This document summarizes a framework for precise object tracking under image deformation. It discusses various types of image deformation including noise, scaling and rotation, blurring, and illumination changes. It proposes techniques to address each deformation type, including denoising filters, linear and radon transformations for rotation, deblurring algorithms, and using color models like YCbCr that are robust to illumination changes. It also describes morphological operations, geometrical modeling for 3D pose estimation, and using an FIR model for motion prediction to track objects under deformation. The framework is aimed at applications like robot vision, surveillance, medical imaging and more.

5. Block Diagram of Object Tracking System Video Camera USB Camera USB Bus Frame grabber PC Image Acquisition Image Processing Output Target

10. The result is the sum of products of the mask coefficients with the corresponding pixels directly under the mask Pixels of image Mask coefficients Linear Spatial Filters f(x-1,y-1) f(x-1,y) f(x-1,y+1) f(x,y-1) f(x,y) f(x,y+1) f(x+1,y-1) f(x+1,y) f(x+1,y+1) w(-1,-1) w(-1,0) w(-1,1) w(0,-1) w(0,0) w(0,1) w(1,-1) w(1,0) w(1,1) w(-1,-1) w(-1,0) w(-1,1) w(0,-1) w(0,0) w(0,1) w(1,-1) w(1,0) w(1,1)

13. Figure 1 The two-dimensional FWT - the analysis filter Wavelet Transform Figure 2 Two-scale of two-dimensional decomposition

16. 2D Cross Correlation Table 1. 2D cross correlation similarity measure Unsharp filter Average filter Gaussian filter Median filter Adaptive filter Proposed filter Salt and paper noise 0.9234 0.9890 0.6983 0.9809 0.7804 0.9984 Gaussian noise 0.5651 0.9861 0.9446 0.9701 0.9701 0.9876 Poisson noise 0.8270 0.9920 0.9900 0.9910 0.9913 0.9961 Speckle noise 0.6349 0.9879 0.7737 0.8341 0.8547 0.9871

17. Peak Signal-to-Noise Ratio (PSNR) dB Table 2. PSNR similarity measure Unsharp filter Average filter Gaussian filter Median filter Adaptive filter Proposed filter Salt and paper noise 18.59 27.37 25.49 36.00 22.97 49.48 Gaussian noise 9.94 26.16 23.80 26.42 26.79 32.80 Poisson noise 14.74 28.71 30.21 31.92 32.80 43.16 Speckle noise 10.86 26.73 25.38 26.71 27.59 37.67

18. Scaling & Rotation Definition: Scaling & rotation is affine Transformation where Straight lines remain straight, and parallel lines remain parallel. Scaling and Rotation: The linear transformation and radon transformation have been used to recover an image from a rotated and scaled origin.

19. Scaled image Original image Scaled &rotated image Figure 4 Rotated and scaled image Scaling & Rotation

20. Figure 5 Control point selection Linear Transformation

21. Original image Scaled & rotated image recovered image Figure 6 Recovered by using linear transformation Linear Transformation

22. Radon transform: This transform is able to transform two dimensional images with lines into a domain of possible line parameters, where each line in the image will give a peak positioned at the corresponding line parameters. Projections can be computed along any angle θ, by use general equation of the Radon transformation : Radon Transformation x' is the perpendicular distance of the beam from the origin and θ is the angle of incidence of the beams.

23. Original image Figure7 Canny edge detection and edge linking Edge detection Edge linking Radon Transformation

24. Figure 8 Radon transform projections along 180 degrees, from -90 to +89 Radon Transformation

25. Original image Rotated image recovered image Figure 9 Recovered by using radon transform Radon Transformation

28. Deblurring using the Blind Deconvolution Algorithm Figure 10 Deblurring using the blind deconvolution algorithm

29. Figure 11, Capability of object tracking under blurring (a, b) with known blur function and after deblurring (c, d (a) Blurred image (b) Person detection under motion deformation (c)Deblurred image (d) Person detection in deblurred image Deblurring Techniques

30. Blurred image correlation with original one Deblurred image using correct parameters correlation Deblurring Techniques

31. Deblurred image using longer PSF correlation Deblurred image using different angle correlation Figure 12, 2D cross correlation with the deblurring form Deblurring Techniques

32. Table 3, 2D cross correlation with the deblurring form Deblurring Techniques Correlation Condition blurred image with the original one 0.0614 deblurred image with the original one using correct parameters 0.3523 deblurred image with the original one using longer PSF 0.0558 deblurred image with the original one using different angle 0.1231

33. Change of Illumination Change of illumination Color model deformation may happen due to the change in illumination Proposed solution Selecting an appropriate color model (RGB, HSV or yc b c r ) to overcome the deformation problem

39. Original image sample Tracked object Homogeneous Object Extraction

40. sample Homogeneous Object Extraction RGB YC b C r HSV Figure 13, Comparison of homogeneous object extraction Original image

41. Original image Tracked object sample Inhomogeneous Object Extraction

42. Original image RGB sample YC b C r HSV Figure 14, Comparison of inhomogeneous object extraction Inhomogeneous Object Extraction

45. Binary object Binary after removing extra pixel Binary object after dilation holes Binary object after closing Morphological operations Figure 15, The effect of the morphological operation

46. Morphological operations Figure 16, Center of gravity, ellipse fitting and bound box of an image

47. Geometrical Modeling Figure 17 object tracking at different distance

50. Motion Estimation and Prediction based on FIR Figure 19, FIR model structures

51. Motion Estimation and Prediction based on FIR Figure 20, Models output w.r.t system output

52. Motion Estimation and Prediction based on FIR Figure 21 Model output w.r.t system output

53. Motion Estimation and Prediction based on FIR Figure 22 The capability of the model to predict the output if the system input is known