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Medical Image Analaysis

Medical Image Analaysis. Atam P. Dhawan. Image Enhancement: Spatial Domain. Histogram Modification. Medical Images and Histograms. Histogram Equalization. f (-1,0). f (0,-1). f (0,0). f (0,1). f (1,0). f (-1,-1). f (-1,0). f (-1,0). f (0,-1). f (0,0). f (0,1). f (0,-1). f (1,0).

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Medical Image Analaysis

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  1. Medical Image Analaysis Atam P. Dhawan

  2. Image Enhancement: Spatial Domain Histogram Modification

  3. Medical Images and Histograms

  4. Histogram Equalization

  5. f(-1,0) f(0,-1) f(0,0) f(0,1) f(1,0) f(-1,-1) f(-1,0) f(-1,0) f(0,-1) f(0,0) f(0,1) f(0,-1) f(1,0) f(1,1) Image Averaging Masks

  6. 1 2 1 2 4 2 1 2 1 Image Averaging

  7. Median Filter

  8. -1 -1 -1 -1 8 -1 -1 -1 -1 Laplacian: Second Order Gradient for Edge Detection

  9. -1 -1 -1 -1 9 -1 -1 -1 -1 Image Sharpening with Laplacian

  10. Center Region Xc Xc Surround Region Feature Adaptive Neighborhood

  11. Feature Enhancement C’(x,y)=F{C(x,y)}

  12. Micro-calcification Enhancement

  13. Frequency-Domain Methods

  14. Low-Pass Filtering

  15. High Pass Filtering

  16. Wavelet Transform • Fourier Transform only provides frequency information. • Windowed Fourier Transform can provide time-frequency localization limited by the window size. • Wavelet Transform is a method for complete time-frequency localization for signal analysis and characterization.

  17. Wavelet Transform.. • Wavelet Transform : works like a microscope focusing on finer time resolution as the scale becomes small to see how the impulse gets better localized at higher frequency permitting a local characterization • Provides Orthonormal bases while STFT does not. • Provides a multi-resolution signal analysis approach.

  18. Wavelet Transform… • Using scales and shifts of a prototype wavelet, a linear expansion of a signal is obtained. • Lower frequencies, where the bandwidth is narrow (corresponding to a longer basis function) are sampled with a large time step. • Higher frequencies corresponding to a short basis function are sampled with a smaller time step.

  19. Continuous Wavelet Transform • Shifting and scaling of a prototype wavelet function can provide both time and frequency localization. • Let us define a real bandpass filter with impulse response y(t) and zero mean: • This function now has changing time-frequency tiles because of scaling. • a<1: y(a,b) will be short and of high frequency • a>1: y(a,b) will be long and of low frequency

  20. Wavelet Decomposition

  21. Wavelet Coefficients • Using orthonormal property of the basis functions, wavelet coefficients of a signal f(x) can be computed as • The signal can be reconstructed from the coefficients as

  22. Wavelet Transform with Filters • The mother wavelet can be constructed using a scaling function f(x) which satisfies the two-scale equation • Coefficients h(k) have to meet several conditions for the set of basis functions to be unique, orthonormal and have a certain degree of regularity. • For filtering operations, h(k) and g(k) coefficients can be used as the impulse responses correspond to the low and high pass operations.

  23. H H 2 H 2 Data G 2 G 2 G 2 Decomposition

  24. Wavelet Decomposition Space

  25. s u b - s a m p l e h - h h s u b - s a m p l e h - g h g X h g - h g g - g g h o r i z o n t a l l y v e r t i c a l l y L e v e l 0 L e v e l 1 Image Decomposition Image

  26. Wavelet and Scaling Functions

  27. Image Processing and Enhancement

  28. Image Segmentation • Edge-Based Segmentation • Gray-level Thresholding • Pixel Clustering • Region Growing and Spiliting • Artificial Neural Network • Model-Based Estimation

  29. Gray-Level Thesholding

  30. Region Growing

  31. Neural Network Element

  32. Artificial Neural Network: Backpropagation

  33. Output Linear Combiner RBF Unit 2 RBF Unit 1 RBF Unit n RBF Layer Input Image Sliding Image Window RBF Network

  34. RBF NN Based Segmentation

  35. Top-Down Scenario Scene-1 Scene-I Object-1 Object-J S-Region-1 S-Region-K Region-1 Region-L Edge-1 Edge-M Pixel (i,j) Pixel (k,l) Bottom-Up Image Representation

  36. Image Analysis: Feature Extraction • Statistical Features • Histogram • Moments • Energy • Entropy • Contrast • Edges • Shape Features • Boundary encoding • Moments • Hough Transform • Region Representation • Morphological Features • Texture Features • Spatio Frequency Features • Relational Features

  37. Image Classification • Feature Based Pattern Classifiers • Statistical Pattern Recognition • Unsupervised Learning • Supervised Learning • Sytntactical Pattern Recognition • Logical predicates • Rule-Based Classifers • Model-Based Classifiers • Artificial Neural Networks

  38. A B Morphological Features

  39. A E H B O D F G C Some Shape Features • Longest axis GE. • Shortest axis HF. • Perimeter and area of the minimum bounded rectangle ABCD. • Elongation ratio: GE/HF • Perimeter p and area A of the segmented region. • Circularity • Compactness

  40. A I C D F E B I A B C D E F Relational Features

  41. Nearest Neighbor Classifier

  42. Input Database Output Database Activity Center Knowledge Rules Focus of Attention Rules Strategy Rules A priori knowledge or models Rule Based Systems

  43. Strategy Rules

  44. FOA Rules

  45. Knowledge Rules

  46. Neuro-Fuzzy Classifiers

  47. Extraction of Ventricles

  48. Composite 3D Ventricle Model

  49. Extraction of Lesions

  50. Extraction of Sulci

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