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!