• Which of the following(s) is/are parameters required for Detection?
– A threshold to exclude the pixels with low f values – The window size to compute Harris matrix
– The value of (u,v) to move the window
– The sigma for Gaussian filter
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Local features: main components
1) Detection: Identify the interest points
2) Description: Extract vector feature descriptor surrounding each interest point.
3) Matching:Determine correspondence between descriptors in two views
x =[x(1),,x(1)] 11d
x =[x(2),,x(2)] 21d
Image transformations • Geometric
• Photometric Intensity change
Harris detector: Invariance properties — Image translation
• Derivatives and window function are shift-invariant
Corner location is covariant w.r.t. translation
Harris detector: Invariance properties — Image rotation
Corner location is covariant w.r.t. rotation
Harris detector: Invariance properties – Affine intensity change
I→a I + b • Only derivatives are used =>
invariance to intensity shift I → I + b • Intensity scaling: I → a I
RR threshold
x (image coordinate)
x (image coordinate)
Partially invariant to affine intensity change
: Invariance Properties • Scaling
All points will be classified as edges
Not invariant to scaling
Scale invariant detection
Suppose you’re looking for corners
Key idea: find scale that gives local maximum of f – in both position and scale
– One definition of f: the Harris operator
Lindeberg et al, 1996 Lindeberg et al., 1996
Implementation
• Instead of computing f for larger and larger windows, we can implement using a fixed window size with a Gaussian pyramid
(sometimes need to create in- between levels, e.g. a 3⁄4 -size image)
• How to make the corner detection robust to scale change?
– Use a larger window size to compute Harris matrix – Randomly select multiple window size to compute
Harris matrix
– Compute the Harris matrix for each of Gaussian pyramid image using different window sizes
– Compute the Harris matrix for each of Gaussian pyramid image using the same window size
• What does window size tell after the region under a window is detected as the corner?
– The region inside the window has corner
– The region outside the window has no corner – The region inside the window has an object
– The scale in which the region becomes corner
– The region where local feature should be extracted from
Feature extraction: Corners and blobs
Another common definition of f • The Laplacian of Gaussian (LoG)
2 g = 2 g + 2 g x2 y2
Laplacian of Gaussian • “Blob” detector
• Find maxima and minima of LoG operator in space and scale
Find local maxima in position-scale space
Lxx()+Lyy() 3 2
List of (x, y, s)
K. Grauman, B. Leibe
Scale-space blob detector: Example
Scale-space blob detector: Example
Scale-space blob detector: Example
Feature descriptors We know how to detect good points
Next question: How to match them?
Answer: Come up with a descriptor for each point, find similar descriptors between the two images
Feature descriptors We know how to detect good points
Next question: How to match them?
Lots of possibilities (this was a popular research area)
– Simple option: match square windows around the point
– Popular approach: SIFT
• , UBC http://www.cs.ubc.ca/~lowe/keypoints/
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