**BIL 407, 2010-2011 Fall**

**Mathematical Techniques in Computer Science**

**Lectures: Thursday 09:00-11:45 @D9**

**Instructor:** Erkut Erdem

**Office:** 114

**Office Hours:** Wed 16:00-17:30

**e-mail:** erkut@cs.hacettepe.edu.tr

**Course Description:**

This course serves as an introduction to image processing for undergraduates. The course will introduce mathematical models to restore/enhance digital images, and describe algorithms for image analysis. We will start with an overview of the basic concepts of digital image processing. Then we will introduce the point operations and histogram processing. We will next explore spatial filtering techniques (linear and nonlinear), and image segmentation methods (boundary-based, region-based, and unified formulations). The last part of the course will cover the Fourier Transform and frequency domain techniques.

**Prerequisites:**

Good math (calculus, linear algebra, statistical approaches) and programming (MATLAB, C) background. Students were not expected to have any prior knowledge of image processing techniques.

**Textbooks:**

The textbook will be available at the reserve desk in the library.

- Digital Image Processing, R. C. Gonzalez, R. E. Woods, 3rd Edition, Prentice Hall, 2008

**Tentative Outline**

- Introduction to Image Processing and Digital Image Fundamentals
- Point Operations and Histogram Processing
- Spatial Filtering (Linear and Nonlinear)
- Image Segmentation (Boundary-based, Region-based, and Unified Formulations)
- Fourier Transform and Frequency Domain Processing

**Assignments Policy**

There will be at least five programming assignments, which will involve implementations in C or MATLAB programming environments and discussion of the obtained experimental results. There will also be some warm-up and reading assignments. Homeworks have to be done individually, i.e. there is no teaming up.

**Grading Policy**

HW 30%, Midterm 30%, Final %40

**Resources**

- Review material offered by the authors of the reference book
- MATLAB Getting Started Guide
- Review material for linear diffusion and Perona-Malik type nonlinear diffusion
- Normalized Cuts and Image Segmentation

J. Shi and J. Malik, IEEE Trans. PAMI, Vol.22, No.8, 888-905, 2000 - On robust estimation and smoothing with spatial and tonal kernels.

P. Mrázek, J. Weickert, A. Bruhn, In R. Klette, R. Kozera, L. Noakes, J. Weickert (Eds.): Geometric Properties from Incomplete Data, 335-352, Springer, Dordrecht, 2006. - A non local algorithm for image denoising

A. Buades, B. Coll, J.M. Morel, IEEE Computer Vision and Pattern Recognition 2005, Vol 2, pp: 60-65, 2005.

**Homework Assignments**

**Reading Assignment #1**Due on Thursday, October 14, 2010

Chapter 1 from David Marr's Vision- Programming Assignment #1 Due on Thursday, November 11, 2010

sample images for the homework **Reading Assignment #2**

Theory of Edge Detection

D. Marr and E. Hildreth, Proc. R. Soc. Lond. B, 207, 187-217, 1980- Programming Assignment #2 Due on Thursday, December 9, 2010
**Reading Assignment #3**Due on Thursday, January 13, 2011

Hierarchy and Adaptivity in Segmenting Visual Scenes

E. Sharon, M. Galun, D. Sharon, R. Basri, A. Brandt, Nature, Vol. 442, 810-813, 2006

Spectral Segmentation with Multiscale Graph Decomposition

T. Cour, F. Benezit, J. Shi, Proc. Conf. Computer Vision and Pattern Recognition (CVPR), Vol. 2, 1124-1131, 2005- Programming Assignment #3 Due on Thursday, January 13, 2011