Geometric Computer Vision
Notes for CMSC733 Classical and Deep Learning Approaches for Geometric Computer Vision taught by Prof. Yiannis Aloimonos.
Convolution and Correlation
See Convolutional neural network.
Traditionally, fixed filters are used instead of learned filters.
Edge Detection
Two ways to detect edges:
- Difference operators
- Models
Image Gradients
- Angle is given by \(\displaystyle \theta = \arctan(\frac{\partial f}{\partial y}, \frac{\partial f}{\partial x})\)
- Edge strength is given by \(\displaystyle \left\Vert (\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}) \right\Vert\)
Sobel operator is another way to approximate derivatives:
\(\displaystyle
s_x =
\frac{1}{8}
\begin{bmatrix}
-1 & 0 & 1\\
-2 & 0 & 2\\
-1 & 0 & 1
\end{bmatrix}
\) and
\(\displaystyle
s_y =
\frac{1}{8}
\begin{bmatrix}
1 & 2 & 1\\
0 & 0 & 0\\
-1 & -2 & -1
\end{bmatrix}
\)
You can smooth a function by convolving with a Gaussian kernel.
- Laplacian of Gaussian
- Edges are zero crossings of the Laplacian of Gaussian convolved with the signal.