CS 395/495-26: Spring 2004 IBMR: 2-D Conics: Introduction Jack Tumblin [email protected].
The Trilateral Filter for High Contrast Images and Meshes Prasun Choudhury and Jack Tumblin Sp...
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Transcript of The Trilateral Filter for High Contrast Images and Meshes Prasun Choudhury and Jack Tumblin Sp...
The Trilateral Filter for High Contrast Images and Meshes
Prasun Choudhury and Jack Tumblin Speaker: Di jiantao
Feb 28,2008
About the author---Prasun Choudhury
Current: Computer Scientist at Adobe Systems Inc.
Past: Computer Graphics Research Engineer at Nokia Research Center. Staff software Engineer at Intel Corp. Simulation Software Engineer at Immersion Corp.
Education: Northwestern University Indian Institute of Science Jadavpur University RKM Narendrapur
About the author---Jack Tumblin
Associate Professor, EECS Department, Computer Science, Northwestern University.
Research interests: Computational Photography & Illumination. Computer Vision and Interactive Computer
Graphics. High Dynamic Range (HDR) Images and Image
Processing. Digital Archives of Visual Appearance for Museum
Collections. Human Visual Perception, Psychophysics, and
Physiology.
Filter methods: Gaussian Filter
1( ) ( ) ( )out inI x I x c d
k
2 2/ 2( ) cc e
* =
( )k c d
Filter methods: Bilateral Filter
1( ) ( ) ( ) ( ( ) ( ))
( )out in in inI x I x c s I x I x dk x
( ) ( ) ( ( ) ( ))in ink x c s I x I x d
2 2/ 2( ) cc e 2 2/ 2( ) ss e
Filter methods: Bilateral Filter
* =
Gaussian, Bilateral and Trilateral Filter Windows
The changes of Trilateral filter: Tilting. S measures its closeness to the plane through I(x). Adaptive neighborhood.
Step 1 of Trilateral Filter for Image
Bilateral smooth gradients
1( ) ( ) ( ) (|| ( ) ( ) ||)
( ) in in inG x I x c s I x I x dk x
( ) ( ) (|| ( ) ( ) ||)in ink x c s I x I x d
( , ) ( ( 1, ) ( , ), ( , 1) ( , ))in in in in inI m n I m n I m n I m n I m n
Step2 of Trilateral Filter for Image
Trilateral smooth image Compute approximate value
Compute
Filter
( , ) ( )inP x I x G ( , )I x
( , ) ( ) ( , )inI x I x p x
1( ) ( ) ( , ) ( ) ( ( , )) ( , )
( )out inI x I x I x c s I x f x dk x
( ) ( ) ( ( , )) ( , )k x c s I x f x d
1 || ( ) ( ) ||( , )
0 .
if G x G x Rf x
otherwise
Results
Results
Results
Application 1: Contrast Reduction
Contrast reduction method based on edge-preserving filters.
Base is compressible and Details are incompressible. Compress:
1, 0 1out inI M I M
Results of Contrast Reduction
Results of Contrast Reduction
Results of Contrast Reduction
Application 2: Mesh Smoothing
A two-step process: Trilateral normal filtering.
Bilateral smooth vertex normal. Trilateral vertex filtering.
Signs Definition
---vertex positionVX VN ---vertex normal
F ---mesh face
FX ---face center point FN ---face normal
VN ---bilaterally smoothed vertex normal
( , )V VP X ---tangent plane pass through VX
Trilateral normal filter
1( ) ( ) ( ( )) ( , )
( )F
Vout V F N F N F FFN F
N N N c s N f Vk
( ) ( ) ( ( )) ( , )F
N F N F N F FF
k c s N f V
( )F V FN N N 1 || ||
( , )0
V F
F
if N N Rf V
otherwise
Trilateral Vertex Filter
( ) ( ) ( ( )) ( , )( )
F
VoutVout V F V F V F F
FV F
NX X X c P s X f V
k
( ) ( ) ( ( )) ( , )F
V F V F V F FF
k c P s X f V
FP is the projection of on the plane FX ( , )V VP X
Results of Mesh Smoothing
Original Model
Noisy Model
Smoothed Model
Results of Mesh Smoothing
Results of Mesh Smoothing
Thank you!