72 lines
2.4 KiB
Markdown
72 lines
2.4 KiB
Markdown
# CSE559A Lecture 19
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## Feature Detection
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### Behavior of corner features with respect to Image Transformations
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To be useful for image matching, “the same” corner features need to show up despite geometric and photometric transformations
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We need to analyze how the corner response function and the corner locations change in response to various transformations
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#### Affine intensity change
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Solution:
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- Only derivative of intensity are used (invariant to intensity change)
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- Intensity scaling
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#### Image translation
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Solution:
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- Derivatives and window function are shift invariant
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#### Image rotation
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Second moment ellipse rotates but its shape (i.e. eigenvalues) remains the same
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#### Scaling
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Classify edges instead of corners
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## Automatic Scale selection for interest point detection
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### Scale space
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We want to extract keypoints with characteristic scales that are equivariant (or covariant) with respect to scaling of the image
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Approach: compute a scale-invariant response function over neighborhoods centered at each location $(x,y)$ and a range of scales $\sigma$, find scale-space locations $(x,y,\sigma)$ where this function reaches a local maximum
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A particularly convenient response function is given by the scale-normalized Laplacian of Gaussian (LoG) filter:
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$$
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\nabla^2_{norm}=\sigma^2\nabla^2\left(\frac{\partial^2}{\partial x^2}g+\frac{\partial^2}{\partial y^2}g\right)
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$$
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#### Edge detection with LoG
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#### Blob detection with LoG
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### Difference of Gaussians (DoG)
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DoG has a little more flexibility, since you can select the scales of the Gaussians.
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### Scale-invariant feature transform (SIFT)
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The main goal of SIFT is to enable image matching in the presence of significant transformations
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- To recognize the same keypoint in multiple images, we need to match appearance descriptors or "signatures" in their neighborhoods
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- Descriptors that are locally invariant w.r.t. scale and rotation can handle a wide range of global transformations
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### Maximum stable extremal regions (MSER)
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Based on Watershed segmentation algorithm
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Select regions that are stable over a large parameter range
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