Image Processing in Mathematica

1
Image Processing in Mathematica

• David Olsen
• Laboratory for Intelligent Systems

2
Introduction

• My Research
• Image processing in Mathematica
• Tutorial for students
• Further research
• Student Research at UMD

3
Student Research at UMD

• UROP
• Undergraduate Research Opportunities Program
• Faculty
• Grants
• Independent

4
My Project

• Digital Image Processing
• Mathematica

5
Digital Image Processing

• A digital representation of images
• Digital manipulation of images
• Uses
• Computer image recognition
• Medical imaging
• Graphic design and arts

6
Mathematica

• Advanced technical computing
• Developed by Wolfram Research
• Symbolic calculations
• Advanced mathematics
• Version 4 support for digital processing / images

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Exact Factorial of 1000

• In1
• 1000!
• Out1
• 40238726007709377354370243392300398571937486421071
  4632543799910429938512398629\
• 02059204420848696940480047998861019719605863166687
  2994808558901323829669944590\
• 99742450408707375991882362772718873251977950595099
  5276120874975462497043601418\
• 27809464649629105639388743788648733711918104582578
  3647849977012476632889835955\
• 73543251318532395846307555740911426241747434934755
  3428646576611667797396668820\
• 29120737914385371958824980812686783837455973174613
  6085379534524221586593201928\
• 09087829730843139284440328123155861103697680135730
  4216168747609675871348312025\
• 47858932076716913244842623613141250878020800026168
  3151027341827977704784635868\
• 17016436502415369139828126481021309276124489635992
  8705114964975419909342221566\
• 83257208082133318611681155361583654698404670897560
  2900950537616475847728421889\
• 67964624494516076535340819890138544248798495995331
  9101723355556602139450399736\
• 28075013783761530712776192684903435262520001588853
  5147331611702103968175921510\
• 90778801939317811419454525722386554146106289218796
  0223838971476088506276862967\
• 14667469756291123408243920816015378088989396451826
  3243671616762179168909779911\
• 90375403127462228998800519544441428201218736174599
  2642956581746628302955570299\

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Visualizations
9
Image Processing Tutorial

• Table of Contents
• Basic Image Processing
• Basic Mathematical Operations
• Histograms
• Area Selection
• Convolutions
• Edge Detection
• Filtering

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Basic Image Processing

• Importing Images
• Extracting Data
• Displaying Images

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Mathematical Operations
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Inverting
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Interpolation and Distortions
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Differentiation
17
Adding Images
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Adding Continue
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Subtracting Images
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Subtract continue
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Histograms

• Number of each color
• Ratios of colors or gray levels
• Characteristic of image

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Histogram
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Slicing and Histogram
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3D Histogram
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Edge Detection
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Vertical and Horizontal Sobel Edge Kernals
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ContourPlot
28
Filtering High Pass
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Filtering Low Pass
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Low Pass 2 (Heavy Blur)
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Conclusions

• Starting Point for Image Processing
• Teaches tricks of Mathematica
• Research is rewarding!

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