1
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- Problem: Match when viewing conditions change a lot.
- Lighting changes: brightness constancy false.
- Viewpoint changes: appearance changes, many viewpoints.
- One Solution: Match using edge-based features.
- Edges less variable to lighting, viewpoint.
- More compact representation can lead to efficiency.
- Match image or object to image
- If object, matching may be asymmetric
- Object may be 3D.
- Line finding was an example: line=3Dobject; points=3Dimage.
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2
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3
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- An Image is a set of 2D geometric features, along with positions.
- An Object is a set of 2D/3D geometric features, along with positions=
.
- A pose positions the object relative to the image.
- 2D Translation; 2D translation + rotation; 2D translation, rotation=
and
scale; planar or 3D object positioned in 3D with perspective or sca=
led
orth.
- The best pose places the object features nearest the image features<=
/li>
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4
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- Build feature descriptions
- Search possible poses.
- Can search space of poses
- Or search feature matches, which produce pose
- Transform model by pose.
- Compare transformed model and image.
- Pick best pose.
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5
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- Already discussed finding features.
- First discuss picking best pose since this defines the problem.
- Second discuss search methods appropriate for 2D.
- Third discuss transforming model in 2D and 3D.
- Fourth discuss search for 3D objects.
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6
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7
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- We look at this first, since it defines the problem.
- Again, no perfect measure;
- Trade-offs between veracity of measure and computational
considerations.
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8
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9
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10
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- Sum a different distance
- f(d) =3D d2
- or Manhattan distance.
- f(d) =3D 1 if d < threshold, 0 otherwise.
- This is called bounded error.
- Use maximum distance instead of sum.
- This is called: directed Hausdorff distance.
- Use other features
- Corners.
- Lines. Then position =
and
angles of lines must be similar.
- Model line may be subset of image line.
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11
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- Enforce each image feature can match only one model feature.
- Enforce continuity, ordering along curves.
- These are more complex to optimize.
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12
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- Already discussed finding features.
- First discuss picking best pose since this defines the problem.
- Second discuss search methods appropriate for 2D.
- Third discuss transforming model in 2D and 3D.
- Fourth discuss search for 3D objects.
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13
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- Simplest approach is to try every pose.
- Two problems: many poses, costly to evaluate each.
- We can reduce the second problem with:
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14
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15
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- Compute once.
- Fast algorithms to compute it.
- Makes Chamfer Matching simple.
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16
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17
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- It’s only done once, per problem, not once per pose.
- Basically a shortest path problem.
- Simple solution passing through image once for each distance.
- First pass mark edges 0.
- Second, mark 1 anything next to 0, unless it’s already
marked. Etc….=
li>
- Actually, a more clever method requires 2 passes.
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18
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- Match enough features in model to features in image to determine pos=
e.
- Examples:
- match a point and determine translation.
- match a corner and determine translation and rotation.
- Points and translation, rotation, scaling?
- Lines and rotation and translation?
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19
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20
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- Like Hough Transform, but for general shapes.
- Example: match one point to one point, and for every rotation of the
object its translation is determined.
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21
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- Already discussed finding features.
- First discuss picking best pose since this defines the problem.
- Second discuss search methods appropriate for 2D.
- Third discuss transforming model in 2D and 3D.
- Fourth discuss search for 3D objects.
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22
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- Solve I =3D S*P.
- In Structure-from-Motion, we knew I.
- In Recognition, we know P.
- This is just set of linear equations
- Ok, maybe with some non-linear constraints.
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23
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24
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25
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26
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27
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- A bit trickier. Some
results:
- 2D rotation and translation.
Need 2 points.
- 3D scaled orthographic. Need
3 points, give 2 solutions.
- 3D perspective, camera known.
Need 3 points. =
Solve
4th degree polynomial.&n=
bsp;
4 solutions.
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28
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29
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30
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- Find features in model and image.
- Match enough to determine pose.
- Such as 3 points for planar object, scaled orthographic projection.=
- Determine pose.
- Project rest of object features into image.
- Look to see how many image features they match.
- Example: with bounded error, count how many object features project
near an image feature.
- Repeat steps 2-5 a bunch of times.
- Pick pose that matches most features.
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31
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32
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- Previous approach will work.
- But slow. RANSAC consi=
ders n3m3
possible matches. Abou=
t m3
correct.
- Solutions:
- Grouping. Find featur=
es
coming from single object.
- Viewpoint invariance. Match
to small set of model features that could produce them.
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33
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34
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- Connected lines likely to come from boundary of same object.
- Boundary of object often produces connected contours.
- Different objects more rarely do; only when overlapping.
- Connected image lines match connected model lines.
- Disconnected model lines generally don’t appear connected.
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35
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- Parallelism
- Convexity
- Common region
- ….
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36
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37
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38
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39
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40
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41
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42
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43
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- Smooth 3D objects.
- Can we find the guaranteed optimal solution?
- Indexing with invariants.
- Error propagation.
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