HDRToneMap1 - space range normalization 29 29 ∑ ∈ = S I...

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Unformatted text preview: space range normalization ( 29 ( 29 ∑ ∈-- = S I I I G G W I BF q q q p p p q p | | || || 1 ] [ r s σ σ space range p q p Depends on spatial distance and intensity difference Pixels across edges have almost influence q p output input ( 29 ( 29 ∑ ∈-- = S I I I G G W I BF q q q p p p q p | | || || 1 ] [ r s σ σ p reproduced from [Durand 02] For each pixel p For each pixel q Compute 8 megapixel photo: 64,000,000,000,000 iterations! V E R Y S L O W ! V E R Y S L O W ! ( 29 ( 29 ∑ ∈-- = S I I I G G W I BF q q q p p p q p | | || || 1 ] [ r s σ σ ( 29 ( 29 q q p q p I I I G G | | || || r s-- σ σ Complexity = “how many operations are needed, how this number varies” &#2; S = space domain = set of pixel positions &#2; | S | = cardinality of S = number of pixels In the order of 1 to 10 millions &#2; Brute-force implementation: ) | (| 2 S Ο Idea: Far away pixels are negligible For each pixel p a. For each pixel q such that || p – q || < cte × σ s looking at all pixels looking at neighbors only Complexity: &#2; Fast for small kernels: σ s ~ 1 or 2 pixels &#2; BUT: slow for larger kernels ) | (| 2 s σ × S Ο neighborhood area Input Image Gaussian blur * * * input output Same Gaussian kernel everywhere. Bilateral Filtering σ r = 0.1 * * * input output The kernel shape depends on the image content. [Aurich 95, Smith 97, Tomasi 98] σ r = 0.25 σ r = ∞ (Gaussian blur) σ s = 2 σ s = 6 σ s = 18 σ r = 0.1 σ r = 0.25 σ r = ∞ (Gaussian blur) input σ s = 2 σ s = 6 σ s = 18 ( 29 ( 29 ∑ ∈-- = S I I I G G W I BF q q q p p p q p | | || || 1 ] [ r s σ σ ( 29 ( 29 ∑ ∈-- = S G G W I BF q q q p p p C C C q p || || || || 1 ] [ r s σ σ For gray-level images For color images intensity difference color difference The bilateral filter is The bilateral filter is extremely easy to adapt to your need. extremely easy to adapt to your need. scalar 3D vector (RGB, Lab) input output Denoising &#2; Tone mapping &#2; Edge-aware Brush &#2; … Noisy input Bilateral filter 7x7 window Bilateral filter Median 3x3 Bilateral filter Median 5x5 Bilateral filter Bilateral filter – lower sigma Bilateral filter Bilateral filter – higher sigma Small spatial sigma (e.g. 7x7 window) &#2; Adapt range sigma to noise level &#2; Maybe not best denoising method, but best simplicity/quality tradeoff No need for acceleration (small kernel) But the denoising feature in e.g. Photoshop is better Input: high-dynamic-range image (floating point per pixel) Large scale = bilateral (log intensity) Output [Durand & Dorsey 2002] Bilateral...
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This note was uploaded on 08/22/2010 for the course CAP 6701 taught by Professor Staff during the Spring '10 term at University of Central Florida.

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HDRToneMap1 - space range normalization 29 29 ∑ ∈ = S I...

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