Date 
Content of the Lecture 
Assignments/Readings/Notes 
16/09 (Tue) 

Face recognition: intro; Principal components analysis for face recognition (eigenfaces): intro, concept of covariance matrix, description of algorithm and its computational complexity


19/09 (Fri) 

Faster version of eigenfaces algorithm; meaning of principal components analysis (PCA); derivation of PCA and hence eigenfaces; selection of 'k' in eigenfaces algorithm


23/09 (Tue) 

Personspecific eigenspaces; explanation of Lagrange multipliers; PCA for compression;
Introduction to the Singular value decomposition; applications in image compression; Eckart Young theorem introduction


26/09 (Fri) 

SVD, SVD and its relationship to eigenvectors and eigenvalues, SVDbased image compression, Eckart Young theorem, geometric interpretation;
Introduction to image restoration


30/09 (Tue) 

Image restoration: defocus blur, motion blur model; inverse filter and its problems; spread spectrum blurs: cameras with coded apertures and fluttershutter camera


7/10 (Tue) 

Wiener filter: aim, assumptions, derivation, interactive Wiener filter;
Concept of convolution as multiplication with a circulant matrix; Concept of computing inverse Fourier transform as multiplication with Fourier matrix;
deconvolution by matrix inverse and its relation to Fourierbased inverse filter; blockcirculant matrix; Fourier matrix for 2D signal as Kronecker product
of two Fourier matrices for 1D signals


10/10 (Fri) 

Use of PCA for image denoising: ideas using nonlocal means (patchbased filtering), PCA and Wiener filter;
Regularized least squares deblurring using image Laplacian as a regularizer


14/10 (Tue) 

Image segmentation: problem introduction, Kmeans clustering, concept of medoid; Histograms and Kernel density estimation; cluster centers as modes of a probability density function


17/10 (Fri) 

Histograms and Kernel density estimation; cluster centers as modes of a probability density function; gradient ascent; mean shift algorithm; mean shift as adaptive gradient ascent;
mean shift for image smoothing and its relationship to bilateral filtering; mean shift for image segmentation (and its caveats); selection of smoothing parameters in kernel density
estimation.


21/10 (Tue) 

Edge detection: types of edges (ramp, step, roof); digital derivative operators in 1D and 2D, zero crossing of second derivative, image Laplacian and its rotational invariance;
Robert and Sobel operators; MarrHildreth edge detector; Canny edge detector: gradient magnitude and orientation computation, nonmaximal suppresion and hysterisis thresholding.
Hough transform for detection of lines, circles and ellipses


28/10 (Tue) 

Image compression paradigms: lossy and lossless, motivation for lossy compression; Overview of JPEG standard: discrete cosine transform, its relationship to discrete Fourier transform,
relationship between discrete cosine transform and PCA.


31/10 (Fri) 

Relationship between DCT and DFT; steps of JPEG: quantization, Huffman encoding and run length encoding; JPEG for color images: YCbCr color space, and PCA on RGB values; Modes of JPEG compression

