Digital Image Processing

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An introduction to Digital Image Processing as a continuation of a classic Digital Signal Processing course delivered at the University of Plymouth (2011)

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  • Why should we bother to get involved with Digital Image Processing?
  • To display an image the process is reversed! The Focusing Apparatus + Transducer Is Your “Analogue IO”
  • Exposure Control: Lens Diameter, Aperture, Time, Filters
  • Focusing can further be controlled through image processing.
  • What if the filter or image are not square?What if the filter is not of odd symmetry?What if the filter has both a real and imaginary part?
  • Digital Image Processing

    1. 1. Digital Image Processing Athanasios Anastasiou Signal Processing & MultimediaCommunications Research Group UoP
    2. 2. Learning Objectives• Get The Bigger Picture Of Digital Image Processing And Its Applications• Understand And Be Able To Carry Out Basic Operations – +,-,/,*, Filtering, Correlation, Image Transforms – MATLAB (and other software)• Extend What You Already Know From DSP To Higher Dimensions
    3. 3. Topics What Can You Do With Digital Image Why Digital Image Processing? Processing? How Does A 2DFourier Spectrum Look Like? What Is An Image? Is There Aliasing In What‟s This Thing Digital Image Who Is Lenna Processing? Called “Spatial Soderberg? Are There 3D Frequency”? „Images‟? What Are The Relationships Transforms Used In Between DSP and Digital Image DIP? Are There 4D Processing? Images?…How Do How Do You Filter They Look Like? An Image? What Is The Fourier Transform For What Is The Fourier Images? Transform For Volumetric Data?
    4. 4. Why Digital Image Processing?• Convenience, Practicality• Capture – Obtain The Representation Of A Scene• Process – Pre Process – Extract Information • Make Sense Of The Image / Scene – Further Processing • Classify, Modify, Combine,…• Visualise – Not As Simple As You May Think – Transform Image• Transmit / Store – Data Format – Compression
    5. 5. Why Digital Image Processing?• Emergent Applications – Machine Vision – Augmented Reality – (More) Surveillance – Gaming• …To The Limits Of Your Imagination And Beyond (!)
    6. 6. Breadth & Depth Of D.I.P Demonstrators• Simultaneous Localisation And Mapping – S.L.A.M.• Merging And Making Sense Of Images On (A Ridiculously Large) Scale – Microsoft PhotoSynth – Giga & Peta Pixel Panoramic Photography • Gigapixel Panoramas • Petapixel Panorama – Scene Completion Using Millions Of Photographs – Scale Invariant Feature Transform • (S.I.F.T & S.U.R.F)• Augmented Reality – Bluring The Divide Between The Real And The Virtual – Tracking Facial Features – Lip Sync A Virtual Character – Recognise If Someone Is Bored By Their Facial Expression • Make A Game To Respond To That• Making Sense Of Images – MS Kinect – Eye Pet
    7. 7. Capturing Digital Images R R Focusing R E Control, AcquisitionR O Transducer Apparatus & Digitisation •Mechanical •Photoelectric •Exposure! •Optical •Valve •Electromechanical •CCD D •Electronic •Photodiode •Photoresistor •PiezoElectric •Inductive •Capacitive •Other Digital Image •Medium / Format •Film •Paper •Digital •R: Some Form Of Radiation •O: Object •E: Electric Charge •D: Digital Signals
    8. 8. The Concept Of Exposure• Controls How Much Radiation Is Captured H E t• E: Radiation Flux – Depends On The Focusing Mechanism & Transducer • Spectral Response! / Aperture! – Units: • Energy / Surface (Watts / m2)• t: Time – Unit: Seconds• Remarks – Exposure Creates Contrast (!!!) – Exposure Is A Product (!) • When E Goes Down, t Must Go Up To Maintain The Same H
    9. 9. Photography Visible Light Flash!!! RCHEESE! R Focusing R E Control, Acquisition O Transducer Apparatus & Digitisation Light Is Reflected Lens System CCD Or Emitted By An D Object Digital ImageImage Credit: http://www.jiscdigitalmedia.ac.uk/images/slr02.jpg JPG
    10. 10. Radar / Sonar Radio Frequencies R R Focusing R E Control, Acquisition O Transducer Apparatus & Digitisation Sound Waves Are Electronic / Inductive Reflected By An Electromechanical D Object Digital Image HDF, DEM, GRB & OthersImage Credits: Wikipedia, Microwave Journal, Defense Industry Daily, Met Office
    11. 11. Radiography (X-Ray, CT)What‟s Up Doc? R O R Focusing R Transducer E Control, Acquisition Apparatus & DigitisationX-Rays Absorbed Mechanical (*) X-Ray Sensitive Coating By Object Secondary Radiation D CCD Digital Image *: CT Stands For Computed Tomography Image Credits: apex.it, aapm.org, Wikipedia, Medscape.com DICOM
    12. 12. Nuclear Imaging (SPECT, PET) SPECT / γ - Camera Positron Emission Tomography R R Focusing R E Control, Acquisition RO Transducer R Apparatus & Digitisation Gamma Rays Mechanical Scintillator Emitted By The Object Photomultiplier(How Did It Get In There?) D “You Will Feel A Tiny Prickle Now…” Digital Image Image Credits: Utah.edu, msha.com, PET ISLLC DICOM
    13. 13. Ultrasonography (Ultrasound) UltraSound R R Focusing R E Control, Acquisition O Transducer Apparatus & Digitisation Sound Waves Are Mechanical / Piezoelectric Crystal Reflected By An Electronic / D Object Electromechanical Digital Image DICOMImage Credits: Wrightwoodmedical.com, zhweichao.com, UoC MIG, examiner.com|
    14. 14. Magnetic Resonance Imaging RF Pulses R R Focusing R E Control, Acquisition O Transducer Apparatus & Digitisation Electronic Inductive D Paramagnetic Atom Precession To Initial Digital Image SpinImage Credits:sarctrials.com, pedimaging.com, UoL, Wikimedia.co DICOMm
    15. 15. What Is A Digital Image?• How Does Radiation Varies Across Space? – Samples Across Space• A Two Dimensional Signal – Higher Dimensions Are Possible (3D, 4D) • How Does A Quantity Varies Across Volume? • How Does A Quantity Varies Across Volume & Time?• A Two Dimensional Projection Of A 3D Scene (!)• An Array – X(i,j) 0,1,1,0,0,0 0,1,1,0,0,0 0,1,1,0,0,0 0,1,1,1,1,0 0,1,1,1,1,0
    16. 16. Space!!!• Spatial Frequency – Large Objects • Low Frequencies • Form – Fundamental Shape – Small Objects • High Frequencies • Details! – Edges!!!• Spatial Resolution – What Is The Smallest Object I Can Observe? – Is It Uniform???
    17. 17. Characteristics Of Digital Images• Samples – Picture Elements • Pixels• Resolution – Pixel • 512x512 pixels • Dimensions – Spatial • 50m * 50m • 5mm * 5mm• Dynamic Range – Color Depth • “Number Of Colors” – Contrast
    18. 18. DSP VS DIP• x(t) • x(i,j) – Amplitude – Intensity • • “Brightness” – Frequency – Spatial Frequency – Sampling Frequency – Resolution • • Nyquist Theorem? – Phase – Orientation!!!
    19. 19. Aliasing• A Byproduct Of Sampling• Images Sample Space Constrain The Spatial Bandwidth To Fs/2
    20. 20. Interlude Aliasing In Video I(I,j,t)• How Many RPM? What Direction? – Wheel – Rotor – Prop• How Would These Questions Translate In DSP Terms?
    21. 21. Basic Operations• Add, Subtract (“Mix” Two Images)• Multiply, Divide (Modulation)• What About Negative Or Over The Range Values???
    22. 22. “Out Of Range” Values The Use Of Windows• What Is A „Window‟? – What Is An Image Histogram?• Why Do We Need One?• How Does It Look Like?• How Is It Used?• Demo
    23. 23. Convolution & Correlation Nh y ( m) h(i ) x(m i ) i 0 N hX N hY y(m, n) h(i, j ) x(m i, n j) i 0 j 0 *: Discrete Formulas
    24. 24. 2D Filters & Image Filtering 0.4 0.35 0.3 0.25 0.2 Amplitude 0.15 0.1 0.05 0 -0.05 0 10 20 30 40 50 60 70 Sample / TimeImage Filters (2D) Are An Extension Of Signal Filters (1D) Think In Terms Of Spatial Frequency
    25. 25. 2D Filters & Image Filtering 1.2 0.12 1 0.1 0.08 0.8 0.06 0.6 0.04 0.4 70 0.02 0.2 70 0 60 0 60 -0.02 50 -0.2 70 50 70 60 40 60 40 50 30 50 30 40 40 30 20 20 30 LP 20 10 0 10 HP 20 10 0 10 0 00.6 0.60.5 0.50.4 0.40.3 0.3 0.20.2 0.10.1 70 70 0 0 60 -0.1 60-0.1 50 -0.2 50 70 70 60 40 40 60 50 30 50 30 40 40 BP 30 20 10 10 20 BR 30 20 10 10 20 0 0 0 0
    26. 26. 2D Filters & Image FilteringHow Does A Filtered Image Look Like?
    27. 27. 2D Filters & Image Filtering Meet LennaLena Soderberg : Model Playmate 1972: Picture Includes Only The Interesting PartsPhotography :Dwight Hooker
    28. 28. 2D Filters & Image Filtering 1.2 0.12 1 0.1 0.08 0.8 0.06 0.6 0.04 0.4 70 0.02 0.2 70 0 60 0 60 -0.02 50 -0.2 70 50 70 60 40 60 40 50 30 50 30 40 40 30 20 20 30 LP 20 10 0 10 HP 20 10 0 10 0 00.6 0.60.5 0.50.4 0.40.3 0.3 0.20.2 0.10.1 70 70 0 0 60 -0.1 60-0.1 50 -0.2 50 70 70 60 40 40 60 50 30 50 30 40 40 BP 30 20 10 10 20 BR 30 20 10 10 20 0 0 0 0
    29. 29. 2D Filters & Image Filtering How Does It Look Like? 50 50 100 100 150 150 200 200 250 250 300 300 350 350 400 400 450 450 500 500 550 550 50 100 150 200 250 300 350 400 450 500 550 50 100 150 200 250 300 350 400 450 500 550 50 50 100 100 150 150 200 200 250 250 300 300What Is The DSP Name 350 350For That Frame Around 400 400 The Filtered Images? 450 450 500 500 550 550 50 100 150 200 250 300 350 400 450 500 550 50 100 150 200 250 300 350 400 450 500 550
    30. 30. Applications Of Filtering In Digital Signal Processing• Art – Image Effects• Key Preprocessing Stage – „Noise‟ Reduction – Image Pyramids• Feature Extraction – Where Are The Edges Of An Object?
    31. 31. Convolution & Correlation Nh y ( m) h(i ) x(m i ) i 0 A Simple Metric Of Similarity Why Does It Work?X (m), Y (m) with m 0 N N 1 1 cov X , Y X X Y Y X X m m 0 N 1 2 1 2 1: Alike (X ) X m X N m 0 cov X , Y cor X , Y 0: No Rel X 2 X X Y -1: Rev Rel
    32. 32. Applications Of Correlation In Digital Image Processing “Dude! Where’s My Airplane?” Correlation (And Satellite Imaging)Tells You! N hX N hY y(m, n) h(i, j ) x(m i, n j) i 0 j 0 x : An Image h : Commonly Referred To As A Template (What To Look For) y(m,n) : How “Similar” Is The Patch Centred Around m,n With h??Similar As In: “Locally The Samples Go Over And Under The Mean Value (More Or Less) Frequently”
    33. 33. Correlation In Digital Image Processing Dude, Where’s My Airplane?Find In
    34. 34. Correlation In Digital Image Processing Sir, We Have Three Potential Matches 100 200 300 400 500 600 700 800 900 1000 200 400 600 800 1000 1200 1400 1600The Maxima Of y(m) Are The Centre Locations Of Positive Matches. Why Does It Find More Than One Targets?
    35. 35. Correlation In Digital Image Processing A More Down To Earth Example… (ROITracker Demo)
    36. 36. Transforms In Digital Image Processing• K(i,j) = F(x(i,j) * kernel(i,j)) – K(i,j) = F(Rows) + F(Columns)• Fourier Transform – Decomposition Into Spatial Frequencies (!!!) • Some Spatial Frequency – Shifting The Origin (Optionally)• Wavelet Transform – Decomposition Into Elementary „Tiles‟• The 2D Spectrum• The 2D Filter
    37. 37. The Discrete Fourier Transform N 1 2 ikn1D DFT  N X k xn e n 0 N X 1 NY 1 kn lm 2 i N X NY2D DFT  X k, l x n, m e n 0 m 0 lMaking Sense f k ,l k 2 l 2 , d k ,l tan 1Of The 2D kSpectrum  2 2 A k,l X r k,l X i k,l 1 X i (k , l ) P(k , l ) tan X r k,lNote: A logarithmic transformation is usually applied to f or A because of therelative magnitude distribution
    38. 38. The Image Spectrum(A Very) Representative Example 50 100 150 200 250 300 350 400 450 500 50 100 150 200 250 300 350 400 450 500What Is TheFundamental FunctionIn This Spectrum?  12 10 140 120 8 6 100 4 2 80 0 60 140 120 100 40 80 60 20 40 20 0 0
    39. 39. The Image Spectrum(Another) Representative Example 5050 100100150 150200 200250 250300 300350 350400 400450 450500 500 50 100 150 200 250 300 350 400 450 500 50 100 150 200 250 300 350 400 450 500 What Is The 0.07 Fundamental Function 0.06 0.05 In This Spectrum?  0.04 0.03 0.02 0.01 140 0 120 140 120 100 100 80 80 60 60 40 40 20 20 0 0
    40. 40. The Image SpectrumSome More Examples 50 100 150 200 250 300 350 400 450 500 50 100 150 200 250 300 350 400 450 500 100 200 300 400 500 600 700 100 200 300 400 500 600 700
    41. 41. The Image SpectrumA Realistic Example 50 100 150 200 250 300 350 400 50 100 150 200 250 300 350 400
    42. 42. References

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