference
  sub-image (template).

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Binary Correlation

• Template overlaid on image at many different
  locations.
• At each location, goodness of match evaluated.
• Location with best match is the location of
  object in image.
• Matching at each location involves logical
  AND-ing of template with image.
• Resulting Pixel 1, if pixels in image and
  template are both one.

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Binary Correlation

• Image M x N, Template m x n.
• No. of Translations (M-m1)(N-n1)
• For 352 x 288 image, 97 x 106 template 46,848
  translations.
• Matlab takes 469 seconds ! (0.01 sec per block
  AND operation on 733 MHz machine)

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Need to smoothen the edges

• Methods like correlation that use edge-pixels
  directly sensitive to noise.
• Solution smoothen the edges of the edge-image.
• Use the DISTANCE TRANSFORM

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Distance Transform

• Operator normally only applied to binary images.
• Input Binary edge image.
• Output Grayscale image with graylevel intensity
  of each pixel that is set to off in the edge
  image changed to show the distance to its closest
  edge (on) pixel.
• Distance Euclidean/approximation to Euclidean

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Distance Transform

• DTs are global transformations.
• Reduce computational complexity consider
  edge-pixels in immediate neighbourhood of edge
  pixels (local transform).
• DT at a pixel can be deduced from the values at
  its neighbors.

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DT Algorithm

• Start with zero-infinity image set each edge
  pixel to 0 and each non-edge pixel to infinity.
• Make 2 passes over the image with a mask
• 1. Forward, from left to right and top to bottom
• 2. Backward, from right to left and from bottom
  to top.

Backward Mask
Forward Mask
d1 and d2, are added to the pixel values in the
distance map and the new value of the zero pixel
is the minimum of the five sums.
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DT Algorithm

• For each position of mask on image,
• Vi,j minimum(vi-1,j-1d2,vi-1,j
  d1,vi-,j1d2,
• vi,j-1d1,vi,j)

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Matching Meausures

• Smoothed edge image obtained.
• Matching measures between image and model
• 1. Chamfer Distance.
• 2. Hausdorff Distance.
• 3. Simplified Hausdorff Distance
• (DT Binary Correlation).

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Chamfer Matching

• Edge-model translated over Distance Image.
• At each tranlsation, edge model superimposed on
  distance image.
• Average of distance values that edge model hits
  gives Chamfer Distance.
• Perfect fit between Edge model and Distance Image
  will give Chamfer Distance of zero.
• Root mean square Chamfer Distance chosen
• Chamfer Distance
• n
• 1/3(v(S vi2)/n)
• i1
• Vi distance value, n number of points

Chamfer Distance 1.12
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Hausdorff Distance

• Given two sets of points and
• the Hausdorff Distance is defined as
• where
• is any metric between the points
  a and b.
• For simplicity,
  
• which is the Euclidian distance between a(x1,y1)
  and b(x2,y2)

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Forward Hausdorff Distance

• Forward Hausdorff Distance
• The Forward Hausdorff distance, h(A,B), measures
  the degree of mismatch between two sets, as it
  reflects the distance of the point of A that is
  farthest from any point of B.
• Intuitively If h(A,B) d, then every point of
  A must be within distance d of some point of B.

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Forward Hausdorff example

• Consider the point sets Aa1,a2,a3 and
  Bb1,b2,b3.
• 1.Find a point in A thats the farthest away from
  any point in B.
• 2. h(A,B) is the distance from this point to
  the closest point in B.

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Forward Hausdorff example

• a2 is the point of A that is farthest away from
  any point in B (b2).

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Forward Hausdorff example

• d is the distance from a2 to the closest point in
  B (b3).
• This is the Forward Hausdorff Distance between
  point sets A and B.

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Forward Hausdorff for 2 similar point sets

• For 2 similar point sets that are correctly
  aligned, h(A,B) becomes small.

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Searching for object in image
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Translation of object over image
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h(A,B) will be minimum when model is perfectly
aligned with object in image
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Brute force algorithm to compute h(A,B)

• 1. h 0
• 2. for every point ai of A,
• 2.1 shortest Inf
• 2.2 for every point bj of B
• dij ai bj
• If dij lt shortest then shortest dij
• 2.3 If shortest gt h then h shortest

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Forward Hausdorff Distance in terms of set
containment

• Let ,where is a disk
  of radius d and is the Minkowski sum.
• (For two point sets P and Q,
  
• )
• By definition if and only if
  ,
• because in order for every point of A to be
  within distance d of B it must be contained in
  B.
• B is also called the dilated version of B.
• B has been dilated by d

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Dilation of B by d to get B.

• Intuitively, B' is the set obtained by replacing
  each point of B with a disk of radius d, and
  taking the union of all of these disks.

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Identify model M in image I

• Use the Hausdorff distance to identify instances
  of some model M in some image I.
• Seek translation for which h(I, Mt) lt d
• Method Dilation by d and correlation.

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Simpified Hausdorff Dilation and Correlation

• Dilate the image I by d to get
• Then compute the correlation of Mt with I (the
  logical and of Mt and I).
• For each translation t of M w.r.t I, the
  correlation determines p the number of points of
  Mt superimposed with I.

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Distance Transform as a method to compute dilated
images

• To search for the object in the image, we search
  for a minimum radius d that the image set I must
  be dilated with to cover k/m points of the model
  set M. (k/m threshold fraction)
• Could involve many dilations of image I, which is
  computationally quite expensive.
• Solution Distance Transform the image and then
  threshold it by different amounts to form
  different dilated image sets.

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Image pre-processing
Original Image
Edge Image
Dilation (d 4)
DT Image
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Different dilations
Dilation (d 8)
Dilation (d 20)
DT only needs to be computed once. dilation by
any factor available from this!
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Image and Object Template
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Our Algorithm

• Off-line Create a database of edge detected
  object-images.
• On-line
• Capture a snapshot of what the robot is seeing.
  
• Perform edge-detection and the Distance Transform
  on it, and threshold-ing to get a dilated edge
  detected picture of what the robot is seeing.
• Translate and position the model at various
  positions of the image, and calculate the Forward
  Hausdorff measure for each position of the model
  over the image.
• The best match Translation with the maximum
  Hausdorff measure.

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ALGORITHM
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Summary

• Target recognition
• Colour -gt Grayscale -gt Edge Image (binary).
• Perform Distance Transform on binary image.
• Match image with model using similarity measure
• Chamfer Distance
• Hausdorff Distance.

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Olympus Mons, Mars 2012 A.D.
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References

• www-cgrl.cs.mcgill.ca (Hausdorff Distance)
• www.cs.cornell.edu (Hausdorff Distance)
• www.tele.ucl.ac.be (Chamfer Distance)
• www.gavrila.net (Chamfer Distance)
• www-ece.rice.edu (Edge Detection)