Future Classes' schedule

Topics Covered So Far  along with Handouts or Sections to read from the Book or Papers/Weblinks

Introduction to Image Processing

Review of Signal Processing

Review of Linear Algebra

Review of probability/random proc.

Sampling & Quantization

Image Transforms

Image Enhancement

Image Restoration

Edge Detection, Boundary Tracing, Edge Linking

Segmentation (Detection/Classification, Clustering (Alt. Max), EM algorithm )

Segmentation (Contour Estimation: Hough tfm, Snakes & GVF, Level set method)

Tomographic Reconstruction (Radon transform & Inverse Radon)

• Introduction to Image Processing:  Slides
  
• Review of Signal Processing: AK Jain 2.2, 2.3, 2.4. For details, see EE 224 class notes
•  Review of Signal Processing Handout
  
• Sampling, Reconstruction, Nyquist criterion, aliasing
  
• Continuous time Fourier transforms, DTFT, DFT and connection, properties, FT pairs
  
• Decimation and Interpolation
• 2D DFT
  
• Review of Linear Algebra: AK Jain, 2.7  & for more infor see http://www.maths.mq.edu.au/~wchen/lnlafolder/lnla.html
• Definitions: Hermitian, Symmetric, Trace, Rank, Eigenvalues, Eigenvectors
• Toeplitz & Circulant matrices & properties
• ABCD lemma
• Diagonalization of circulant, unitary & symmetric positive definite matrices
• Diagonalization of any matrix (not needed, just for your information)
  
• Review of basic probability/random processes: EE 322 class notes & AK Jain 2.9, 2.11, 2.12
  
• Definitions: PDF, PMF, Autocorrelation, Covariance
• Stationarity and wide sense stationarity
• Markov property
• Spectral density function (or Power Spectral Density) definition
• Minimum mean squared error (MMSE) estimate & linear MMSE estimate
• Sampling & Quantization: AK Jain, 4.2, 4.3 (before hexagonal sampling), 4.4, 4.5, 4.6 (Pg 99-103,112)
• 2D Sampling & Reconstruction, Nyquist, Aliasing, Bandlimited Image (extensions of 1D)
• Nyquist sampling theorem for stationary random fields
• Interlacing or more generally Nonrectangular grid sampling (skipHexagonal & optimal sampling)
• Practical issues
• Practical interpolation filters: nth order hold, n=0, 1(linear),2,3(cubic),...infty (Gaussian)
  
• Concept of resolution loss versus interpolation error
• Sampling aperture acting as an anti-aliasing filter
• Display aperture acting as a circularly symmetric Gaussian interpolation function
• Moire effect (effect of interpolation error) & flat field response
  
• Image Quantization: Only Uniform & Llyod Max quantizers Pg 99-103,112
• Image Transforms: AK Jain 2.8, 5.1, 5.2, 5.4, 5.5 (skip Pg 150), 5.6 (basics), 5.11
  
• Concept of a separable transform: See 2.8 (specially Table 2.7 properties)
• Arranging an image as a vector and the transform as an N^2 x N^2 matrix
• Kronecker product
• Properties of 2D Unitary transforms:  Error in equation 5.13, it should be A_M U A_N*'  (the conjugate transpose on A_N is missing). Also fix 5.14
  
• If separable, i.e. if can write in the form V=AUB', then A & B are also unitary
  
• Separable transforms: computation reduces from O(N^4) to O(N^3),
  
• Fast transforms: computation reduces from O(N^3) to O(N^2 log_2 N)
• Concept of transform frequency
• 1D DFT matrix, properties, fast tfm (FFT exists), diagonalizing a circulant matrix (know proof),  circular convolution, converting linear conv to circular conv, why do it?
• 2D DFT
  
• Discrete Cosine Transform (basic ideas)
  
• formula, why used in audio, image compression?
  
• diagonalizes a specific type of symmetric tridiagonal matrix  (eq 5.95) which is "close" to covariance matrix of a Markov, highly correlated sequence
• KL Transform & Principal Components analysis: everything in 5.11
• Image enhancement: Chapter 7
  
• Contrast enhancement: linear contrast stretching, clipping, thresholding
• Contrast enhancement:  histogram equalization, histogram modification
• Denoising: Linear spatial filtering, Nonlinear filtering (median filtering),
  
• Bandpass filtering
• Edge crispening or edge enhancement
• Image Resotaration: Chapter 8 of AK Jain, also Chapter 5 of Gonzalez Woods
  
• Image Restoration Handout
• Inverse & Pseudo inverse filtering,
  
• Wiener filtering (technically smoothing), FIR Wiener smoothing
  
• Smoothing splines and Constrained Least squares
• Correcting for Geometric distortion (also called Image Registration)
• Notch filtering
• Specke noise reduction
• Edge detection, Boundary Tracing & Edge Linking:  9.4, 9.5 of AK Jain, Milan Sonka's notes
• Edge detection, Boundary tracing Handout
• Edge detection: first derivative, second derivative + smoothing (LoG), Canny, compass
  
• Edge linking: link the edges to obtain a boundary
  
• Boundary tracing (trace the boundary of a segmented object)
• Image Segmentation
• Segmentation as detection/classification/clustering problem
  
• Thresholding: fixed & adaptive, choosing thresholds optimally (classification problem)
  
•  Alternating Maximization and EM algorithm & application to segmentation Handout
• K means clustering (or Alternating maximization): useful when multidimensional data (e.g. colored images, or if want to cluster intensity and x-y locations)  K means  Demo 
  
• EM algorithm: review paper 1   intuition for its convergence   more rigorous version    original Dempster et al paper
  
• An old handout on segmentation
• Region growing, merging splitting
• After any of the above methods, need to do boundary tracing to get the contour
  
• Segmentation as a contour estimation problem
  
• Hough transform: AK Jain, Section 9.5
• Calculus of variations
  
• Snakes: parametric active contours
  
• Calculus of variations Handout
• Snakes Handout
• A ppt talk available online
  
• Kass,Witkin,Terzopolous paper IJCV 1987
  
• Gradient vector flow (GVF) snakes
• Xu & Prince paper
• GVF webpage with intuition, videos, publications
• Snake growing: Sonka's webpage
• Geometric Contour Representation & Level set method
  
• Handout
• Slides with examples of edge and region based methods described below
• Important Papers to Read
  
• Level set method introduction & papers
• "Geometric" Edge-based level set method for segmentation: Kichenassamy et al ICCV 1995 
  
• "Geometric" Region-based level set method for segmentation: Yezzi, Tsai, Wilsky, LIDS Technical Report, 1999   
  
• "Geometric" Region-based level set method: Chan,Vese, Trans IP 2001 
  
• Tomographic Reconstruction
• A.K. Jain Chapter 10, 10.1 - 10.6, 10.9, 10.10
• Slides with intuition & some pictures (will post)
  
• Radon Transform intuition (measures -log of attenuation along a ray)
  
• Radon Transform definition,
  
• Back projection operator, Projection Slice Theorem
  
• 3 Reconstruction Algorithms
• Discretization for Implementing Convolution Back Projection & Filtered Back projection for Reconstruction
• Fan Beam Geometry & Fan Beam Reconstruction
• Introduced Alebgraic Reconstruction Techniques (ART)  & 3-D Tomography (10.11, 10.12 of AK Jain)

Last 5 classes starting April 11

• Recap of everything we've studied till now.
  
• Registration, Tracking
• April 23: Project 2, first set of talks
• Object Recognition