Date |
Content of the Lecture |
Assignments/Readings/Notes |
| 29/7 (Tue) |
Overview
- Course content
- Course policies
- Applications of image processing
|
|
| 2/8 (Fri) |
Image alignment
- Image basics: pixel, domain, size, resolution
- Digital and physical correspondence, concept of image alignment
- Motion models: rotation, translation, affine, scaling, shearing, matrix representation, low rank transforms, composition of transformations
- Control-point based image alignment
- MSSD/MSE based image alignment, concept of field of view
- Image warping: forward and reverse, bilinear interpolation
|
- Slides
- Read sections 2.4.3, 2.4.4, 2.6.5 of the book by Gonzalez and Woods
|
| 6/8 (Tue) |
- Image alignment when intensity profiles are not the same: transformed MSSD, Normalized cross-correlation, joint entropy
- Concept of image histograms, joint image histograms, entropy and joint entropy, use of joint entropy for image alignment
- Applications of image alignment: template matching, panorama generation
- Clarifications regarding concept of field of view in image alignment
|
- Slides
- Read sections 2.4.3, 2.4.4, 2.6.5 of the book by Gonzalez and Woods
|
| 9/8 (Fri) |
- Concept of joint image histograms, entropy and joint entropy, use of joint entropy for image alignment
- Applications of image alignment: template matching, panorama generation
Image Enhancement
- Concept of image intensity transformation and image enhancement
- Negatives, logarithmic, power-law (gamma) transformations, linear contrast stretching
|
- Slides
- Read sections 3.2, 3.3 of the book by Gonzalez and Woods
|
| 13/8 (Tue) |
- Histogram equalization and specification: derivation, examples
- Local/Adaptive Histogram equalization
MATLAB examples
|
- Slides
- Read sections 3.2, 3.3, 3.4, 3.5 of the book by Gonzalez and Woods
|
| 16/8 (Fri) |
- Local spatial filters
- Convolution and correlation operations: examples, properties, derivation of correlation (template matching) and convolution (Linear time/space-invariant systems)
- Mean and median filtering; examples of linear and non-linear filters
- Image Noise Models
MATLAB examples
|
- Slides
- Read sections 3.2, 3.3, 3.4, 3.5 of the book by Gonzalez and Woods
|
| 20/8 (Tue) |
- Derivative operators in 1D and 2D, and their properties
- Laplacian-based sharpening filter, unsharp masking
- Laplacian of Gaussians, Sobel filter
- Separable convolution filters and their advantages
- Bilateral filters and their advantages, cross-bilateral filters
|
- Slides
- Read sections 3.6, 10.2.1 of the book by Gonzalez and Woods
|
| 23/8 (Fri) |
- Bilateral filters and their advantages, cross-bilateral filters
- Bokeh filters
Edge and Corner Detection
- Derivative operators in 1D and 2D, and their properties
- Laplacian of Gaussians, Sobel filter, Prewitt filter
- Marr-Hildreth edge detector
- Canny edge detector with non-maximal suppression and hysterisis thresholding
|
|
| 27/8 (Tue) |
Edge and Corner Detection
- Corner detection: importance of corners in image matching
- Harris corner detection criterion
- Structure tensor and its eigen-analysis; behaviour in constant intensity regions, regions with edge, regions with a corner
|
|
| 30/8 (Fri) |
Hough Transform
- Hough transform for line (with normal line representation instead of slope-intercept), circle and ellipse detection
- Pros and cons of Hough transform
Image Segmentation
- Image segmentation: concept
- Segmentation as a clustering problem
- KMeans algorithm and its limitations
|
|
| 3/9 (Tue) |
- KMeans algorithm and its limitations
- Concept of gradient ascent; mode finding given a PDF
- Concept of nonparametric probability density estimation using kernels (kernel density estimation)
- Mean shift algorithm
|
|
| 6/9 (Fri) |
- Mean shift algorithm: discussion
Fourier Analysis
- Fourier series: formula and basic properties
- Fourier transform: examples, intuition, properties: linearity, shift theorem and its variant, convolution theorem and its variant, Parseval's theorem
|
|
| 10/9 (Tue) |
- Fourier transform: examples, intuition, properties: linearity, shift theorem and its variant, convolution theorem and its variant, Parseval's theorem
- Brief mention of applications of a Fourier Transform
- Bandlimited versus time-limited signals
|
|
| 13/9 (Friday) |
- Fourier transforms in 2D
- Brief mention of applications of a Fourier Transform
- Fourier transform of a Gaussian
- Differentiability of bandlimited signals
- General discussion regarding midsem: discussion on problems including teaser problems on image enhancement and image alignment
|
|
| 24/9 (Tuesday) |
- Genesis of the discrete fourier transform (DFT)
- Properties of the DFT
- Circular convolution and concept of zero-padding
- Motivation for implementing convolutions via the fourier transform, introduction to fast fourier transform (FFT)
|
|
| 27/9 (Fri) |
- 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
|
|
| 1/10 (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: Radon transform
- Beer's law in tomography
- Shannon's sampling theorem, concept of Nyquist rate, concept of aliasing
|
|
| 4/10 (Fri) |
Face Recognition
Face recognition: intro
Face recognition, face detection, face verification, challenges in face recognition, concept of training and test phase of a face recognition system
PCA algorithm
A faster algorithm for PCA on a small (N) number of large-sized images (N < d case).
|
|
| 8/10 (Tue) |
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
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)
|
| 11/10 (Fri) |
Illumination invariance in face recognition: Removal of top three eigenfaces
Person-specific eigenfaces
Image compression using PCA
Face recognition from other modalities
|
|
| 15/10 (Tue) |
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
- SVD: geometric interpretation; applications in linear algebra
- PCA/eigenfaces algorithm using SVD, brief mention of other applications of SVD
|
|
| 18/10 (Fri) |
Image Compression
- Image Compression: lossless and lossy
- 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
- Motivation for using DCT in JPEG
|
|
| 22/10 (Tue) |
- Motivation for using DCT in JPEG
- DCT quantization matrix, quantization step in JPEG, derivation of quantization matrix
- Huffman encoding and run length encoding in JPEG
- Structure of Huffman encoder and decoder
- Properties of Huffman encoding: optimality, prefix-free nature
|
|
| 25/10 (Fri) |
- JPEG decoding
- JPEG for Color image compression, YCbCr color scheme
- Typical JPEG artifacts; modes of JPEG compression (sequential, hierarchical, progressive)
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
|
| 29/10 (Tue) |
- Code blur camera (see code demo), flutter shutter camera - spread spectrum filtering
- Concept of Wiener filter and formula, interpretation of the formula
- Derivation of Wiener filter
|
|
| 1/11 (Fri) |
- Concept of Wiener filter and formula, interpretation of the formula
- Regularized restoration using gradient penalty terms
- PCA for image denoising: algorithm description and sample outputs
- Derivation of Wiener filter for PCA denoising
|
|
| 5/11 (Tue) |
- PCA for image denoising: algorithm description and sample outputs: recap
- Derivation of Wiener filter for PCA denoising
- Practical application of Wiener filtering to clear concepts regarding noise statistics, image statistics and estimation of blur kernels
|
|
| 8/11 (Fri) |
Color Image Processing
- 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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