### EPfilter

```Energy Preserving
Non-linear Filters
Presented by
Wei-Yin Chen (R94943040)
Outline

Introduction
 Problem
and Goal
 Source of Noise


Filter Model
Algorithm and Application
 Monte
Carlo

Result and Conclusion
2
Introduction

Problem
 Noise

Goal
 Enhance

image quality without more samples
 Preserve energy
 Doesn’t blur details

Usage
 Filter
before tone mapping
3
Source of Noise

“Small probability” area in Monte-Carlo
method
 Not

noise actually
This happens at a region, not at a pixel
 Average
the “noise” in a larger region
4
Required sample

Define noise
 Pixels
not converging within range D (typically 13)
after tone map

Huge samples are required in the worst case
 >1e4

Most regions are smooth
 Good

samples for 1e-4 accuracy
average case
Target on the noisy regions
5
Filter Model

Constant-width filter
 Inherently

preserve energy
Variable-width filter
 Not
energy preserving on
the boundary
 Region of support

Variable-width filter with
energy preserving
 Source
oriented perspective
 Region of influence
6
Algorithm for Monte Carlo
rendering

Pre-render a small image (100x100x16)
 Find
a visual threshold Ltvis = Laverage/128 (1 after tone
map)
 Find a threshold of sample density that most pixels
converge within D


Render with the sampling density at full
resolution
For unconverged pixels
 Distribute
Lexcess=Lu-Ln (average of converged
neighbors) to a region, region area = Lexcess/Ltvis
7

 A rendering
system
 Super-sampled
 StDev unknown for the filter

Work-around
 Regard
extreme values as unconverged
pixels
8
Result
9
10