# Math 155: General Course Outline

## Catalog Description

**155. Mathematical Imaging. (4) **Lecture, three hours; discussion, one hour. Requisites: courses 32B, 33B, 115A, Program in Computing 10A. Imaging geometry. Image transforms. Enhancement, restoration, and segmentation. Descriptors. Morphology. P/NP or letter grading.

Math 155 is an introductory course on mathematical models for image processing and analysis. The students will become familiar with basic concepts (such as image formation, image representation, image quantization, change of contrast, image enhancement, noise, blur, image degradation), as well as with mathematical models for edge and contour detection (such as the Canny edge detector), filtering, denoising, morphology, image transforms, image restoration, image segmentation, and applications. All theoretical concepts will be accompanied by computer exercises.

## Textbook

R. Gonzalez and R. Woods, *Digital Image Processing, New edition*, Prentice-Hall. Book is Subject to Change Without Notice.

Outline update: L. Vese, 2/03

## Schedule of Lectures

Lecture | Section | Topics |
---|---|---|

1 |
2.2-2.3 |
Introduction: A Simple image model (2.2); Sampling and Quantization (2.3) |

2 |
2.5 |
Imaging Geometry |

3 |
3.1 |
Introduction to the Fourier Transform |

4 |
3.2 |
The Discrete Fourier Transform |

5 |
3.3 |
Some Properties of the Two-Dimensional Fourier Transform |

6 |
3.3 |
Some Properties of the Two-Dimensional Fourier Transform |

7 |
3.4 |
The Fast Fourier Transform |

8 |
3.5 |
Other Separable Image Transforms |

9 |
3.5 |
Other Separable Image Transforms |

10 |
3.6 |
The Hotelling Transform |

11 |
4.1 |
Image Enhancement |

12 |
4.2 |
Enhancement by Point Processing |

13 |
4.2 |
Enhancement by Point Processing |

14 |
4.3 |
Spatial Filtering |

15 |
4.4 |
Enhancement in the Frequency Domain |

16 |
5.1 |
Image Restoration: Degradation Model |

17 |
5.4 |
Inverse Filtering |

18 |
7.1 |
Detection of Discontinuities |

19 |
7.2 |
Edge Linking and Boundary Detection |

20 |
7.3 |
Thresholding |

21 |
7.4 |
Region-Oriented Segmentation |

22 |
7.5 |
The Use of Motion in Segmentation |

23 |
8.1 |
Representation Schemes |

24 |
8.2 |
Boundary Descriptors |

25 |
8.3 |
Regional Descriptors |

26 |
8.4 |
Morphology |

27 |
8.4 |
Morphology |

28 |
8.4 |
Morphology |