8D040 Basis beeldverwerking Feature Extraction

1. 8D040 Basis beeldverwerkingFeature Extraction Anna Vilanova i Bartrolí Biomedical Image Analysis Group bmia.bmt.tue.nl

2. N=M=30 What is an image? Image is a 2D rectilinear array of pixels (picture element) N=M=256

3. Binary Image L=1 (1 bit) L=3 (2 bits) L=15(4 bits) L=255 (8 bits) What is an image? No continuous values - Quantization 8 170 15 255

4. An image is just 2D? No! – It can be in any dimension Example 3D: Voxel-Volume Element

5. Segmentation VERY DIFFICULT

6. Why feature extraction ? Reduction of dimensionality Pixel level Image of 256x256 and 8 bits 256 65536 ~ 10 157826 possible images

7. Incorporation of cues from human perception Transcendence of the limits of human perception The need for invariance Why feature extraction ?

8. Apple detection …

9. Transformation (Rotation)

10. How do we transform an image? How do we know which Q belongs to P? We transform a point P How do we transform an image f(P)?

11. How do we transform an image? How do we know which Q belongs to P? We know T which is the transformation we want to achieve. How do we transform an image f(P)?

12. Apple detection …

13. Feature Characteristics • Invariance (e.g., Rotation, Translation) • Robust (minimum dependence on) • Noise, artifacts, intrinsic variations • User parameter settings • Quantitative measures

15. We extract features from… Segmented Objects Region of Interest

16. Features Texture Based (Image & ROI) Shape (Segmented objects) Classification

17. Shape Based Features • Object based • Topology based (Euler Number) • Effective Diameter (similarity to a circle to a box) • Circularity • Compactness • Projections • Moments (derived by Hu 1962) • …

18. Adjacency and Connectivity – 2D 4-neighbourhood of 8-neighbourhood of • Notation: k-Neighbourhood of is

19. 6-neighbourhood 18-neighbourhood 26-neighbourhood Adjacency and Connectivity – 3D

20. Objects or Components (Jordan Theorem) In 2D – (8,4) or (4,8)-connectivity In 3D – (6,26)-,(26,6)-,(18,6)- or (6,18)-connectivity

21. Connected Components Labeling Each object gets a different label

22. Connected Components Labeling B Raster Scan C A Note: We want to label A. Assuming objects are 4-connected B, C are already labeled. Cortesy of S. Narasimhan

23. Connected Components Labeling X 0 X 0 0 1   label(A) = new label label(A) = “background” 0 C 1  label(A) = label(C)  label(A) = label(B) B B If label(B) = label(C) then, label(A) = label(B)  0 1 C 1 Cortesy of S. Narasimhan

24. Connected Components Labeling B What if label(B) not equal to label(C)?  C 1

25. Connected Components Labeling Each object gets a different label

26. Features Texture Based (Image & ROI) Shape (Segmented objects) Classification

27. Topology based – Euler Number Euler Number E describes topology. C is # connected components H is # of holes.

28. Euler Number 3D E=1+0-1=0 E=1+0-1=0 E=1+1-0=2 • Euler Number E describes topology. • Cis # connected components • Cav is # of cavities • G is # of genus

29. Euler Number 3D E=2+0-0=2 E=1+1-0=2 • Euler Number E describes topology. • Cis # connected components • Cav is # of cavities • G is # of genus

30. 3D Euler Number • The Euler Number in 3D can be computed with local operations • Counting number of vertices, edges and faces of the surfaces of the objects

31. Simple Shape Measurements • 2D area - 3D volume • Summing elements • 2D perimeter - 3D surface area • Selection of border elements • Sum of elemets with weights • Error of precision

32. Similarity to other Shape • Effective Diameter • Circularity (Circle C=1) • Compactness – (Actually non-compactness)(Circle Comp= )

33. Moments • Definition • Order of a moment is • Moments identify an object uniquely • ?is the Area • Centroid

34. Central Moments Moments invariant to position Invariant to scaling

35. Moments to Define Shape and Orientation Inertia Tensor

36. Eigenanalysis of a Matrix • Given a matrixS, we solve the following equation • we find the eigenvectors and eigenvalues • Eigenvectors and eigenvalues go in couples an usually are ordered as follows:

37. Eigenanalysis of the Inertia Matrix Eigenanalysis Sphere Flatness Elongated

38. Eigenanalysis of the Inertia Matrix Eigenanalysis Sphere Flatness Elongated

39. Orientation in 2D • Using similar concepts than 3D • Covariance or Inertia Matrix • Eigenanalysis we obtain 2 eigenvalues and 2 eigenvectors of the ellipse

40. Moments Invariance • Translation • Central moments are invariant • Rotation • Eigenvalues of Inertia Matrix are invariant • Scaling • If moment scaled by (3D) (2D)

41. Moments invariant rotation-translation-scaling • For 3D three moments (Sadjadi 1980) For 2D seven moments

42. Features Texture Based (Image & ROI) Shape (Segmented objects) Classification

43. Image Based Features Gonzalez & Woods – Digital Image Processing Chapter 11 – 11.3.3 Texture • Using all pixels individually • Histogram based features • Statistical Moments (Mean, variance, smoothness) • Energy • Entropy • Max-Min of the histogram • Median • Co-occurrance Matrix

44. Histogram P(bi) bi L=9

45. How do the histograms of this images look like?

46. Bimodal Histogram

47. Trimodal Features

48. Histogram Features • Mean • Central Moments

49. Histogram Features • Mean • Variance • Relative Smoothness • Skewness

50. Histogram Features Energy (Uniformity) Entropy