Gradient Domain HDRI Compression Final Report

256*256
Original 512*512
128*128
64*64
32*32 16*16
Fig 5. Gaussian pyramid of Lena
At each level k, we compute the gradients using central differences:
∇H k = ( H k ( x + 1, y) − H k ( x −1, y) H k ( x, y + 1) − H k ( x, y −1) , ) k +1 k +1 2 2
Note: All the computations are done on the logarithm of the luminance rather than the luminance itself (a) The logarithm of the luminance is a crude approximation to the perceived brightness; (b) gradients in the log domain correspond to ratios in the luminance domain.
Final Report
Speaker: Fang Ying 2011.12.6
Content
Ⅰ. Introduction
1. What is HDRI? *Dynamic range: dimensionless quantity, a single extreme ratio between the max and min image intensities. The dynamic range of natural scenes exceeds three log units. *High Dynamic Range Image(HDRI) : Accuracy (1)Entire color gamut; (2)Full range of luminance that is visible to a human observer. *Applications: surveillance, remote sensing, space research, medical applications,…
(x,y-1) (x-1,y) (x, y) (x,y+1) (x+1,y)
For boundaries: Padding for boundaries
(2) At each level k a scaling factor φk(x,y) is determined for each pixel based on the magnitude of the gradient there:
(1) Construct a Gaussian pyramid H0,H1,…,Hd, H0: the full resolution HDR image Hd: the coarsest level in the pyramid
Fig 4. Gaussian Pyramid
As we move up the pyramid, both size and resolution decrease.
4. Generate the attenuated G
G( x, y) = ∇H ( x, y)φ ( x, y)
5. Get div G
divG ≈Gx (x, y) −Gx (x −1, y) +Gy (x, y) −Gy (x, y −1)
G 6. Solve the Poisson Equation ∇²I=div How to solve Poisson equation? *Use FFT to solve ∇²I=div G First consider the continuous Poisson equation:
Fig 3. Flow chart of gradient domain HDR compression
Detailed Description
0. Input the original HDR image 1. Get the radiance map of the input image (RGB→YUV) Y= 0.299R + 0.587G + 0.114B
the first item of the left could be discrete as:
i.e. K=1: K=2: …… K=6:
H1 ( x +1, y) − H1 ( x −1, y) H1 ( x, y +1) − H1 ( x, y −1) ∇H1 = ( , ) 2 2 2 2 H ( x +1, y) − H2 ( x −1, y) H2 ( x, y +1) − H2 ( x, y −1) ∇H2 = ( 2 , ) 3 3 2 2
ϕk (x, y) =
α
|| ∇Hk (x, y)||
|| ∇Hk (x, y)|| β ( )
α
Set α to 0.1 times the average gradient magnitude, β between 0.8 and 0.9
(3) The full resolution gradient attenuation function Ф(x,y) is computed in a top-down fashion:
φd ( x, y) = ϕd ( x, y) φk ( x, y) = L(φk +1 )( x, y)ϕk ( x, y) φ ( x, y) = φ0 ( x, y)
L is an upsampling operator with linear interpolation.
Bilinear interpolation
(1,1) (1,1) (2,1) (1,2) (2,2) (2,1) (1,2) (2,2) (3,2) (4,2) (1,3) (2,3) (3,3) (4,3) (1,4) (2,4) (3,4) (4,4)
→
(3,1) (4,1)
H1: 2*2
H2: 4*4
H2(1,1)=H1(1,1); H2(1,2)=(H1(1,1)+H1(1,2))/2; H2(1,3)=(H1(1,1)+H1(2,1))/2; H2(1,4)=((H1(1,1)+H1(1,2)+H1(2,1)+H1(2,2))/4;
2. Get gradient map ∇H(x,y)
3. Generate attenuation factor Ф(x,y) -----A multi-resolution edge detection scheme This method achieves HDR compression by attenuating the magnitudes of the HDR image gradients by a factor of Ф(x,y) at each pixel. Real-world images contain edges at multiple scales. In order to detect all of the significant intensity transitions, we must employ a multi-resolution edge detection scheme. Our solution is to propagate the desired attenuation from the level it was detect at to the full resolution image.
* TRCs: Advantage: simplicity and computational efficiency Disadvantage: must be one-to-one and monotonic in order to avoid reversals of local edge contrast, hard to preserve local contrasts * TROs: Advantage: take local spatial context into account when deciding how to map a particular pixel Disadvantage: suffer from halo artifacts and dark bands around small bright visible light sources, overemphasize details, take a substantial amount of time
Fig 1. A series of differently exposed photographs
Fig 2. A model of HDR compression
3. How?
(1). Global (spatially invariant) mappings;
--- Tone reproduction curves (TRCs) Ward Larson (1997) (2). Local (spatially variant) mappings. --- Tone reproduction operators (TROs) Low curvature image simplifier (LCIS)
Gradient domain high dynamic range compression
Raanan Fattal Dani Lischinski Michael Werman School of Computer Science and Engineering The Hebrew University of Jerusalem