1. LCIS: A Boundary Hierarchy For Detail-Preserving Contrast Reduction Jack Tumblin and Greg Turk Georgia Institute of Technology SIGGRAPH 1999 Presented by Rob Glaubius Jack Tumblin and Greg Turk Georgia Institute of Technology SIGGRAPH 1999 Presented by Rob Glaubius

2. Motivation  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

3. Motivation  Simple scene intensity adjustment I d = F(m·I s  ) I d : display intensity I s : scene intensity m: scale factor  : compression/expansion term F: enforces boundary conditions  Simple scene intensity adjustment I d = F(m·I s  ) I d : display intensity I s : scene intensity m: scale factor  : compression/expansion term F: enforces boundary conditions

4. LCIS - 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

5. LCIS - 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

6. LCIS vs. Linear Filter Hierarchies

7. Anisotropic Diffusion  Treat intensity as heat fluid  Temperature wants to flow from hot to cold I t =  ·(C(x,y,t)  I) I t : 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 I t =  ·(C(x,y,t)  I) I t : derivative of temperature change w.r.t. time C : Conductivity  Constant conductivity  repeated convolution with a Gaussian filter (isotropic diffusion)

8. Anisotropic 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

9. Anisotropic Diffusion Illustrated

10. LCIS vs. Anisotropic Diffusion

11. LCIS - Theory  3 rd order derivatives instead of 2 nd order  Equalize curvature rather than intensity I t (x,y,t) =  ·(C(x,y,t)F(x,y,t))  F: motive force from high to low curvature F = (I xxx + I yyx, I xxy + I yyy )  C: Conductivity C(x,y,t) = g(0.5(I 2 xx + I 2 yy ) + I 2 xy )  3 rd order derivatives instead of 2 nd order  Equalize curvature rather than intensity I t (x,y,t) =  ·(C(x,y,t)F(x,y,t))  F: motive force from high to low curvature F = (I xxx + I yyx, I xxy + I yyy )  C: Conductivity C(x,y,t) = g(0.5(I 2 xx + I 2 yy ) + I 2 xy )

12. LCIS - Implementation  Discrete images, so quantities are approximate, based on 4-connected neighbors and a constant time step

13. LCIS Hierarchy Convert (R in,G in,B in )  LCIS K 0 = 0 LCIS K 1 LCIS K 2 LCIS K 3 ++ + (R out,G out,B out ) exp()  w color w0w0 w1w1 w2w2 w3w3 log(L) log(R/L,G/L,B/L)