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3D Vision. Interest Points. correspondence and alignment. Correspondence: matching points, patches, edges, or regions across images. ≈. correspondence and alignment. Alignment: solving the transformation that makes two things match better. T.

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3d vision

3D Vision

Interest Points


Correspondence and alignment
correspondence and alignment

  • Correspondence: matching points, patches, edges, or regions across images


Correspondence and alignment1
correspondence and alignment

  • Alignment: solving the transformation that makes two things match better

T



Example tracking points
Example: tracking points corresponds two views

x

x

x

frame 22

frame 0

frame 49

Your problem 1 for HW 2!


Human eye movements
Human eye movements corresponds two views


Human eye movements1
Human eye movements corresponds two views


Interest points
Interest points corresponds two views

  • Suppose you have to click on some point, go away and come back after I deform the image, and click on the same points again.

    • Which points would you choose?

original

deformed


Overview of keypoint matching
Overview of Keypoint Matching corresponds two views

1. Find a set of distinctive key- points

2. Define a region around each keypoint

A1

B3

3. Extract and normalize the region content

A2

A3

B2

B1

4. Compute a local descriptor from the normalized region

5. Match local descriptors


Goals for keypoints
Goals for Keypoints corresponds two views

Detect points that are repeatable and distinctive


Choosing interest points
Choosing interest points corresponds two views

Where would you tell your friend to meet you?


Moravec corner detector 1980
Moravec corner detector (1980) corresponds two views

  • We should easily recognize the point by looking through a small window

  • Shifting a window in anydirection should give a large change in intensity


Moravec corner detector
Moravec corner detector corresponds two views

flat


Moravec corner detector1
Moravec corner detector corresponds two views

flat


Moravec corner detector2
Moravec corner detector corresponds two views

flat

edge


Moravec corner detector3
Moravec corner detector corresponds two views

corner

isolated point

flat

edge


Moravec corner detector4

Window function corresponds two views

Shifted intensity

Intensity

Moravec corner detector

Change of intensity for the shift [u,v]:

Four shifts: (u,v) = (1,0), (1,1), (0,1), (-1, 1)

Look for local maxima in min{E}


Problems of moravec detector
Problems of Moravec detector corresponds two views

  • Noisy response due to a binary window function

  • Only a set of shifts at every 45 degree is considered

  • Responds too strong for edges because only minimum of E is taken into account

  • Harris corner detector (1988) solves these problems.


Harris corner detector
Harris corner detector corresponds two views

Noisy response due to a binary window function

  • Use a Gaussian function


Harris corner detector1
Harris corner detector corresponds two views

Only a set of shifts at every 45 degree is considered

  • Consider all small shifts by Taylor’s expansion


Harris corner detector2
Harris corner detector corresponds two views

Equivalently, for small shifts [u,v] we have a bilinear approximation:

, where M is a 22 matrix computed from image derivatives:


Harris corner detector3
Harris corner detector corresponds two views

Responds too strong for edges because only minimum of E is taken into account

  • A new corner measurement


Harris corner detector4
Harris corner detector corresponds two views

Intensity change in shifting window: eigenvalue analysis

1, 2 – eigenvalues of M

direction of the fastest change

Ellipse E(u,v) = const

direction of the slowest change

(max)-1/2

(min)-1/2


Harris corner detector5
Harris corner detector corresponds two views

2

edge 2 >> 1

Corner

1 and 2 are large,1 ~ 2;E increases in all directions

Classification of image points using eigenvalues of M:

1 and 2 are small;E is almost constant in all directions

edge 1 >> 2

flat

1


Harris corner detector6
Harris corner detector corresponds two views

Measure of corner response:

(k – empirical constant, k = 0.04-0.06)


Another view
Another view corresponds two views


Another view1
Another view corresponds two views


Another view2
Another view corresponds two views


Harris corner detector input
Harris corner detector (input) corresponds two views


Corner response r
Corner response R corresponds two views


Threshold on r
Threshold on R corresponds two views


Local maximum of r
Local maximum of R corresponds two views


Harris corner detector7
Harris corner detector corresponds two views


Harris detector summary
Harris Detector: Summary corresponds two views

  • Average intensity change in direction [u,v] can be expressed as a bilinear form:

  • Describe a point in terms of eigenvalues of M:measure of corner response

  • A good (corner) point should have a large intensity change in all directions, i.e. R should be large positive


Harris detector some properties

threshold corresponds two views

R

R

x(image coordinate)

x(image coordinate)

Harris Detector: Some Properties

  • Partial invariance to affine intensity change

  • Only derivatives are used => invariance to intensity shift I I+b

  • Intensity scale: I  aI


Harris detector some properties1
Harris Detector: Some Properties corresponds two views

  • Rotation invariance

Ellipse rotates but its shape (i.e. eigenvalues) remains the same

Corner response R is invariant to image rotation


Harris detector is rotation invariant
Harris Detector is rotation invariant corresponds two views

Repeatability rate:

# correspondences# possible correspondences


Harris detector some properties2
Harris Detector: Some Properties corresponds two views

  • But: non-invariant to image scale!

All points will be classified as edges

Corner !


Harris detector some properties3
Harris Detector: Some Properties corresponds two views

  • Quality of Harris detector for different scale changes

Repeatability rate:

# correspondences# possible correspondences


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