Course summary

Introduction

Image acquisition Image format Image representation

Color and human perception

color representation human perception illusions

= + +

Quantification, Sampling, Reconstruction, Interpolation

Uniform quantification Theory of reconstruction Sampling Application to 2D transformations (rotation, scaling)

OR ?

Image Segmentation

convolution based operators (Roberts, Sobel, Prewitt, Kirsch, Laplace) region detection basic algorithms (thresholding, weatersheed, split and merge, ...) morphomathematical operators (erosion, dilatation, opening, closing, squeleton, ) advanced methods: PDE based deformable contours (bsplines, levelsets)

Image Restauration

noise (salt and pepper noise, additive gaussian noise) filtering: mean filter, gaussian filter, conservative filter, median filter

Image Compression

information theory principles LZW, Huffman GIF, PNG, JPEG, JPEG2000

Video Processing

history video formats (analog/digital, MJPEG, DV, MPEG, ...) video processing (segmentation, restauration) video compression (MPEG1,2 , MPEG4, MPEG7, DIVX, WMV)

Course materials

• Lesson 1: Image Processing Introduction - slides in pdf
• Lesson 2: Java Introduction - notes in pdf
• Lesson 3: Image Quantification - slides in pdf
• Lessons 4 and 5: Image Sampling and applications - slides in pdf
• Lesson 6: Noise and Image restauration - slides in pdf
• Lessons 7 and 8: Image segmentation: basics - slides in pdf
• Lesson 9: Image segmentation: advanced methods - slides in pdf
• Lesson 10: Image and Video Compression - slides in pdf

Math. exercises about this course

• Image Quantification
  • Consider the case of logarithmic quantification using n bits. Determine the values for the di (bounds of intervals) and ri (reconstruction levels)
• Image Sampling and applications
  • Demonstrate the property on slide 16
  • Demonstrate the properties on slide 17
  • Demonstrate the property on slide 19
  • Demonstrate the property on slide 20
  • Explain again how to do the interpolation using the Michel polynoms
• Noise and Image restoration
  • Exercice on slide 50

Project

Proposition of project about the Mitchell's polynoms: try to find the best B and C values for the interpolation. You can first work on one image, using for example 10 rotations of 36 degrees and compare the results obtained. Different methods could be used:
• try different values (from 0 to 2 ?), with a constant step (0.1 ?)
• try to use more appropriate methods based on your math. skills.
• draw the curves of the polynom that is solution and of others around the solution. Observe if this polynom is closer to sinx/x or not.
Try to find other polynoms defined in [-3;3] or [-4;4]. Can you obtain better results ? (for example using 36 rotations of 10 degrees)

Homework

• Blez: Image format (basics format, color encoding, compression or not)
• Jeoffrey: Quantification
• Dakila: Sampling and Interpolation
• Filame: Noise and restoration
• Isa: Edge detection using convolution operators

Bibliography

• "Mathematical Models in Computer Vision", Springer, 2005. Olivier Faugeras, edited with Nikos Paragios and Yunmei Chen
• "Digital Image Processing" by W. K. Pratt, John Wiley & Sons, inc., Third Edition, 2001
• "Digital Image Processing" by Gonzalez et Woods, Prentice Hall, Second Edition, 2002
• A course in english
• Books available on the web
• Computer Vision Online
• Vetterli's talks (wavelets, ..)

About Java programming

• Download Java Developpment Kit (JDK) at java.sun.com
• API documentation
• Sun's tutorials
• A book from wikibooks : Java Programming
• Entering "learning Java" in Google, you will find a lot of informations. For example, a course from Yale University