3D Vision

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# 3D Vision - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about ' 3D Vision' - dominique-derick

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Presentation Transcript

### 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

Example: tracking points

x

x

x

frame 22

frame 0

frame 49

Your problem 1 for HW 2!

Interest points
• 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

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

Detect points that are repeatable and distinctive

Choosing interest points

Where would you tell your friend to meet you?

Moravec corner detector (1980)
• 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

corner

isolated point

flat

edge

Window function

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
• 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

Noisy response due to a binary window function

• Use a Gaussian function
Harris corner detector

Only a set of shifts at every 45 degree is considered

• Consider all small shifts by Taylor’s expansion
Harris corner detector

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

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

Harris corner detector

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

• A new corner measurement
Harris corner detector

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 detector

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 detector

Measure of corner response:

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

Harris Detector: Summary
• 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

threshold

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 Properties
• 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

Repeatability rate:

# correspondences# possible correspondences

Harris Detector: Some Properties
• But: non-invariant to image scale!

All points will be classified as edges

Corner !

Harris Detector: Some Properties
• Quality of Harris detector for different scale changes

Repeatability rate:

# correspondences# possible correspondences