Date |
Content of the Lecture |
Assignments/Readings/Notes |
| Lectures 1 and 2 |
Principal Components Analysis
- 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).
|
- Check moodle: Slides
- Read section 3.8.1 of "Pattern Classification" by Duda and Hart (2nd edition)
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Information about projects: select topic by 12th October (read the instructions!)
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| Lecture 3 |
- Derivation of PCA algorithm for k=1 case, sketch of proof for k=2 case
- Eigenvalue decay in eigenfaces derived from well-aligned face images
- Choice of k in PCA
|
- Slides: check moodle
- Read section 3.8.1 of "Pattern Classification" by Duda and Hart (2nd edition)
-
Information about projects: select topic by 12th October (read the instructions!)
|
| Lecture 4 |
- Person or pose specific eigenfaces
- Illumination invariance in face recognition: Removal of top three eigenfaces
- PCA for compression of sets of similar images
- A word about face recognition under lighting variations; 3D face recognition; cross-modality face recognition
|
- Slides
- Read section 3.8.1 of "Pattern Classification" by Duda and Hart (2nd edition)
-
Information about projects: select topic by 12th October (read the instructions!)
|
| Lectures 5 and 6 |
- Clarification of mathematical derivations: orthonormality of eigenvectors of symmetric matrix, why covariance matrix is SPD, Lagrange multipliers, concept of vector derivatives (especially of expressions such as e^tSe and e^te w.r.t. vector e)
Singular Value Decomposition
- Singular value decomposition (SVD): varied expressions
- Application of SVD for image compression
- Eckart Young theorem for low rank approximation using SVD
- SVD: geometric interpretation; applications in linear algebra
- PCA/eigenfaces algorithm using SVD
|
- Slides for PCA and SVD: check moodle.
- Read section 3.8.1 of "Pattern Classification" by Duda and Hart (2nd edition)
|
| Lecture 6 |
Discrete Fourier Transform
- Discrete fourier transform (DFT): Fourier transform of a sampled version of a continuous signal, frequency-domain sampling of such a Fourier transform to get the DFT
- Orthonormality of DFT matrix; reason for equal number of time domain and frequency domain samples
- Implicit periodicity in DFT and IDFT, other basic properties of the DFT
- Discrete (circular) convolution - wrap-around issues and zero-padding, implementation using DFT and IDFT
- 2D-DFT and IDFT, basic properties, importance of phase in Fourier transforms
|
|
| 12/10 (Sat) |
- Fast Fourier transform (FFT) algorithm
- 2D-DFT and IDFT, basic properties, importance of phase in Fourier transforms
- Interpretation of DFT of images; power law in natural images
- Visualization of 2D DFT
- Fourier rotation theorem
- Frequency domain filtering: ideal low pass filter (LPF) and ringing artifacts, Butterworth and Gaussian LPF; ideal, Butterworth and Gaussian high pass filters (HPF);
- Gaussian kernel - in spatial and Fourier domain
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|
| 15/10 (Tue) |
- Frequency domain filtering: ideal low pass filter (LPF) and ringing artifacts, Butterworth and Gaussian LPF; ideal, Butterworth and Gaussian high pass filters (HPF); Notch filters
- Gaussian kernel - in spatial and Fourier domain
- Applications of Fourier transform: Hybrid images
- Introduction to tomography: Fourier slice theorem (projection slice theorem)
- Fourier transforms in action: optics (phase retrieval), Magnetic resonance imaging (MRI) -- brief mention only
|
|
| 18/10 (Fri) |
- Introduction to image restoration - differences between enhancement and restoration
- Introduction to blur models - spatially varying and spatially invariant blur, defocus blur
- Blur models: defocus blur, motion blur, derivation of motion blur frequency response for in-plane constant velocity translational motion, interpretation of fourier transform of a motion blurred image
- Inverse filter: definition, limitations
- Code blur camera (see code demo), flutter shutter camera - spread spectrum filtering
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| 19/10 (Sat) |
- Concept of Wiener filter and formula, interpretation of the formula
- Derivation of Wiener filter
- Regularized restoration using gradient penalty terms
- PCA for image denoising: algorithm description and sample outputs
- Derivation of Wiener filter for PCA denoising
|
|
| 22/10 (Tue) |
Image Compression
- Discrete cosine transform - definition and basic properties
- Discrete cosine transform - definition and basic properties
- 1D and 2D DCT - concept of Kronecker product of 1D DCT bases to yield a 2D DCT basis
- Comparison between DCT and DFT: DCT computation using fft (see code), DCT energy compaction
- Relationship between DCT and PCA - see code here.
|
|
| 25/10 (Fri) |
- DCT and first order stationary Markov processes
- Quantization in JPEG and its relation to the quality factor (Q); principles for derivation of quantization matrix
- Huffman encoding and run length encoding in JPEG
- JPEG decoder step
- Modes of JPEG encoding and decoding: progressive, sequential
- JPEG for color image compression: YCbCr color model and its relation to PCA on RGB values
|
|
| 29/10 (Tue) |
- Video compression: MPEG standard, predictive coding
- Motion compensated rediduals
- Concept of I,B,P frames
|
|
| 1/11 (Fri) |
Color Image Processing and Color Models
- Color models: RGB, CMY(K), HSI, YCbCr, merits and demerits of hue
- Human visual system: rods and cones
- Discussion about hue and illumination models with specular, ambient and diffuse lights
|
|
| 5/11 (Tue) |
- Discussion about hue and illumination models with specular, ambient and diffuse lights
- Color image processing: bilateral filtering, histogram equalization, color image gradients
- YCbCr color space
|
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| 8/11 (Fri) |
- Hyperspectral images: visualization, utility
- Color Image demosaicing
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