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Pawel FORCZMANSKI (West Pomeranian University of Technology) "Advanced digital image processing methods"

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– Digital image acquisition, classes of images
– Image quality assessment
– Simple image features and their application
– Image filtering in the spatial and spectral domains
– Extracting certain features of images (corners, circles, edges)
– Exemplary applications

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Pawel FORCZMANSKI (West Pomeranian University of Technology) "Advanced digital image processing methods"

  1. 1. Erasmus+seminar,18/04/2016 1 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Advanced Digital Image Processing: problems, methods and applications Paweł Forczmański Chair of Multimedia Systems, Faculty of Computer Science and Information Tech- nology, West Pomeranian University of Technology, Szczecin Vilnius University, Institute of Mathematics and Informatics, 18/04/2016
  2. 2. Erasmus+seminar,18/04/2016 2 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin AgendaAgenda Introduction (objectives, problems, image classes, acquisition) Introduction (objectives, problems, image classes, acquisition) Image filtering methodsImage filtering methods Image quality estimation (concpets, exemplary metrics) Image quality estimation (concpets, exemplary metrics) Simple image features and their applicationSimple image features and their application
  3. 3. Erasmus+seminar,18/04/2016 3 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Computer graphics Data processing Signal processing Digital image processing Pattern recognition IntroductionIntroduction
  4. 4. Erasmus+seminar,18/04/2016 4 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin DIP: Application AreasDIP: Application Areas OCR Criminal Forensic CAD Robotics GIS Media and Entertainment CT MRI USG Bar codes Text processing
  5. 5. Erasmus+seminar,18/04/2016 5 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin ObjectivesObjectives Image quality improvement compression Image representation transformation Objective (computer) transmission Subjective (human) coding storing Image quality improvement
  6. 6. Erasmus+seminar,18/04/2016 6 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Image classesImage classes
  7. 7. Erasmus+seminar,18/04/2016 7 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin . . . M N K . . . Tyical color image is in a raster form which has: M columns N rows i K layers: Sample image with MxNx3 (YUV color- space) Data representation (1)Data representation (1)              kNMkM kNk k NM Kk xx xx X ,,,1, ,,1,1,1   
  8. 8. Erasmus+seminar,18/04/2016 8 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Light sensors matrixLight sensors matrix cones cones cones rods Bayer matrix Human eye
  9. 9. Erasmus+seminar,18/04/2016 9 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Bryce Bayer - patent (U.S. Patent No. 3,971,065) - 1976 MegaPixels?MegaPixels?
  10. 10. Erasmus+seminar,18/04/2016 10 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Bayer Matrix vs Foveon X3Bayer Matrix vs Foveon X3
  11. 11. Erasmus+seminar,18/04/2016 11 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Image acquisitionImage acquisition quantization discretization Digital image quantization quantization discretization discretization
  12. 12. Erasmus+seminar,18/04/2016 12 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Nadajnik Trans. channel Signal quality estimation Source Reconstruction and presentation Perception and un- derstanding processing, storing and transmission Acquisition and registration Signal source Knowlegde about distortions Knowlegde about receiver and application Knowlwdge about source and transmitter Receiver ➔ Imaging systems can introduce certain signal distortions or artifacts, there- fore, it is an important issue to be able to evaluate the quality. Quality estimationQuality estimation
  13. 13. Erasmus+seminar,18/04/2016 13 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin The quality of an image can be reduced during ● Image acquisition ● Image transmisson ● Image processing Quality measure may be a determinant of quality degradation Classification of methods I: perceptual (perceptive, subjective) objective (calculative). Classification of methods II: Scalar-based, Vector-based (sets of scalars) Classification of methods III: Full-reference, No-reference, Partial-reference Image QualityImage Quality
  14. 14. Erasmus+seminar,18/04/2016 14 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin • Related works – Pioneering work [Mannos & Sakrison ’74] – Sarnoff model [Lubin ’93] – Visible difference predictor [Daly ’93] – Perceptual image distortion [Teo & Heeger ’94] – DCT-based method [Watson ’93] – Wavelet-based method [Safranek ’89, Watson et al. ’97] Philosophy: degraded signal = reference signal + error reference signal → ideal quantitive estimation of distortions level Standard model of IQA: Image Quality AssessmentImage Quality Assessment
  15. 15. Erasmus+seminar,18/04/2016 15 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Motivation – simulating elementary characteristics of HVS Main features: Channel decomposition  linear transformation Frequency weigthing  contrast sensitivity function Masking  intra-channel interactions Reference signal Evaluation Channel decomposition Error normalization. . . Aggregation Pre- processing . . .   /1 ,        l k kleE Evaluated sugnal Standard model of IQAStandard model of IQA (Image Quality Assessment)(Image Quality Assessment)
  16. 16. Erasmus+seminar,18/04/2016 16 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin + + _ = + +... ... structural distortion + distorted image original image = + + + nonstructural distortion cK+1 . c1 . cK+2 . c2 . cM . cK .+ + nonstructural distortion components structural distortion components Standard model of IQA (Image QualityStandard model of IQA (Image Quality Assessment): Adaptive Linear SystemAssessment): Adaptive Linear System
  17. 17. Erasmus+seminar,18/04/2016 17 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin
  18. 18. Erasmus+seminar,18/04/2016 18 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Structural content Normalized Cross-Colerraltion Peak Absolute Error (PAE) Image Fidelity Average Difference
  19. 19. Erasmus+seminar,18/04/2016 19 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Mean Square Error Zhou Wang and Alan C. Bovik, Mean Squared Error: Love It or Leave It? A New Look at Signal Fidelity Measures, IEEE Signal Processing Magazine vol. 26, no. 1, pp. 98-117, Jan. 2009
  20. 20. Erasmus+seminar,18/04/2016 20 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Peak Mean Square Error Normalized Absolute Error Normalized Mean Square Error Lp norm (Minkowski) Peak Signal-to-Noise Ratio Signal-to-Noise Ratio
  21. 21. Erasmus+seminar,18/04/2016 21 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin RMSE 9.5 (blurred)(blurred) RMSE 5.2 Pixel by Pixel ComparisonPixel by Pixel Comparison Prikryl, 1999
  22. 22. Erasmus+seminar,18/04/2016 22 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin X. Shang, “Structural similarity based image quality assessment: pooling strategies and ap- plications to image compression and digit recognition” M.S. Thesis, EE Department, The University of Texas at Arlington, Aug. 2006. Structural Similarity (SSIM) IndexStructural Similarity (SSIM) Index
  23. 23. Erasmus+seminar,18/04/2016 23 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin i k j x xi + xj + xk = 0 x - x O luminance change contrast change structural change xi = xj = xk ),(),(),(),( yxyxyxyx sclSSIM  1 22 12 ),( C C l yx yx      yx c(x , y)= 2 σx σ y+C2 σx 2 + σ y 2 +C2 3 3 ),( C C s yx xy      yx [Wang & Bovik, IEEE Signal Processing Letters, ’02] [Wang et al., IEEE Trans. Image Processing, ’04] Structural Similarity (SSIM) IndexStructural Similarity (SSIM) Index
  24. 24. Erasmus+seminar,18/04/2016 24 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin MSE=0, MSSIM=1 MSE=225, MSSIM=0.949 MSE=225, MSSIM=0.989 MSE=215, MSSIM=0.671 MSE=225, MSSIM=0.688 MSE=225, MSSIM=0.723 Zhou Wang Image Quality Assessment: From Error Visibility to Structural Similarity MSE vs mSSIMMSE vs mSSIM
  25. 25. Erasmus+seminar,18/04/2016 25 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin original image JPEG2000 compres- sed image absolute error map SSIM index map
  26. 26. Erasmus+seminar,18/04/2016 26 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin original image Gaussian noise cor- rupted image absolute error map SSIM index map
  27. 27. Erasmus+seminar,18/04/2016 27 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin original image JPEG com- pressed image absolute error map SSIM index map
  28. 28. Erasmus+seminar,18/04/2016 28 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Zhou Wang and Alan C. Bovik, Mean Squared Error: Love It or Leave It? A New Look at Signal Fidelity Measures, IEEE Signal Processing Magazine vol. 26, no. 1, pp. 98-117, Jan. 2009 Comparison of quality measuresComparison of quality measures
  29. 29. Erasmus+seminar,18/04/2016 29 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Image 2 Image 1 Psychometric Function Probability Summation Visualisationof Differences Amplitude Nonlinear. Amplitude Nonlinear. Contrast Sensitivity Function Contrast Sensitivity Function + Cortex Transform Cortex Transform Masking Function Masking Function Unidirectional or Mutual Masking [Daly ‘93, Myszkowski ‘98] Visible Differences Predictor (VDP)Visible Differences Predictor (VDP) ➔ Predicts local differences between images ➔ Takes into account important visual charac- teristics: ➔ Amplitude compression ➔ Advanced CSF model ➔ Masking ➔ Uses the cortex transform, which is a pyra- mid-style, invertible & computationally effi- cient image representation
  30. 30. Erasmus+seminar,18/04/2016 30 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin VDP: ResultsVDP: Results Reference Analysed Pixel differences: Reference - Analysed Pixel differences The VDP response: probability of perceiving the differences VDP response
  31. 31. Erasmus+seminar,18/04/2016 31 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin image f(x,y) Conversion to digital form Image pre-processing Features extraction Conversion to output form Output image Features DIP schemeDIP scheme local transform point transform global transform
  32. 32. Erasmus+seminar,18/04/2016 32 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin f(x) x b H(b) 180 200 220 240 0 50 100 e H(e) 180200220240 0 50 100 Histogram stretching along a defined line changes the distribution of in- tensities in an image by the alterna- tion of intensity assignment in each interval Each interval changes its width: where b –pixel intensity before: e –pixel intensity after stretching; f(b) –stretching function. The tangent of an angle of function f(b) is the coeficient that changes the width of each histogram interval d e= f 'bd b Histogram modellingHistogram modelling
  33. 33. Erasmus+seminar,18/04/2016 33 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin The most simple is a linear stretching: Where a can is equal to: where x1 , x2 – boundaries of intensity. E – maximum possible intensity f (x)= { 0 for x<0 ax E for x>E a= E x2−x1 Simple linear caseSimple linear case 50 100 150 200 0 1000 2000 3000 b H(b) f(x) x 50100150200 0 1000 2000 3000 e H(e) x1 x2
  34. 34. Erasmus+seminar,18/04/2016 34 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin histogramSource image Non-linear cases (examples)Non-linear cases (examples)
  35. 35. Erasmus+seminar,18/04/2016 35 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin It usually increases the global contrast of images, especially when the usable data of the image is represented by close contrast values. Through this adjustment, the intensities can be better distributed on the histo- gram. Areas of lower local contrast gain a higher contrast. Histogram equalizationHistogram equalization 0 2 4 6 8 0 1 2 3 b H(b) mean 0 2 4 6 8 0 1 2 3 e H(e) mean
  36. 36. Erasmus+seminar,18/04/2016 36 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Work in RGB spaceWork in RGB space originalRGB equalized
  37. 37. Erasmus+seminar,18/04/2016 37 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Work in HSL spaceWork in HSL space HSL equalized
  38. 38. Erasmus+seminar,18/04/2016 38 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin RGB and HSL comparisonRGB and HSL comparison original RGB equalized HSL equalized
  39. 39. Erasmus+seminar,18/04/2016 39 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin One-dimensional histogram if defined by function f : f : X×Y  Z f −1 : Z  2 X ×Y f −1 : {x , y∣f x , y=z } 1D vs 2D histogram1D vs 2D histogram Two-dimensional histogram if defined by functions f and g : f : X×Y  Z g : X ×Y  V f −1 : Z  2 X ×Y g−1 : V  2 X ×Y f −1 : {x , y∣f x , y=z } g−1 : {x , y∣gx , y=v}
  40. 40. Erasmus+seminar,18/04/2016 40 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin There are many 2D histograms! One of the most useful is coocur- rence matrix M 1= [ 0 0 0 0 0 1 1 1 0 1 2 2 0 1 2 3 ]; z=[0123] ; H1(z)=[7531]; M 2 = [ 1 3 2 0 2 0 1 0 1 0 2 0 0 0 1 1 ]; z=[0 1 2 3 ]; H 2z=[7 5 3 1]; Co-occurrence matrixCo-occurrence matrix r={x , y,x , y1}; Cr=H fg z ,v; f x , y=gx , y1; Cr1 = [ 3 3 0 0 0 2 2 0 0 0 1 1 0 0 0 0 ]; Cr2 = [ 1 2 1 0 2 1 0 1 3 0 0 0 0 0 1 0 ]; ← 1D Histograms → ← 2D Histograms →
  41. 41. Erasmus+seminar,18/04/2016 41 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Example of calculation on real image – it helps when we want to tell if the image is crisp or blurred ExampleExample
  42. 42. Erasmus+seminar,18/04/2016 42 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin exampleexample Intensity thresholding for for
  43. 43. Erasmus+seminar,18/04/2016 43 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin In digital image processing convolutional filtering plays an important role in: ➔ Edge detection and related processes; ➔ Sharpening; ➔ Blurring; ➔ Special effects (motion blur) ➔ Etc... Traditional computing (sequential programming); Parallel computing (mult processors/cores, GPU: „stencil computing”). Convolutional filteringConvolutional filtering
  44. 44. Erasmus+seminar,18/04/2016 44 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin In practice, f and g are vectors or matrices with discrete values, and integral operator is changed into sum. Convolutional filteringConvolutional filtering h[ x]=∑ t=t1 t=tn f [x−t]g [t ] f1 f2 f3 f4 f5 f6 f7 f8 g3 g2 g1 * * * h1 h2 h3 h4 h5 h6  norm (window .*mask) norm f ∗g=∫−∞ ∞ f (x−t)g(t)dt
  45. 45. Erasmus+seminar,18/04/2016 45 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin 1 1 1 1 1 1 1 1 1 Norm=9 1 1 1 1 1 2 1 1 1 Norm=10 1 1 1 1 1 3 1 1 1 Norm=11 0 1 0 0 0 1 1 0 0 Norm=3 Averaging filterAveraging filter 1 1 1 1 1 Norm=5 1 1 1 1 1 Norm=5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Norm=21 1 1 1
  46. 46. Erasmus+seminar,18/04/2016 46 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin An image f is filtered with a mask gσ which is a discrete appro- ximation of two-dimensional Gauss function: Gauss filteringGauss filtering decides about blurring effect
  47. 47. Erasmus+seminar,18/04/2016 47 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Edge detectionEdge detection Edges can be detected using various gradient operators: ➔ First derivative of an image shows the edge and its direction ➔ Point of sign change of second derivative (zero crossing), can also be used to detect edges The main problem is false detection, which comes from the amplification of noise! Second derivative image Intensty projection First derivative The edge is a local change in image intensity and its vertical (or horizontal) projection can look like that presented above
  48. 48. Erasmus+seminar,18/04/2016 48 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin 8 2 222 Horizontal lines Vertical lines+45o -45opoint detection Line detectionLine detection
  49. 49. Erasmus+seminar,18/04/2016 49 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin ow( j ,k)=√[ A4− A8 ] 2 +[A5− A7 ] 2 0 Roberts vs PrewittRoberts vs Prewitt A0 A1 A2 A3 A4 A5 A6 A7 A8 ow  j ,k =X 2 Y 2 X =A2 2 A3 A4 −A0 2 A7 A6  Y =A0 2 A1 A2 − A6 2 A5  A4  ow (j,k) ow (j,k) Roberts filtering Prewitt filtering
  50. 50. Erasmus+seminar,18/04/2016 50 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Prewitt vs SobelPrewitt vs Sobel PrewittPrewitt SobelSobel
  51. 51. Erasmus+seminar,18/04/2016 51 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Laplace operator (Laplasian) is defined as a second derivative of image f at the location (x,y) Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Laplace operatorLaplace operator or
  52. 52. Erasmus+seminar,18/04/2016 52 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin ow( j ,k)=max {1, max i∈〈0 ;7〉 ∣5Si −3Ti∣ } Si =Ai + Ai+1+ Ai +2 Ti= Ai+3+ Ai+ 4+ Ai+ 5+ Ai+6+ Ai+7 i∈〈0 ;7〉 indexes change modulo 8 KirschKirsch where
  53. 53. Erasmus+seminar,18/04/2016 53 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Canny edge detectorCanny edge detector ➔ multi-stage algorithm to detect a wide range of edges in images ➔ developed by John F. Canny in 1986 ➔ Canny also produced a computational theory of edge detection explaining why the technique works. An "optimal" edge detector means: good detection – the algorithm should mark as many real edges in the image as possible. good localization – edges marked should be as close as possible to the edge in the real image. minimal response – a given edge in the image should only be marked once, and where possible, image noise should not create false edges.
  54. 54. Erasmus+seminar,18/04/2016 54 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin 1. Image smoothing using Gaussian 2. Derivatives calulation using masks: [-1 0 1] i [-10 1]'. Canny Edge DetectorCanny Edge Detector
  55. 55. Erasmus+seminar,18/04/2016 55 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin 3. Non-maximum suppression as an edge thin- ning technique. A 3x3 filter is moced over an image and at every lo- cation, it suppresses the edge strength of the center pixel (by setting its value to 0) if its magnitude is not greater than the magnitude of the two neigh- bors in the gradient direction 4. Tracing edges through the image and hy- steresis thresholding Canny Edge DetectorCanny Edge Detector
  56. 56. Erasmus+seminar,18/04/2016 56 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Non-linear filteringNon-linear filtering Output image's pixels result from a nonlinear transform of input image's pixels and a filter mask Example: Media filter Input set: A={9,88,1,15,43,100,2,34,102} Sort elements in A (increasing➔ order): B=sort(A) B={1,2,9,15,34,43,88,100,102} Select median of B (middle element):➔ median(B)=34
  57. 57. Erasmus+seminar,18/04/2016 57 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Non-linear filteringNon-linear filtering
  58. 58. Erasmus+seminar,18/04/2016 58 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Adaptive filteringAdaptive filtering
  59. 59. Erasmus+seminar,18/04/2016 59 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Detecting charactersitic pointsDetecting charactersitic points Objects/scene detection can be based on detecting charac- teristic points ●Matching point Pij in the image j to the point Pik in the image k ●Removing false candidates ● Certain points Pij in the image j have no corresponding points Pik in the image k ●Ambiguity ● Several points Pij in the image j correspond to a point Pik ●Noise
  60. 60. Erasmus+seminar,18/04/2016 60 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin How?How? Corner operator is one solution...
  61. 61. Erasmus+seminar,18/04/2016 61 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin IdeaIdea It is a possibility that such interesting point may be detected by looking at the image through some small window. By sliding this window over the image we can de- tect significant changes in intensity in a certain di- rection ● Morevec detector ● Harris detector
  62. 62. Erasmus+seminar,18/04/2016 62 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Moravec detectorMoravec detector There are 3 cases:  ● If an area is uniform (flat), the dif- ferences calculated in all directions will be not significant ● If it is an edge, the diferences along its direction will be small, while in the perpendicular direction – large ● If there is an isolated point, the di- ferences in most of directions will be significant ● Finally, the maxima of points with the highest differences are selected flat edge corner isolated point
  63. 63. Erasmus+seminar,18/04/2016 63 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin Harris detectorHarris detector R(x,y)=det(M) - (trace(M)) 2
  64. 64. Erasmus+seminar,18/04/2016 64 / 64 Faculty of Computer Science and Information Technology West Pomeranian University of Technology, Szczecin ComparisonComparison Harris Moravec

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