Corners and the Structure Tensor
From a windowed SSD to the second-moment matrix, its eigenvalues, and the Harris and Shi-Tomasi responses.
Key Terms
Windowed SSDTaylor ExpansionStructure TensorEigenvaluesHarris ResponseShi-Tomasi
Python Tools
OpenCVNumPyMatplotlib
Textbook Reference
Szeliski Ch.7
Topics Covered
- 1Windowed sum-of-squared-differences under a small image shift
- 2First-order Taylor expansion of the shifted patch
- 3The second-moment matrix M and its accumulation over a window
- 4Eigenvalue analysis: flat, edge, and corner regimes
- 5Harris response, Shi-Tomasi minimum-eigenvalue criterion, thresholding, and non-maximum suppression
Learning Outcomes
- Derive the structure tensor from a Taylor expansion of the windowed SSD
- Classify local image structure from the eigenvalues of M
- Compare the Harris and Shi-Tomasi corner criteria and their parameters
Lecture Infographics
2 image files
Lecture Infographics
Lecture PDFs
Corners and the Structure Tensor
The embedded PDF preview is disabled to reduce Vercel bandwidth usage. Open the lecture file directly in Google Drive for viewing, downloading, or presenting.