Fast Bilateral Filtering for the Display of High-Dynamic-Range Images

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1 Contributions ing for the Display of High-Dynamic-Range Images for HDR images Local tone mapping Preserves details No halo Edge-preserving filter Frédo Durand & Julie Dorsey Laboratory for Computer Science Massachusetts Institute of Technology High-dynamic-range (HDR) images CG Images Match limited contrast of the medium Preserve details Multiple eposure photo [Debevec & Malik 997] HDR sensors Recover response curve HDR value for each piel Real world Picture 0-6 High dynamic range Low contrast A typical photo Sun is overeposed Foreground is undereposed Gamma compression X > X γ s are washed-out Input Gamma

2 Gamma compression on intensity s are OK, but details (intensity high-frequency) are blurred Gamma on intensity Chiu et al. 993 Reduce contrast of low-frequencies Keep high frequencies Low-freq. Reduce low frequency High-freq. The halo nightmare For strong edges Because they contain high frequency Low-freq. Reduce low frequency Our approach Do not blur across edges Non-linear filtering Large-scale High-freq. Multiscale decomposition Multiscale retine [Jobson et al. 997] Low-freq. Mid-freq. Mid-freq. High-freq. Edge-preserving filtering Blur, but not across edges Input Gaussian blur Edge-preserving Compressed Compressed Compressed Perceptual filters [Pattanaik et al. 998] Anisotropic diffusion [Perona & Malik 90] Blurring as heat flow LCIS [Tumblin & Turk] filtering [Tomasi & Manduci, 98]

3 Edge-preserving filtering & LCIS [Tumblin & Turk 999] Multiscale decomposition using LCIS (anisotropic diffusion) Layer decomposition [Tumblin et al. 999] For 3D scenes Reduce only illumination layer Simplified (at multiple scales) Compressed s Illumination layer Compressed Reflectance layer Comparison with our approach We use only 2 scales Can be seen as illumination and reflectance Different edge-preserving filter from LCIS Large-scale Plan Review of bilateral filtering [Tomasi and Manduchi 998] Theoretical framework Acceleration Handling uncertainty Use for contrast reduction Compressed Start with Gaussian filtering Start with Gaussian filtering Here, is a step function + noise Spatial Gaussian f J = f I = J f I

4 Start with Gaussian filtering is blurred Gaussian filter as weighted average Weight of depends on distance to J = f I J () = f (, ) The problem of edges Principle of filtering Here, pollutes our estimate J() It is too different [Tomasi and Manduchi 998] Penalty g on the intensity difference J () = f (, ) J () = f (, ) g( I( ) I( )) ) I() I() filtering filtering [Tomasi and Manduchi 998] Spatial Gaussian f J () = f (, ) g( I( ) I( )) ) [Tomasi and Manduchi 998] Spatial Gaussian f Gaussian g on the intensity difference J () = f (, ) g( I( ) I( )) )

5 Normalization factor [Tomasi and Manduchi 998] )=, f ( ) g( I( ) I( )) J () = f (, ) g( I( ) I( )) ) filtering is non-linear [Tomasi and Manduchi 998] The weights are different for each piel J () = f (, ) g( I( ) I( )) ) Plan Review of bilateral filtering [Tomasi and Manduchi 998] Theoretical framework Acceleration Handling uncertainty Use for contrast reduction Theoretical framework Framework of robust statistics = estimator at each piel Less influence to outliers (because of g) Unification with anisotropic diffusion Mostly equivalent Some differences s and other insights in paper Spatial support Spatial support Anisotropic diffusion cannot diffuse across edges Support of anisotropic diffusion

6 Spatial support Anisotropic diffusion cannot diffuse across edges filtering can Larger support => more reliable estimator Acceleration Non-linear because of g J () = f (, ) g( I( ) I( )) ) Support of anisotropic diffusion Support of bilateral Acceleration Linear for a given value of I() Convolution of g I by Gaussian f J () = f (, ) g( I( ) I( )) ) Acceleration Linear for a given value of I() Convolution of g I by Gaussian f Valid for all with same value I() J () = f (, ) g( I( ) I( )) ) Acceleration Discretize the set of possible I() Perform linear Gaussian blur (FFT) Linear interpolation in between J () = f (, ) g( I( ) I( )) ) Handling uncertainty Sometimes, not enough similar piels Happens for specular highlights Can be detected using normalization ) Simple fi (average with of neighbors) ) treated similarly Weights with high uncertainty Uncertainty

7 Contrast too high! Reduce contrast Reduce contrast Preserve!

8 Live demo X GHz Pentium Whatever PC Reduce contrast Preserve! Conclusions Edge-preserving filter Framework of robust statistics Acceleration Handling uncertainty Can handle challenging photography issues Richer sensor + post-processing Future work Uncertainty fi Other applications of bilateral filter (meshes, MCRT) Video sequences High-dynamic-range sensors Other pictorial techniques Informal comparison Informal comparison Gradient-space [Fattal et al.] [Durand et al.] Photographic [Reinhard et al.] Gradient-space [Fattal et al.] [Durand et al.] Photographic [Reinhard et al.]