Date |
Content of the Lecture |
Assignments/Readings/Notes |
| 14/09 (Wed) |
-
Face recognition: intro; Principal components analysis for face recognition (eigenfaces): intro, concept of covariance matrix, description of algorithm and its computational complexity; a faster
algorithm for PCA on a small (N) number of large-sized images (N << d case).
|
- Slides
- Read section 3.8.1 of "Pattern Classification" by Duda and Hart (2nd edition)
-
Information about projects: select topic by 5th October (read the instructions!)
|
| 16/09 (Fri) |
-
Derivation of the PCA algorithm for k = 1 based on the criterion of minimizing reconstruction error; derivation sketch for k >= 2 directions;
concept of global eigenspace versus person-specific eigenspace; cross-validation method for choice of k
|
- Slides
- Read section 3.8.1 of "Pattern Classification" by Duda and Hart (2nd edition)
-
Information about projects: select topic by 5th October (read the instructions!)
|
| 17/09 (Sat) |
-
Clarifications regarding vector derivatives and Lagrange multipliers in the PCA derivation; application of PCA to compression; 3D face recognition; final discussions
about the eigenfaces algorithm;
- Introduction to the Singular Value decomposition: basic properties, applications to image compression and the Eckart Young theorem (role of SVD in
low rank approximation)
|
|
| 17/09 (Sat) |
-
SVD properties: inverse, determinant, Frobenius norm, geometric interpretation
- Implementing eigenfaces using SVD
- Other applications of SVD
- Discrete Fourier transform: genesis
- Matrix and vector interpretation of DFT, DFT basis matrix
|
|
| 17/09 (Sat) |
-
SVD properties: inverse, determinant, Frobenius norm, geometric interpretation
- Implementing eigenfaces using SVD
- Other applications of SVD
- Discrete Fourier transform: genesis
- Matrix and vector interpretation of DFT, DFT basis matrix
|
|
| 04/10 (Tue) |
- DFT properties, discrete (circular) convolution and importance of zero-padding, convolution using discrete Fourier transforms, Fast Fourier transform algorithm
- 2D DFT, properties of 2D DFT - shifting and rotation, importance of DFT phase
|
|
| 07/10 (Fri) |
- Displaying the DFT - concept of "fftshift"
- Properties of the DFT of natural images (strong low frequency components), weaker high frequency components, DFT of some simple images
- 2D Convolution and 2D convolution theorem
- Fourier domain filtering: low pass filter (ideal LPF, Gaussian LPF, Butterworth LPF); high pass filter (idea, Gaussian, butterworth); gradient operations as HPFs; notch filters with examples
- Limitations of the DFT
|
|
| 14/10 (Fri) |
- Algorithm for applying the frequency domain filter: the importance of zero-padding
- Boosting higher frequencies using frequency domain filters
- Hybrid image generation using high pass and low pass filters
- Image restoration: problem definition and mathematical models, difference from image enhancement
- Defocus and motion blur: derivation of frequency response of motion blur kernel
- Inverse filter for image restoration and its limitations
|
|
| 15/10 (Sat) |
- Inverse filter for image restoration and its limitations
- Concept of Wiener filter: definition, criterion of optimization, assumptions, formula and interpretation of the formula as a method to overcome the limitations of the inverse filter; interactive Wiener filter (derivation to be done in the next class)
- Image deblurring in computational photography using spread-spectrum filters: coded exposure photography and the flutter shutter camera
- Non-local PCA algorithm for image denoising
|
|
| 18/10 (Tue) |
- Non-local PCA algorithm for image denoising - complete derivation
- Concept of Wiener filter: derivation of Wiener filter
- Extension of the same derivation to the case of non-local PCA
- Regularized restoration using penalty on gradients
|
|
| 19/10 (Wed) |
- Image compression - problem statement; lossy and lossless compression with examples
- Overview of JPEG algorithm: encoder and decoder; quality factor in JPEG
- Discrete Cosine Transform in 1D and 2D and its use in JPEG; comparison with DFT; matrix view of DCT
|
|
| 21/10 (Fri) |
- Discrete Cosine Transform in 1D and 2D and its use in JPEG; comparison with DFT; matrix view of DCT
- Mathematical relationship between DFT and DCT (code)
- The relationship between DCT and PCA - reasons why DCT is used in the JPEG algorithm (code)
|
|
| 25/10 (Tue) |
- Quantization step in JPEG; quantization matrices and their (experimental) derivation
- Lossless encoding in JPEG: Huffman encoding, zig-zag ordering of quantized DCT coefficients, run-length encoding and the concept of triples
- JPEG header, block diagram of JPEG encoder and decoder
- JPEG for color images: YCbCr scheme (decorrelated color space) and its relationship with PCA
|
|
| 26/10 (Wed) |
- MPEG video compression standard: overview of MPEG-1
- Concept of predictive coding and its use in video compression; concept of motion compensation and motion compensated predictive coding; concept of P, B, I frames in MPEG
|
- Slides
- Read chapter 8.2.9 from the textbook (subsection on predictive coding) up to but not including lossy predictive coding
|
| 28/10 (Fri) |
- Color spaces: RGB, CMY(K), HSI and their usage scenarios; Human color perception - rods and cones
- Concept of hue in the HSI scheme - hue as an illumination invariant; disadvantages of hue
|
- Slides
- Read chapter 6 of the textbook.
|
| 4/11 (Fri) |
- Color image processing: histogram equalization, bilateral filtering, concept of edge/gradient in a color image
- Concept of hyperspectral and multispectral image; PCA on the pixel values of a hyperspectral image; visualization of hyperspectral images
- Color image demosaicing: problem definition, concept of CFA - Bayer pattern as example of CFA; description of demosaicing algorithm implemented by MATLAB
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