LCIS: A Boundary Hierarchy For Detail-Preserving Contrast

Reduction

LCIS: A Boundary Hierarchy For Detail-Preserving Contrast

Reduction

Jack Tumblin and Greg TurkGeorgia Institute of Technology

SIGGRAPH 1999

Presented by Rob Glaubius

Jack Tumblin and Greg TurkGeorgia Institute of Technology

SIGGRAPH 1999

Presented by Rob Glaubius

MotivationMotivation

Detail visible almost everywhere in a scene Difficult to capture rich detail in high-

contrast scenes CRT contrast: 100:1 Target scene contrast: ~100,000:1

Detail visible almost everywhere in a scene Difficult to capture rich detail in high-

contrast scenes CRT contrast: 100:1 Target scene contrast: ~100,000:1

MotivationMotivation

Simple scene intensity adjustment

Id = F(m·Is)

Id: display intensity

Is: scene intensity

m: scale factor

: compression/expansion term

F: enforces boundary conditions

Simple scene intensity adjustment

Id = F(m·Is)

Id: display intensity

Is: scene intensity

m: scale factor

: compression/expansion term

F: enforces boundary conditions

LCIS - A PreviewLCIS - A Preview

“Mathematically mimic a well-known artistic technique for rendering high contrast scenes”

Coarse-to-fine rendering of boundaries and shading

“Mathematically mimic a well-known artistic technique for rendering high contrast scenes”

Coarse-to-fine rendering of boundaries and shading

LCIS - A PreviewLCIS - A Preview

Low Curvature Image Simplifier Hierarchy of sharp boundaries and smooth

shadings Goal - low contrast, highly detailed images

Low Curvature Image Simplifier Hierarchy of sharp boundaries and smooth

shadings Goal - low contrast, highly detailed images

LCIS vs. Linear Filter Hierarchies

LCIS vs. Linear Filter Hierarchies

Anisotropic DiffusionAnisotropic Diffusion

Treat intensity as heat fluid Temperature wants to flow from hot to cold

It = ·(C(x,y,t) I)• It : derivative of temperature change w.r.t. time• C : Conductivity

Constant conductivity repeated convolution with a Gaussian filter (isotropic diffusion)

Treat intensity as heat fluid Temperature wants to flow from hot to cold

It = ·(C(x,y,t) I)• It : derivative of temperature change w.r.t. time• C : Conductivity

Constant conductivity repeated convolution with a Gaussian filter (isotropic diffusion)

Anisotropic Diffusion, cont’dAnisotropic Diffusion, cont’d

Conductivity depends on image - as local “edginess” increases, conductivity decreases

C(x,y,t) = g(||I||)

where

g(m) = (1+(m/K)2)-1

K is a conductance threshold for m

Conductivity depends on image - as local “edginess” increases, conductivity decreases

C(x,y,t) = g(||I||)

where

g(m) = (1+(m/K)2)-1

K is a conductance threshold for m

Anisotropic Diffusion IllustratedAnisotropic Diffusion Illustrated

LCIS vs. Anisotropic DiffusionLCIS vs. Anisotropic Diffusion

LCIS - TheoryLCIS - Theory

3rd order derivatives instead of 2nd order Equalize curvature rather than intensity

It(x,y,t) = ·(C(x,y,t)F(x,y,t))

F: motive force from high to low curvature

F = (Ixxx + Iyyx, Ixxy + Iyyy)

C: Conductivity

C(x,y,t) = g(0.5(I2xx + I2

yy) + I2xy)

3rd order derivatives instead of 2nd order Equalize curvature rather than intensity

It(x,y,t) = ·(C(x,y,t)F(x,y,t))

F: motive force from high to low curvature

F = (Ixxx + Iyyx, Ixxy + Iyyy)

C: Conductivity

C(x,y,t) = g(0.5(I2xx + I2

yy) + I2xy)

LCIS - ImplementationLCIS - Implementation

Discrete images, so quantities are approximate, based on 4-connected neighbors and a constant time step

Discrete images, so quantities are approximate, based on 4-connected neighbors and a constant time step

LCIS HierarchyLCIS Hierarchy

Convert(Rin,Gin,Bin)

LCISK0 = 0

LCISK1

LCISK2

LCISK3

+ +

+

(Rout,Gout,Bout)

exp()

wcolor w0 w1 w2 w3

log(L)

log(R/L

,G/L

,B/L

)