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Mestrado em Ciência de Computadores

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  1. VC 14/15 – TP8Segmentation Mestrado em Ciência de Computadores Mestrado Integrado em Engenharia de Redes e Sistemas Informáticos Miguel Tavares Coimbra

  2. Outline • Thresholding • Geometric structures • Hough Transform Acknowledgements: Most of this course is based on the excellent courses offered by Prof. Shree Nayar at Columbia University, USA and by Prof. Srinivasa Narasimhan at CMU, USA. Please acknowledge the original source when reusing these slides for academic purposes. VC 14/15 - TP8 - Segmentation

  3. Topic: Thresholding • Thresholding • Geometric structures • Hough Transform VC 14/15 - TP8 - Segmentation

  4. Boundaries of Objects Marked by many users http://www.eecs.berkeley.edu/Research/Projects/CS/vision/grouping/segbench/bench/html/images.html VC 14/15 - TP8 - Segmentation

  5. Boundaries of Objects from Edges Brightness Gradient (Edge detection) • Missing edge continuity, many spurious edges VC 14/15 - TP8 - Segmentation

  6. Boundaries of Objects from Edges Multi-scale Brightness Gradient • But, low strength edges may be very important VC 14/15 - TP8 - Segmentation

  7. Machine Edge Detection Image VC 14/15 - TP8 - Segmentation Human Boundary Marking

  8. Boundaries in Medical Imaging Detection of cancerous regions. VC 14/15 - TP8 - Segmentation [Foran, Comaniciu, Meer, Goodell, 00]

  9. Boundaries in Ultrasound Images Hard to detect in the presence of large amount of speckle noise VC 14/15 - TP8 - Segmentation

  10. Sometimes hard even for humans! VC 14/15 - TP8 - Segmentation

  11. Separation of the image in different areas. Objects. Areas with similar visual or semantic characteristics. What is ‘Segmentation’? Not trivial! It is the holy grail of most computer vision problems! VC 14/15 - TP8 - Segmentation

  12. A ‘correct’ segmentation result is only valid for a specific context. Subjectivity! Hard to implement. Hard to evaluate. Subjectivity What is the correct segmentation? Face Person Suitcase VC 14/15 - TP8 - Segmentation

  13. Divide the image into two areas: 1, if f(x,y)>K 0,if f(x,y)<=K Not easy to find the ideal k magic number. Core segmentation technique Simple Reasonably effective Core Technique: Thresholding Adequate threshold VC 14/15 - TP8 - Segmentation

  14. Finding the ‘magic number’ Wrong! (k = 128) Correct (k = 74) VC 14/15 - TP8 - Segmentation

  15. Global thresholds are notalways adequate... VC 14/15 - TP8 - Segmentation http://www.cee.hw.ac.uk/hipr/html/adpthrsh.html

  16. Adapt the threshold value for each pixel. Use characteristics of nearby pixels. How? Mean Median Mean + K ... Adaptive Thresholding Mean of 7x7 neighborhood VC 14/15 - TP8 - Segmentation

  17. 7x7 window; K = 7 75x75 window; K = 10 VC 14/15 - TP8 - Segmentation

  18. Topic: Geometric structures • Thresholding • Geometric structures • Hough Transform VC 14/15 - TP8 - Segmentation

  19. What is a point? Pixel with a significant illumination difference to its neighbors. Group of pixels? Spatial Mask! Need to define a threshold K. Points VC 14/15 - TP8 - Segmentation

  20. Spatial filter One per line direction Sensitive to line width Lines Horizontal Vertical Diagonal? VC 14/15 - TP8 - Segmentation

  21. Edges • Edge: • Spatial discontinuity of pixel amplitude. • High spatial gradient • First derivative (peak) • Second derivative (zero crossing) VC 14/15 - TP8 - Segmentation

  22. Edge detection Great utility for several problems. Well studied problem. A variety of solutions exists. Popular operators VC 14/15 - TP8 - Segmentation

  23. VC 14/15 - TP8 - Segmentation

  24. Processing Edge Images Edge detection and Thresholding Noisy edge image Incomplete boundaries Image Edge Tracking Thinning VC 14/15 - TP8 - Segmentation

  25. Edge Tracking Methods • Adjusting a priori Boundaries Given: Approximate Location of Boundary Task: Find Accurate Location of Boundary • Search for STRONG EDGES along normals to approximate boundary. • Fit curve (eg., polynomials) to strong edges. VC 14/15 - TP8 - Segmentation

  26. Edge Tracking Methods • Divide and Conquer Given: Boundary lies between points A and B Task: Find Boundary • Connect A and B with Line • Find strongest edge along line bisector • Use edge point as break point • Repeat VC 14/15 - TP8 - Segmentation

  27. Fitting Lines to Edges (Least Squares) Given: Many pairs Find: Parameters Minimize: Average square distance: Using: Note: VC 14/15 - TP8 - Segmentation

  28. Topic: Hough Transform • Thresholding • Geometric structures • Hough Transform VC 14/15 - TP8 - Segmentation

  29. Hough Transform • Elegant method for direct object recognition • Edges need not be connected • Complete object need not be visible • Key Idea: Edges VOTE for the possible model VC 14/15 - TP8 - Segmentation

  30. Image and Parameter Spaces Equation of Line: Find: Consider point: ImageSpace Parameter Space Parameter space also called Hough Space VC 14/15 - TP8 - Segmentation

  31. Line Detection by Hough Transform Algorithm: • Quantize Parameter Space • Create Accumulator Array • Set • For each image edge increment: • If lies on the line: • Find local maxima in Parameter Space VC 14/15 - TP8 - Segmentation

  32. ? Better Parameterization NOTE: Large Accumulator More memory and computations Improvement: Line equation: Here Given points find Image Space (Finite Accumulator Array Size) Hough Space Hough Space Sinusoid VC 14/15 - TP8 - Segmentation

  33. Image space Votes Horizontal axis is θ, vertical is rho. VC 14/15 - TP8 - Segmentation

  34. VC 14/15 - TP8 - Segmentation

  35. VC 14/15 - TP8 - Segmentation

  36. Difficulties how big should the cells be? (too big, and we merge quite different lines; too small, and noise causes lines to be missed) How many lines? Count the peaks in the Hough array Treat adjacent peaks as a single peak Which points belong to each line? Search for points close to the line Solve again for line and iterate Mechanics of the Hough Transform VC 14/15 - TP8 - Segmentation

  37. Fewer votes land in a single bin when noise increases. VC 14/15 - TP8 - Segmentation

  38. Adding more clutter increases number of bins with false peaks. VC 14/15 - TP8 - Segmentation

  39. Real World Example Original Found Lines Edge Detection Parameter Space

  40. Other shapes Edges when using circle model Original VC 14/15 - TP8 - Segmentation

  41. Resources • Gonzalez & Woods – Chapter 7 • N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Sys., Man., Cyber., vol. 9, pp. 62–66, 1979. VC 14/15 - TP8 - Segmentation