Geometric Computer Vision

Notes for CMSC733 Classical and Deep Learning Approaches for Geometric Computer Vision taught by Prof. Yiannis Aloimonos.

• Course webpage

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.