Image Enhancement Using Calibrated Lens Simulations
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1 Image Enhancement Using Calibrated Lens Simulations Jointly Image Sharpening and Chromatic Aberrations Removal Yichang Shih, Brian Guenter, Neel Joshi MIT CSAIL, Microsoft Research 1
2 Optical Aberrations All lenses have optical aberrations [Seidel, 1856] Spherical aberration Ray Tracing Focused PSF, but still has finite size Chromatic aberration (caused by dispersion of the glasses) 2 Ray Tracing R/G/B are separate
3 Taken by Nikkon D80 + kit lens
4 Effect of Optical Aberrations Blur even the camera is focused Chromatic aberration and geometric distortion on the boundary 4
5 Image Enhancement The aberrations can be removed by deconvolution [B.A. Scalettar, et al 1995] The quality of deconvolved image depends on the PSF PSFs measurement is a tremendous and expensive work - PSFs are spatially variant - PSFs depends on focal plane distance - Point light sources are impossible Impossible to measure PSF at every position/focal plane Our method: Simulate PSFs by ray tracing using lens model 5
6 Applications Image enhancement by cloud computing - The server has an accurate lens prescription for each lens - The user takes an image. Uploads to the server for deconvolution - Remove chromatic aberrations, distortions, and sharpen the image simultaneously. Target applications: mobile phone cameras - In our work, we use small lenses. (Eg. Edmund 58202, D=9mm) - Most mobile phone camera lenses are prime lens. Easier to model. 6
7 Simulate PSFs by Ray Tracing Given a lens prescription, we trace each light ray to generate the PSFs. Lens prescription: Lens model - number of glasses - dispersion function of each glass n 2-1 = C 1 λ 2 /(λ 2 -C 2 ) + C 3 λ 2 /(λ 2 -C 4 ) + C 5 λ 2 /(λ 2 -C 6 ) (n:refraction index) Parameters - radius, xyz position of each glass - coefficients of the dispersion functions (C1 C6) Wave optics must be considered. Left: geometric ray tracing only Right: with Huyguens ray tracing 7
8 Verification by PSF Measurement Set up for PSFs measurement Measured PSFs Lens Camera Pinhole arrays (light sources) 20x20 holes 8
9 The results are unsatisfying Measured Synthesized by our simulator Edmund Our assumption: model is correct, but parameters are incorrect - Tolerances in manufacturing - Small variations between lenses have a noticeable effect Our method: Fit the synthetic PSFs by measured PSFs to find out the more accurate lens prescription 9
10 Lens Fitting Initial Lens Model Current Lens Model Ray tracing Simulated PSFs from spec Update the lens Lens Fitting (Optimization) Measured PSFs 1. We measure few PSFs to fit an accurate lens model 2. Then simulate accurate PSFs for image enhancement 10
11 Lens Fitting (Optimization) Objective function: L2 norm between measured & synthetic PSFs Variables: lens parameters Optimization: gradient descent Initial parameters: provided lens prescription Algorithm: 1. Calculate the difference D between the measured PSFs and the synthetic PSFs by current model 2. Calculate the gradient of each variables to find out the Jacobian J 3. Move the current model by pseudoinv(d)*j 4. Go back to step 1 11
12 Fitting set Fitted measured unfitted Fitted measured unfitted Fitted measured unfitted Testing set 12
13 Deconvolution Results Using Lucy-Richardson method Original unfitted Fitted measured Original unfitted Fitted measured 13
14 Edmund Edmund Double Gauss 14
15 Validation: Focus at Different Depths Distance A Distance B Lens Model: Edmund Fitting using measurement at distance A Synthesize PSFs at distance B Fitted A = 279mm B = 368mm Measured Unfitted A = 368mm B = 279mm Fitted Measured 15 Unfitted
16
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18 Conclusion Our method can predict PSFs at - Different spatial positions - Different focal planes But requires calibration on every lens Deconvolution with synthetic PSFs can sharpen the image and remove the chromatic aberrations simultaneously Distortion can be corrected in our framework 18
19
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