upgrade structures and migrate to nextra v4

content/CSE559A/CSE559A_L19.md

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+# CSE559A Lecture 19
+
+## Feature Detection
+
+### Behavior of corner features with respect to Image Transformations
+
+To be useful for image matching, “the same” corner features need to show up despite geometric and photometric transformations
+
+We need to analyze how the corner response function and the corner locations change in response to various transformations
+
+#### Affine intensity change
+
+Solution:
+
+- Only derivative of intensity are used (invariant to intensity change)
+- Intensity scaling
+
+#### Image translation
+
+Solution:
+
+- Derivatives and window function are shift invariant
+
+#### Image rotation
+
+Second moment ellipse rotates but its shape (i.e. eigenvalues) remains the same
+
+#### Scaling
+
+Classify edges instead of corners
+
+## Automatic Scale selection for interest point detection
+
+### Scale space
+
+We want to extract keypoints with characteristic scales that are equivariant (or covariant) with respect to scaling of the image
+
+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
+
+A particularly convenient response function is given by the scale-normalized Laplacian of Gaussian (LoG) filter:
+
+$$
+\nabla^2_{norm}=\sigma^2\nabla^2\left(\frac{\partial^2}{\partial x^2}g+\frac{\partial^2}{\partial y^2}g\right)
+$$
+
+![Visualization of LoG](https://notenextra.trance-0.com/CSE559A/Laplacian_of_Gaussian.png)
+
+#### Edge detection with LoG
+
+![Edge detection with LoG](https://notenextra.trance-0.com/CSE559A/Edge_detection_with_LoG.png)
+
+#### Blob detection with LoG
+
+![Blob detection with LoG](https://notenextra.trance-0.com/CSE559A/Blob_detection_with_LoG.png)
+
+### Difference of Gaussians (DoG)
+
+DoG has a little more flexibility, since you can select the scales of the Gaussians.
+
+### Scale-invariant feature transform (SIFT)
+
+The main goal of SIFT is to enable image matching in the presence of significant transformations
+
+- To recognize the same keypoint in multiple images, we need to match appearance descriptors or "signatures" in their neighborhoods
+- Descriptors that are locally invariant w.r.t. scale and rotation can handle a wide range of global transformations
+
+### Maximum stable extremal regions (MSER)
+
+Based on Watershed segmentation algorithm
+
+Select regions that are stable over a large parameter range