Image Restoration 2 (Digital Image Processing)
- 1. Image Restoration-2 Subject: Image Procesing & Computer Vision Dr. Varun Kumar Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 23 1 / 12
- 2. Outlines 1 Estimation of degradation model By observation By experiment By mathematical modeling 2 Restoration technique Inverse filtering MMSE filtering Constrained least square filter 3 References Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 23 2 / 12
- 3. Degradation model Degradation model g(x, y) = f (x, y) ∗ h(x, y) + η(x, y) (1) and G(u, v) = F(u, v)H(u, v) + N(u, v) (2) and g = Hf + n (3) ⇒ Knowledge of degradation function is essential for acquiring the true image. Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 23 3 / 12
- 4. Observation, experimentation and mathematical modeling ⇒ In all process, there is a requirement of convolution (blind convolution ) operation. The aim of these process are to find the true estimate. 1 Observation: gs(x, y) ⇔ Gs(u, v) fs(x, y) ⇔ Fs(u, v) Hs(u, v) = Gs(u, v) Fs(u, v) Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 23 4 / 12
- 5. Continued– 2 Experimentation: ⇒ Imaging setup similar to original one. ⇒ We need to find the impulse response of imaging set-up. ⇒ For imaging set-up, there is requirement of simulated impulse response. Q How do we simulate the impulse response? Ans. We need a sharp bright spot of beam that can be understand as a simulated impulse response. Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 23 5 / 12
- 6. Continued– F(u, v) = A → F(u, v) ⇔ f (x, y) and G(u, v) = H(u, v)F(u, v) ⇒ H(u, v) = G(u, v) A ⇒ For simulated impulse response the intensity of the light should be very high, so that noise effect could be ignored. Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 23 6 / 12
- 7. Continued– 3 Mathematical modeling: H(u, v) = e−k(u2+v2)5/6 k → Nature of turbulence Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 23 7 / 12
- 8. Basic principle ⇒ f (x, y) → Motion ⇒ x0(t), y0(t) → time varying quantity ⇒ T → Total time, when shutter of the camera is open. Total observed exposure of light can be expressed as g(x, y) = T 0 f x − x0(t), y − y0(t) dt Also G(u, v) = ∞ −∞ ∞ −∞ g(x, y)e−j2π(ux+vy) dxdy or G(u, v) = T 0 ∞ −∞ ∞ −∞ f x − x0(t), y − y0(t) e−j2π(ux+vy) dxdydt Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 23 8 / 12
- 9. Continued– G(u, v) = T 0 ∞ −∞ ∞ −∞ f x − x0(t), y − y0(t) e−j2π(ux+vy) dxdy FT→shifting of position dt Fourier transform f (x − x0(t), y − y0(t)) ⇔ F(u, v)e−j2π ux0(t)+vy0(t) Hence G(u, v) = T 0 F(u, v)e−j2π ux0(t)+vy0(t) dt ⇒ F(u, v) T 0 e−j2π ux0(t)+vy0(t) dt H(u,v) Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 23 9 / 12
- 10. Continued– Let x0(t) = at T and y0(t) = bt T H(u, v) = 1 π(ua + vb) sin π(ua + vb) e−jπ(ua+vb) In above figure, blurring occurs due to the motion of object. Also a = 0.1, b = 0.1 Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 23 10 / 12
- 11. Inverse filtering G(u, v) = H(u, v)F(u, v) ⇒ ˆF(u, v) = G(u, v) H(u, v) General expression for degradation model G(u, v) = H(u, v)F(u, v) + N(u, v) And ˆF(u, v) = F(u, v) + N(u, v) H(u, v) Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 23 11 / 12
- 12. References M. Sonka, V. Hlavac, and R. Boyle, Image processing, analysis, and machine vision. Cengage Learning, 2014. D. A. Forsyth and J. Ponce, “A modern approach,” Computer vision: a modern approach, vol. 17, pp. 21–48, 2003. L. Shapiro and G. Stockman, “Computer vision prentice hall,” Inc., New Jersey, 2001. R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital image processing using MATLAB. Pearson Education India, 2004. Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 23 12 / 12