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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, 3rd Ed., Prentice-Hall.

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