Prof. Heikki Kälviäinen Lappeenranta University of Technolog y, Finland

1. Prof. Heikki Kälviäinen Lappeenranta University of Technology, Finland

2. Applications of Hough Transform for Image Processing and AnalysisHeikki KälviäinenProfessor, Computer Science*Machine Vision and Pattern Recognition LaboratoryDepartment of Information Technology Lappeenranta University of Technology (LUT), FINLANDHeikki.Kalviainen@lut.fihttp/www.lut.fi/~kalviai**Centre for Vision, Speech, and Signal Processing (CVSSP)University of Surrey, UNITED KINGDOM

4. Hough Transform • Shape detection • Lines, circles, ellipses, arbitrary shapes. • Motion detection and estimation • Simple and robust methods in 2D. • Mixed pixel classification • Large data sets of mixed pixels. • Image compression • Compression and better image quality. • Image databases • Matching of images.

5. Hough surveys and comparisons • J. Illingworth, J. Kittler, A Survey of the Hough Transform, Computer Vision, Graphics, and Image Processing, 1988, vol. 44, pp. 87-116. • V.F. Leavers, Survey: Which Hough Transform, CVGIP Image Understanding, 1993, vol. 58, no. 2, pp. 250‑264. • H. Kälviäinen , P. Hirvonen, L. Xu, E. Oja, Probabilistic, non-probabilistic Hough transforms: overview and comparisons. Image, Vision Computing, 1995, vol. 13, no. 4, pp. 239‑251. • N. Kiryati, H. Kälviäinen, S. Alaoutinen, Randomized or Probabilistic Hough Transform: Unified Performance Evaluation, Pattern Recognition Letters, 2000, vol. 21, nos. 13-14, pp. 1157-1164.

7. Compression, Similarity, Matching, Object Recognition

8. Feature extraction using Hough Transform

9. Hough Transform • A method for global feature extraction: • y = a x + b => b = -x a + y. • For each pixel (x,y) compute a curve b = -x a + b into the parameter space. • Alternatively the normal presentation of a line: • Hough Transform detects sets of pixels which represent geometric primitives in a binary image. • Lines, circles, ellipses, arbitrary shapes, etc. • Tolerant to noise and distortions in an image, but traditional versions suffer from problems with time and space complexities. • New variants: probabilistic and deterministic Hough Transforms.

10. Hough Transform(SHT)

11. Kernel of the Hough Transform • Create the set D of all edge points in a binary picture. • Transform each point in the set D into a parameterized curve in the parameter space. • Increment the cells in the parameter space determined by theparametric curve. • Detect local maxima in the accumulator array. Each local maximum may correspond to a parametric curve in the image space. • Extract the curve segments using the knowledge of the maximum positions.

12. Randomized Hough Transform (RHT) • Developed in Lappeenranta University • of Technology (LUT), • FINLAND. • Xu, L., Oja, E., Kultanen, P, ”A New Curve Detection Method: Randomized Hough Transform (RHT), Pattern Recognition Letters, vol. 11, no. 5., 1990, pp. 331-338.

13. Kernel of the Randomized Hough Transform (RHT) • Create the set D of all edge points in a binary edge picture. • Select a point pair (d_i, d_j) randomly from the set D. • If the points do not satisfy the predefined distance limits, go to Step2; otherwise continue to Step4. • Solve the parameter space point (a, b) using the curve equation with the points (d_i, d_j). • Accumulate the cell A(a, b) in the accumulator space. • If the A(a, b) is equal to the threshold t, the parameters a and bdescribe the parameters of the detected curve; otherwise continue to Step 2.

14. Advances of RHT over SHT • Infinite scope parameter space. • Arbitrarily high parameter resolution. • High computational speed. • Small storage.

15. RHT Extensions Kälviäinen, H., Hirvonen, P., Xu, L., Oja, E., ”Probabilistic and Non-probabilistic Hough Transforms: Overview and Comparisons,” Image and Vision Computing, Vol. 13, No. 4, 1995, pp. 239-251.

16. More complex images

17. Motion Detection by RHT (MDRHT) • 2D motion detection as sets of moving pixels. • A set of moving edge points is assumed to illustrate a moving object frame by frame. • The majority of the points are assumed to move rigidly. • Two moving points is the simplest version. • Extensions: (a) rotation and scaling, (b) exploiting gradient information of each edge point, (c) using three or more moving points as evidence, and (d) detecting multiple moving objects.

18. Motion Detection Using RHT (MDRHT) Kälviäinen, H., ”Motion Detection Using the Randomized Hough Transform (RHT): Exploiting Gradient Information and Detecting Multiple Moving Objects,” IEE Proceedings---Vision,Image and Signal Processing, Vol. 143, No.6,1996, pp.361-369.

19. Kernel of Motion Detection Using Randomized Hough Transform (MDRHT) • Create the sets B and C of edge points, each in one of two consecutive frames. • Select point pairs (b_i,b_j) and (c_i,c_j) randomly from sets B and C, respectively. • If the point pairs correspond, calculate the x- and y-translations dx=c_{ix}-b_{ix} and dy=c_{iy}-b_{iy} and go to Step 4; otherwise, go to Step 2. • Accumulate the cell A(dx,dy). • If the A(dx,dy) is equal to the threshold t, motion (dx,dy) has been detected; otherwise, go to Step 2.

21. Detecting partially deformed motion

22. Detecting multiple objects

23. Mixed pixel classification • What is in a mixed pixel?: The identification of the constituent components and their proportions in a mixed pixel. • For applications with large pixels and/or with large sets of mixed pixels (remote sensing). • Bosdogianni, P.*, Kälviäinen, H., Petrou, M.*, and Kittler, J.*, Robust Unmixing of Large Sets of Mixed Pixels, PatternRecognition Letters, Vol. 18, 1997, pp. 415-424. *Centre for Vision, Speech, and Signal Processing (CVSSP), University of Surrey, UK

24. Linear mixing model • w = ax + by + cz • w: reflectance of a mixed pixel (known). • x, y,z: reflectances of pixels that belong to three different pure classes (known). • a,b,c: proportions of the pure classes present in the mixed pixel (unknown). • Assuming that a+b+c=1, we obtain w - z = (x-z)a + (y-z)b.

25. Pure classes with mixed pixels and outliers

26. Mixel pixel classification by RHT • Select one quadruple (x_1,y_1,z_1,w_1) from the first band and another quadruple (x_2,y_2,z_2,w_2) from the second band of the same pixel randomly. • Using two selected quadruples compute one (a,b) value in the parametric (a,b) space by w - z = (x-z)a + (y-z)b. • Accumulate the cell A(a,b) in the accumulator space. • If the A(a, b) is equal to the threshold t, the parameters a and b describe the parameters of the detected proportions; otherwise continue to Step 1.

27. Advantages and questions • Fast computation and the small accumulator => the use of large datasets possible. • Randomized Hough Transform needs less CPU time and memory than Standard Hough Transform when datasets are large. • Hough methods are more robust than classical Least Square Methods in the presence of outliers. • How high threshold? => e.g. with adaptive termination rules like a variable threshold according to data. • More accuracy? => e.g. by averaging several RHT processes.

28. Image Compression with Hough Feature Extraction*P. Fränti, *E. Ageenko, S. Kukkonen, H. Kälviäinen,Using Hough Transform for Context-based Image Compression in Hybrid Raster/Vector Applications, Journal Of Electrical Imaging,2002, vol. 11, no. 2, pp. 236-245*Department of Computer Science University of Joensuu, Finland

29. Goal: To use vector features in context-based compression of binary images • Context-based compression • Feature extraction using Hough transform • Feature-based context modeling • Feature-based filtering • Results • Conclusions

30. Context-based compression

31. Feature extraction using Hough transform

32. Feature-based context modeling (HTC)

33. Feature-based filtering:Near-lossless compression system (HTF-JBIG)

34. Noise removal procedure

35. Filtering procedure

36. Results of the filtering procedure

37. Original, filtered, and difference images

38. Test images:Bolt, Plan, House Chair, Module, Plus

39. Effects of the feature-based context modeling for the Bolt image

40. Image Hybrid compression Filtering only Filtering + Hybrid vector raster (JBIG) raster (HTC) (HTF-JBIG) (HTF-HTC) BOLT 6,438 12,966 11,514 10,536 9,287 PLAN 2,370 5,098 4,578 4,325 3,786 HOUSE 13,398 15,688 13,961 13,336 11,553 CHAIR 16,710 52,384 50,140 51,529 48,023 MODULE 3,468 7,671 7,222 6,431 6,057 PLUS 5,268 17,609 17,132 16,273 15,739 TOTAL 47,652 111,416 104,547 102,430 94,445 Storage sizes in bytes

41. Computation times of the HT-based compression

42. Conclusions • Two methods proposed for improvingcompression performance • Feature image as side information for compression • Feature-based filtering for removing noise • Problems • Is an exact replica of the original image always needed? • How to improve the quality of vectorizing?

43. Image Databases and Image Matching with Hough Features *P. Fränti, A. Mednonogov, V. Kyrki, H. Kälviäinen Content-Based Matching of Line-Drawing Images Using Hough Transform International Journal on Document Analysis and Recognition (IJDAR) 2000, vol. 3, no. 2, pp. 117-124 *Department of Computer Science, University of Joensuu, Finland

44. Applications of Hough Transform for image databases • Content-based matching of line-drawing images using Hough Transform. • Similarity of images in image databases. • Hough Transform as a feature extractor. • Translation-, • rotation-, and • scale-invariant features from the accumulator matrix.

45. Generated 3D images: query images

46. Generated 3D images: test database

47. Symbol library: noisy and rotated test images