Digital Image Processing Hongkai Zhao Department of Mathematics UC Irvine.

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Presentation transcript:

Digital Image Processing Hongkai Zhao Department of Mathematics UC Irvine

Growth of digital information 281 billion gigabytes generated in 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.

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.

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, …

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!

Denoising

Inpainting

Deblurring + inpainting

Segmentation

Shape recognition

Face recognition

Acknowledgement Frederick Park Mickey Hou