1. Digital Image Processing Hongkai Zhao Department of Mathematics UC Irvine

2. Growth of digital information 281 billion gigabytes generated in 2007. digital bits > # of stars in the universe growing by a factor of 10 every 5 years. Growth fueled by multi-media data. 2 billion photoes by Flicker 4.2M UK security cameras In 2007 digital data generated > total storage. By 2011 ½ digital information will have no home. [Source: IDC Whitepaper “The Diverse and Exploding Digital Universe” March 2008] Average American consumes 34 gigabytes of digital information daily by 2009.

3. What is an image? Some form of representation for visual information. A picture worth a thousand words. A digital image is composed of digitized quantities defined on a rectangular grid of pixels. For example, 1024x1024 ~ 1megpixel. Mathematically, a digital image is a matrix of number, or a function on a rectangular domain. An image contains rich information with a lot of redundancy.

4. What is image processing? Enhance, extract wanted information from, analyze and interpret an image. Low level compression, denoising, deblurring, segmentation, … High level recognition/classification, interpretation, …

5. What math has to do with it? Mathematical modeling characterize/quantify features, such as noise, edge, textures, shape, …. Mathematical theory Efficient numerical algorithms For digital image processing, it is all about numbers and math!

6. Denoising

7. Inpainting

8. Deblurring + inpainting

9. Segmentation

10. Shape recognition

11. Face recognition

12. Acknowledgement Frederick Park Mickey Hou