Image Analysis

Examiner and lecturer

Josef Bigun                 

Laboratory Exercises:

Laborartory Exercises are implemented in Matlab.

If you feel that you lack adequate knowledge in Matlab or would like to brush up your knowledge, you might find the link lab0 useful. Please note that lab0 and other exercises cited therein are voluntary and there is no instruction opportunity scheduled for them. The labs of the course comprise lab1 through lab10, only. For each lab exercise, two hours of time is scheduled (with the lab-leader) in a laboratory, equiped with adequate computers in the campus area (see schedule below). Participants will need to have own (normal student) accounts to participate to lab-exercises.

Litterature:

[1] J. Bigun, "Vision with direction",  Springer, (2006).

[2] Laboratory exercises are in Matlab 

Exercise_1, Exercise_2, Exercise_3, Exercise_4, Exercise_5, Exercise_6, Exercise_7,

Exercise_8, Exercise_9, Exercise_10

 
 

Course Contents:

The course consists in two parts: Fundamentals of Image Analysis (in 2D) and Scientific Paper. Examinations of the two parts are independent.

Fundamentals of Image analysis

Contents

 
Signal representation

Lab1 & Lab2

Hilbert space, Schwarz inequality (Ch. 1-3)

Fourier Coefficients (FC), Parseval relationship, Hermitian symmetry of FC. (Ch. 4-5)

Fourier Transform (FT) of continuous functions. (Ch. 6.1-6.2)

Discrete Fourier Transform (DFT), Circular topology of DFT. (Ch. 6.3-6.4).

Lab3 & Lab4

Properties of FT (DFT and FC): FT of box function, Conservation of Scalar Product, Convolution (Ch. 7.1, 7.2, 7.3 ) 

Convolution with separable filters, Translation under FT, FT of Gaussian function (Ch. 7.4, 7.7, Table 7.1) 

Signal representation and sampling, Interpolation functions, Derivation, Gaussians as interpolators (Ch. 8.1, 8.2, Ch. 9.2 ) 

 Multi-resolution analysis and coarseness

Lab5

Gaussian & Laplacian pyramid Ch. 9.1-9.5

 Color

Lab6

Natural color images Ch. 2.1-2.2, Ch. 2.4-2.6

Representing artificial data by color images, especially "angle" data (See Laboratory exercise material and lecture slides)

Texture & Orientation

Lab7

Structure tensor and local orientation Ch. 10.1-10.8, Ch.10.11

Color display of orientation and its use as texture feature (See lab material)

Shape in binary images

Lab8

Histograms & Binarization, Ch. 16.1 (and lab material)

Simple shape parameters: Area, Perimeter, Circularity, Bounding box, Area moments; First paragraph of Ch. 17.2; Ch. 17.3, 17.4, and Equations. 17.19-17.22

Systematic approximation of boundary curves, Fourier descriptors Ch. 17.5 including Equation 17.41  

Lab9

Recognition of binary shape by Fourier descriptors. Equation 17.42 until the end of Ch. 17  

Lab10

Morphological operators: Erosion, Dilation, Thinning, opening, closing, inner and outer boundaries Ch. 17.1 until Equation 17.6

Pattern matching: Hit-Miss function (Last topic in Ch. 17.1)

Scientific paper

As part of the course, the student will be asked to study a scientific paper, which will be evaluated by an exam of its own to result either in Pass or Fail.