Date |
Content of the Lecture |
Assignments/Readings/Notes |
| 18/09 (Tue) |
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).
|
- 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!)
|
| 25/09 (Tue) |
- Derivation of PCA algorithm for k=1 case, sketch of proof for k=2 case
- Person or pose specific eigenfaces
- Choice of k in PCA
- Illumination invariance in face recognition: Removal of top three eigenfaces
|
- 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!)
|
| 28/09 (Fri) |
- 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)
- PCA for compression of sets of similar images
- A word about face recognition under lighting variations; 3D face recognition
|
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| 5/10 (Fri) |
Singular Value Decomposition (SVD)
- Singular value decomposition (SVD): varied expressions
- Application of SVD for image compression
- Eckart Young theorem for low rank approximation using SVD, geometric interpretation, a few mathematical properties
- SVD applications
Discrete Fourier Transform (DFT)
- 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
- Implicity periodicity in DFT and IDFT, other basic properties of the DFT
|
|
| 9/10 (Tue) |
- Discrete (circular) convolution - wrap-around issues and zero-padding, implementation using DFT and IDFT
- 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
|
|
| 12/10 (Fri) |
- 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); Notch filters
- Gaussian kernel - in spatial and Fourier domain
- Applications of Fourier transform: Hybrid images
- Introduction to tomography: Fourier slice theorem (projection slice theorem)
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|
| 16/10 (Tue) |
- Introduction to tomography: Fourier slice theorem (projection slice theorem)
- Fourier transforms in action: optics (phase retrieval), Magnetic resonance imaging (MRI)
Image Restoration
- 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
|
|
| 20/10 (Sat) |
- Inverse filter: definition, limitations
- Concept of Wiener filter and formula, interpretation of the formula
- Derivation of Wiener filter
- Regularized restoration using gradient penalty terms
|
|
| 23/10 (Tue) |
- PCA for image denoising: algorithm description and sample outputs
- Derivation of Wiener filter for PCA denoising
Image Compression
- Introduction to lossless and lossy compression
- Introduction to JPEG standard - basic steps of JPEG, concept of quality factor
|
|
| 26/10 (Fri) |
- 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
|
|
| 30/10 (Tue) |
- 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
|
|
| 2/11 (Fri) |
- Video compression: MPEG standard, predictive coding
- Motion compensated rediduals
- Concept of I,B,P frames
|
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| 3/11 (Sat) |
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
|
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| 9/11 (Fri) |
- Color image histogram equalization and bilateral filtering
- Concept of edges in a color image
- Hyperspectral abd multispectral images: visualization, PCA for hyperspectral/multispectral image compression
- Concept of color filter array (CFA)
- Demosaicing algorithm by Malvar,He and Cutler
- A note on when demosaicing is performed in the camera pipeline
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