NIST GCR 09-926

The Impact of Thermal Imaging 

Camera Display Quality on Fire 

Fighter Task Performance

Justin Lawrence Rowe 

Department of Fire Protection Engineering 

University of Maryland 

College Park, MD 20742 

NIST GCR 09-926

The Impact of Thermal Imaging 

Camera Display Quality on Fire 

Fighter Task Performance

Prepared for 

U.S. Department of Commerce 

Building and Fire Research Laboratory 

National Institute of Standards and Technology 

Gaithersburg, MD 20899-8661

By 

Justin Lawrence Rowe 

Department of Fire Protection Engineering 

University of Maryland 

College Park, MD 20742 

June 2009

U.S. Department of Commerce 

Gary Locke, Secretary 

National Institute of Standards and Technology 

 Patrick D. Gallagher, Deputy Director 
Notice 

This report was prepared for the Building and Fire Research Laboratory of the 

National Institute of Standards and Technology under Grant number 

70NANB7H6005. The statement and conclusions contained in this report are 

those of the authors and do not necessarily reflect the views of the National 

Institute of Standards and Technology or the Building and Fire Research 

Laboratory. 
ABSTRACT 

Title of Document: THE IMPACT OF THERMAL IMAGING 

CAMERA DISPLAY QUALITY ON FIRE 

FIGHTER TASK PERFORMANCE 

 

 Justin Lawrence Rowe, Master of Science, 2008 

 

Directed By: Associate Professor Dr. Frederick W. Mowrer, 

Department of Fire Protection Engineering 

Thermal imaging cameras (TIC) have become a vital fire fighting tool for the first 

responder community but there are currently no standardized quality control 

regulations. The purpose of the study was to understand the impact of TIC display 

image quality on a fire fighter’s ability to perform a hazard recognition task. Test 

subjects were asked to identify a fire hazard by observing infrared images. The 

image matrix considered the interactions of several image characteristics including 

contrast, brightness, spatial resolution, and noise. The results were used to create a 

model function to predict the effect of image quality on user performance. This 

model was recommended to be incorporated in image quality test methods in 

development at the National Institute of Standards and Technology. These 

recommendations will also be provided to the National Fire Protection Association 

for use in an upcoming standard on fire fighting TIC. 
THE IMPACT OF THERMAL IMAGING CAMERA DISPLAY QUALITY ON 

FIRE FIGHTER TASK PERFORMANCE. 

By 

Justin Lawrence Rowe 

Thesis submitted to the Faculty of the Graduate School of the 

University of Maryland, College Park, in partial fulfillment 

of the requirements for the degree of 

Master of Science 

2008 

Advisory Committee: 

Associate Professor Dr. Frederick W. Mowrer, Chair 

Professor Dr. James A. Milke 

Assistant Professor Dr. Peter B. Sunderland 
ii 

Acknowledgements 

The contributions and efforts of many individuals deserve recognition for the 

production of this work. I would like to thank my thesis advisor Dr. Frederick 

Mowrer for his assistance on obtaining the grant to fund this project and helping me 

to obtain my Master of Science degree. I would like to thank Dr. Francine Amon 

from the National Institute of Standards and Technology (NIST) for bringing me onto 

the thermal imaging project as an undergraduate student. She has been a mentor to 

me. I am grateful for the time and energy she devoted to this project and her help 

with the completion of this paper. I would also like to thank Dennis Leber of NIST 

for his assistance particularly on the statistics portion of this work. A great deal of 

time was spent meeting with Francine and Dennis over the past year and this project 

would not have taken shape the way it did without them. I would also like to thank 

others from NIST including Jay McElroy and Roy McLane for their help with the 

construction work and fellow researchers Josh Dinaburg, Aykut Yilmaz, Andrew 

Lock and Jed Kurry who were around to discuss and help with any issues. I would 

like to thank Army’s Night Vision Laboratories, in particular, John Hixson and Jim 

Thomas for allowing NIST to use their perception laboratory and for their support 

with data collection. I would also like to thank Kelly Campbell and Alexandra Ford 

for their graphic design assistance, and Jennifer Davis for her editorial reviews. 

Finally, I would like to thank the members of my thesis committee, Dr. James Milke 

and Dr. Peter Sunderland, and the Fire Protection Engineering Program at the 

University of Maryland for their help in furthering my academic career.
iii 

Table of Contents 

Acknowledgements ....................................................................................................... ii

Table of Contents ......................................................................................................... iii

List of Tables ................................................................................................................ v

List of Figures .............................................................................................................. vi

Chapter 1: TIC Overview.............................................................................................. 1

1.1 Introduction to TIC for First Responders............................................................ 1

1. 2 TIC Background................................................................................................. 2

1.2.1 Basic Function ............................................................................................. 2

1.2.1.1 Infrared Optics ...................................................................................... 4

1.2.1.2 Detector Designs ................................................................................... 5

1.2.2 Applications for Fire Service ....................................................................... 8

1.3 Development of NFPA 1801 .............................................................................. 9

1.3.1 NIST Involvement ....................................................................................... 9

1.3.2 Bench-Scale Test Methods Developed by NIST ....................................... 11

1. 4 Project Goals .................................................................................................... 14

Chapter 2: Image Processing ...................................................................................... 16

2. 1 Introduction to Image Processing .................................................................... 16

2.2 Histograms ........................................................................................................ 16

2. 3 Image Quality Characteristics .......................................................................... 17

2.3.1 Contrast ...................................................................................................... 18

2.3.2 Brightness .................................................................................................. 21

2.3.3 Spatial Resolution ...................................................................................... 23

2.3.4 Nonuniformity and Noise .......................................................................... 28

2.4 Image Processing Techniques ........................................................................... 36

2.4.1. Processing in the Spatial Domain ............................................................. 36

2.4.1.1 Point Processing .................................................................................. 37

2.4.1.2 Histogram Equalization ...................................................................... 41

2.4.1.3 Convolution in the Spatial Domain..................................................... 44

2.4.2 Image Processing in Frequency Domain ................................................... 51

2.4.2.1 Fourier Transforms ............................................................................. 51

4.2.4.1.1 The 1-D Fourier Transform ......................................................... 52

4.2.4.1.2 The 2-D Fourier Transform ......................................................... 55

2.4.2.2 Spatial Frequency Filtering ................................................................. 58

2.4.2.2.1 Filtering Techniques .................................................................... 60

Chapter 3: Human Perception Experimental Design .................................................. 69

3.1 Approach ........................................................................................................... 69

3.2 Night Vision Laboratory (NVL) ....................................................................... 70

3.3 Image Production .............................................................................................. 71

3.3.1 Hazards ...................................................................................................... 71

3.3.2 Scene .......................................................................................................... 74

3.3.3 Image Capturing......................................................................................... 77

3.4 Defining the Scenario Criteria .......................................................................... 78

3.4.1 Robustness Factors..................................................................................... 78
iv 

3.4.2 Primary Factors .......................................................................................... 80

3.5 Defining the Image Set ..................................................................................... 82

3.5.1 Restrictions ................................................................................................ 82

3.5.2 Pristine Image Set ...................................................................................... 82

3.5.3 Primary Factor Design Points .................................................................... 83

3.5.4 Calculations................................................................................................ 85

3.5.4.1 Contrast and Brightness ...................................................................... 85

3.5.4.2 Spatial Resolution ............................................................................... 85

3.5.4.3 Noise and Nonuniformity ................................................................... 88

3.6 Image Processing .............................................................................................. 89

Chapter 4: Modeling Human Perception .................................................................... 94

4.1 Objective ........................................................................................................... 94

4.2 Test Subjects ..................................................................................................... 94

4.3 Experiment ........................................................................................................ 95

4. 4 Data .................................................................................................................. 96

4. 5 Logistic Regression Model .............................................................................. 97

4.6 Cross Validation................................................................................................ 98

4.7 Model Deviance and Partial Deviance ............................................................ 103

4.8 Informal Goodness of Fit Test ........................................................................ 104

4.9 Chi-Square Goodness of Fit Test .................................................................... 107

4.10 Deviance Goodness of Fit Test ..................................................................... 108

4.11 Fitted Values and Confidence Intervals ........................................................ 109

Chapter 5: Summary and Conclusions ...................................................................... 112

5.1 Summary of Model Fit .................................................................................... 112

5.2 Recommendation for Model Use in NFPA 1801 ............................................ 112

5.3 Future Work .................................................................................................... 114

Appendices ................................................................................................................ 116

Appendix A ........................................................................................................... 116

Appendix B Image Processing Program ............................................................... 121

Appendix C Test Subject Background .................................................................. 135

Appendix D Example of Design Point.................................................................. 136

Bibliography ............................................................................................................. 141

 
v 

List of Tables 

Table 1- 1TIC Applications .......................................................................................... 8 

Table 3- 1 Robustness Definitions .............................................................................. 79

Table 3- 2 Primary Factor Definitions ........................................................................ 81

Table 3- 3 Design Points ............................................................................................. 84 

Table 4- 1Primary Factors .......................................................................................... 97

Table 4- 2 Multiple logistic regression coefficients ................................................... 98

Table 4- 3 Informal Goodness of Fit Test with 5 Classes......................................... 105

Table 4- 4 Informal Goodness of Fit Test using 7 Classes ....................................... 106

Table 4- 5 Goodness of Fit Test ................................................................................ 108

 
vi 

List of Figures 

Figure 1- 1 Transmissivity of common combustion products as a function of 

wavelength for a one meter pathlength (Grosshandler 1993) ....................................... 3

Figure 1- 2 Spatial Resolution Source Target, NFPA 1801-F09-ROP ....................... 12 

Figure 2- 1 IR image of an office work station ........................................................... 17

Figure 2- 2 Image histogram of Figure 2- 1 ................................................................ 18

Figure 2- 3 Image with low contrast ........................................................................... 19

Figure 2- 4 Image histogram of Figure 2- 3. ............................................................... 19

Figure 2- 5 Image of office with high brightness ....................................................... 21

Figure 2- 6 Histogram of Figure 2- 5 .......................................................................... 22

Figure 2- 7 Image with low brightness ....................................................................... 22

Figure 2- 8 Histogram of Figure 2- 7 .......................................................................... 23

Figure 2- 9 MTF for a generic imaging system .......................................................... 25

Figure 2- 10 Generic MTFA ....................................................................................... 27

Figure 2- 11 Generic Comparison of MTF curves...................................................... 28

Figure 2- 12 Probability Distribution Histogram of Uniform Noise .......................... 30

Figure 2- 13 Probability Distribution Histogram of Gaussian Distributed Noise ...... 31

Figure 2- 14 Probability Distribution Histogram of Salt and Pepper Noise ............... 33

Figure 2- 15 Image degraded by Gaussian distributed noise ...................................... 33

Figure 2- 16 Image histogram ..................................................................................... 34

Figure 2- 17 Image degraded by salt and pepper noise .............................................. 35

Figure 2- 18 Image histogram ..................................................................................... 35

Figure 2- 19 Linear Mapping ...................................................................................... 38

Figure 2- 20 Image degraded using point processing ................................................. 39

Figure 2- 21 Image Histogram .................................................................................... 40

Figure 2- 22 Point processing using nonlinear transfer functions .............................. 41

Figure 2- 23 Original Image ....................................................................................... 43

Figure 2- 24 Image histogram of Figure 2- 23 ............................................................ 43

Figure 2- 25 Image after histogram equalization ........................................................ 43

Figure 2- 26 Image histogram after equalization ........................................................ 44

Figure 2- 27 Schematic of kernel operations .............................................................. 45

Figure 2- 28 Neighborhood averaging kernel ............................................................. 47

Figure 2- 29 Image corrupt with noise ........................................................................ 48

Figure 2- 30 Image processed using associated kernel shown in Figure 2- 31........... 49

Figure 2- 31 Gaussian kernel ...................................................................................... 49

Figure 2- 32 Image processing used associated kernel shown in Figure 2- 33........... 49

Figure 2- 33 Gaussian Kernel ..................................................................................... 50

Figure 2- 34 Image processing used Gaussian kernel shown in Figure 2- 35 ............ 50

Figure 2- 35 Gaussian Kernel ..................................................................................... 50

Figure 2- 36 Image of a circle ..................................................................................... 56

Figure 2- 37 Frequency Magnitude Spectrum of Figure 2- 36 ................................... 57

Figure 2- 38 Image of square ...................................................................................... 57

Figure 2- 39 Frequency Magnitude Spectrum of Figure 2- 38 ................................... 57

Figure 2- 40 Flow chart of frequency filtering of images ........................................... 59

Figure 2- 41 One-dimensional low pass filter............................................................. 61

Figure 2- 42 Two-dimensional low pass filter ............................................................ 61
vii 

Figure 2- 43 Example of ringing artifacts ................................................................... 62

Figure 2- 44 Butterworth filter curves with varying cutoff frequencies ..................... 64

Figure 2- 45 Butterworth filter curves with varying function orders.......................... 64

Figure 2- 46 Magnitude spectrum of 2-D Butterworth filter ...................................... 65

Figure 2- 47 Original Image ....................................................................................... 65

Figure 2- 48 Image modified using Butterworth filter ................................................ 66

Figure 2- 49 High Pass 2-D Butterworth filter ........................................................... 67

Figure 2- 50 Image processed with high pass Butterworth filter ................................ 67 

Figure 3- 1 Overheated electrical outlets .................................................................... 71

Figure 3- 2 Crushed wire under table leg .................................................................... 72

Figure 3- 3 Buried hotspot in chair ............................................................................. 72

Figure 3- 4 Living room scene .................................................................................... 75

Figure 3- 5 Living room scene .................................................................................... 76

Figure 3- 6 Office scene .............................................................................................. 76

Figure 3- 7 Office scene .............................................................................................. 77

Figure 3- 8 Hazard location divisions ......................................................................... 79

Figure 3- 9 Thermal clutter ......................................................................................... 80

Figure 3- 10 Flowchart of image processing .............................................................. 92 

Figure 4- 1 Average response for design points ......................................................... 96

Figure 4- 2 Formation of modeling and validating datasets ....................................... 99

Figure 4- 3 Main effects only.................................................................................... 100

Figure 4- 4 Main effects + all two term interactions ................................................ 100

Figure 4- 5 Main effects + all two term interactions - contrast/spatial resolution 

interaction ................................................................................................................. 101

Figure 4- 6 Main effects +all two term interactions ................................................. 101

Figure 4- 7 Average deviation from observed values ............................................... 102

Figure 4- 8 Diagnostic plot of estimated proportions with 5 classes ........................ 105

Figure 4- 9 Diagnostic plot of estimated proportions using 7 classes ...................... 106

 
1 

Chapter 1: TIC Overview 

1.1 Introduction to TIC for First Responders

Thermal imaging cameras (TIC)1 are becoming an integral tool to the first responder 

community, particularly firefighters, law enforcement officers, and hazardous material 

personnel, by enhancing visibility in operating conditions such as harsh structural fire 

scenarios and in situations where the only indication of a material is surface temperature 

and/or differences in emissivity (e.g. hazardous gas or liquid materials). In particular, 

fire fighters applying TIC for search and rescue, structural navigation, hose stream 

directing, locating hot spots during overhaul, and fire size-up operations among others. 

TIC are improving first responder’s ability to effectively perform their jobs by decreasing 

response time in hazardous situations and thus improving safety and reducing overall fire 

losses. 

 

Currently, there are no standards or performance regulations TIC for fire fighting, as 

there are for other first responder equipment such as clothing, helmets, SCBA apparatus, 

and PASS devices. Adoption of standardized TIC performance testing methods will 

benefit first responders by providing objective test results to compare the different 

camera models and technologies for deciding the most cost effective purchase while still 

providing adequate performance. Standardized test methods also provide a way for TIC 

manufacturers to evaluate existing cameras and drive the development of newer 

technologies to create better fire fighting tools. 

 

1

 TIC is used as an acronym for both the singular and plural forms of thermal imaging camera(s), 

whichever form is applicable to the context of the sentence. 
2 

1. 2 TIC Background

1.2.1 Basic Function 

Handheld TIC take advantage of infrared (IR) radiative heat transfer by focusing the net 

radiation from an object whether emitted or reflected onto the thermal detector array 

inducing an increase in material temperature which triggers a proportional signal output. 

Radiation is transmitted through the atmosphere in the form of electromagnetic waves at 

specific frequencies. The intensity of the radiation at each frequency is a function of the 

temperature and surface properties. As the temperature of an object increases, the 

wavelength of peak intensity decreases as described by Planck’s formula in Equation1-1 

(Theory of Thermography 2007). 

( )

2

5 /

2

1

b hc kT

hc W

e

λ λ

π

λ

=

−

 1-1 

where Wλb is the blackbody spectral radiant emittance at wavelength λ, c is 3 x 108 m/s 

(speed of light), h is 6.6 x 10-34, k is 1.4 x 10-23 (Boltzmann’s constant), T is the absolute 

temperature (K) of a blackbody, and λ is the wavelength (μm). 

By integrating Planck’s formula in Equation 1-1 over all frequencies, the total radiant 

emittance of a blackbody becomes the Stefan-Boltzmann Law shown in Equation1-2. 

4 W T b =σ 1-2 

Real objects almost never act as a perfect blackbody over an extended range of 

wavelengths and therefore the emissivity of a surface is used to describe the ratio of the 

spectral radiant power from the object to that from a blackbody at the same temperature 

and wavelength (Theory of Thermography 2007). The radiant emittance of real world 
objects is shown in the modified S

account for the emissivity of a surface.

where ε is the emissivity.

TIC detect radiation in the IR

there is a high transmittance of 

for the fire service are tailored to 

range, IR waves are less susceptible to 

particulates in the atmosphere 

Figure 1- 1 Transmissivity of common combustion products as a functi

for a one meter pathlength (Grosshandler 1993)

3 

shown in the modified Stefan-Boltzmann Law shown in Equation

account for the emissivity of a surface.

4 W T = εσ

 is the emissivity.

tect radiation in the IR spectral band of the electromagnetic spectrum because 

there is a high transmittance of IR waves through fire related atmosphere

for the fire service are tailored to focus on the 8-14 μm wavelengths because within this 

IR waves are less susceptible to diffraction or scattering from water

particulates in the atmosphere as shown in Figure 1- 1. 

Transmissivity of common combustion products as a function of wavelength 

for a one meter pathlength (Grosshandler 1993)

shown in Equation 1-3 to 

1-3 

spectral band of the electromagnetic spectrum because 

atmospheres. TIC designed 

because within this 

water vapor or 

on of wavelength 
4 

IR waves transmit extremely well through carbon monoxide, carbon dioxide and water 

and relatively well through smoke. The transmittance at the near visible band, less than 1 

μm, is almost completely blocked by smoke which illustrates the ineffectiveness of the 

human eye and other visual optical systems in smoky combustion environments and 

emphasizes the need for TIC in the fire service. 

Incident radiative transfer onto the detector array is not the only important form of heat 

transfer. The radiative heat lost from the detector pixels to the surroundings acts to cool 

the detector pixel, increasing the response time of the TIC. Heat loss also occurs through 

conduction. Each detector pixel is attached to a substrate by supporting legs. Heat is lost 

through conduction from the detector pixel down the supporting leg to the substrate. In 

some detector designs such as the hybrid layout discussed in more detail in the following 

sections, conduction also occurs when heat transfers from one detector pixel to a 

neighboring pixel. This process, known as thermal spreading, is critical to avoid when 

designing thermal arrays because it affects the resolution [Kruse 1997]. 

1.2.1.1 Infrared Optics 

TIC for the fire service are designed with IR optics to focus the radiation onto an array of 

thermal detectors. The IR optics are similar to that of any optical system except for the 

materials used for the lens and optic focal lengths. A standard transparent lens transmits 

electromagnetic waves in the visual spectrum but not at the IR wavelengths so TIC use 

materials that transmit well in the 8-14 μm wavelengths, such as Zinc Selenide and 

Germanium. The optics of TIC also have a wide field of view (FOV) and a far focusing 
5 

distance. Fire fighters need the ability to see a wide FOV to survey a scene more rapidly. 

Typically, TIC for the fire service are designed with a FOV between 40-60o. The 

focusing distance ranges from 1 m out to infinity with no manual focusing options. The 

FOV and minimum 1 m focal length makes the TIC hard to perform testing in a bench 

scale lab because large targets and ample space are required to fill the FOV of the 

camera’s with thermal targets and measuring equipment. Finally, the optics are designed 

to avoid narcissus and glare. Narcissus occurs when there is a reflection in the optic 

components in which the detectors see themselves (Holst 1998). Coatings are applied to 

the optics to avoid internal reflections. 

1.2.1.2 Detector Designs 

The development of uncooled IR imaging arrays in the 1980’s offered a substantial 

advantage over cooled IR detectors in that they did not have be cryogenically cooled. 

TIC could therefore be produced at low cost and designed to be lightweight to be used for 

countless applications for the military and civilian sectors, including fire fighting. 

Handheld TIC utilize IR arrays that operate using thermal detectors because they do not 

require cooling systems and large power supplies (Dinaburg 2007). 

Thermal IR detectors utilize a sensitive material that has some measureable property that 

changes dramatically with temperature. The most common detection mechanisms used 

for handheld TIC are the resistive microbolometer and pyroelectric detectors (Holst 

2000). The microbolometer detectors utilize a material with a temperature-dependent 

resistance to measure a change in resistance of each detector pixel due to the absorption 

of the IR radiation (Kruse 1997). The two most common materials used in 
6 

microbolometers are vanadium oxide (VOx) and amorphous silicon. Both of these 

materials have high temperature coefficients of resistance (TCR), one of the most 

important properties in determining the voltage response of a detector because the TCR is 

directly proportional to the voltage response (Muralt 2001). 

Pyroelectric detectors utilize the ability of certain materials to change in polarization due 

to a change in temperature or otherwise known as the pyroelectric effect. When a 

material is heated (or cooled) positive and negative charges migrate to opposite faces of 

the sensor creating polarization. The change in surface charge is measured during the 

transient temperature change resulting from the incoming radiation. Because pyroelectric 

detectors measure transient temperature changes, they require a chopper to continuously 

reference the temperature of each pixel to ambient. The detectors are usually made from 

materials that have very low thermal mass so the temperature change is rapid (Tsai and 

Young 2003). The most common material used in TIC is a ferroelectric material called 

barium strontium titanate (BST). Ferroelectic materials offer an additional advantage 

because with the application of an external electric field, the pyroelectric coefficient is 

increased. The pyroelectric coefficient is directly proportional to the change in charge of 

the material. This phenomenon is known as the field-enhanced pyroelectric effect 

(Muralt 2001). 

In either type of detector design, the detector array is attached to a readout integration 

circuit (ROIC) which functions to read in and format the detector’s signal output. Due to 

the sensitivity of the thermal detector’s response to small temperature changes and the 

heat transfer physics, thermal isolation is critical to the quality of the TIC. Because of the 
7 

importance of thermal isolation the primary methods for attaching the thermal detector 

array to the ROIC will be discussed. 

The support structure provides three main functions; mechanical support, and a thermal 

and electrically conducting path. One of the most important aspects of the design of the 

supporting structure is to minimize the thermal conductance of the supporting legs that 

are attached to the detector pixels to increase response time. The detector pixels must 

also be thermally isolated to avoid thermal spreading. The two main approaches for 

providing the support are the monolithic and hybrid design. In the hybrid approach the 

detector pixel layer is separated from a silicon substrate layer which typically 

incorporates the ROIC. The two layers are joined by a bump bond at two supporting legs 

which provides the mechanical support as well as the high electrical conduction and low 

thermal conduction. The monolithic approach is to have the sensor and electronic 

elements on the same layer. 

There are advantages and disadvantages to both types of support structures. The 

monolithic design sacrifices image quality for a relatively lower cost to manufacture than 

the hybrid design. Because the detector pixel, supporting structure, and read-out 

electronics are on the same layer, the detector pixels must be placed farther away from 

each other. The layout is beneficial to minimize thermal spreading because the substrate 

acts as a heat sink. However, this also produces a poor fill factor. The two layer hybrid 

design typically use a laser scribed technique to separate the detector pixels creating a 

better fill factor and image quality but at a greater cost to manufacturer. 
8 

1.2.2 Applications for Fire Service

A workshop entitled “Thermal Imaging Research Needs for First Responders” was 

hosted by Amon et al. to gain input from the first responder community as well as TIC 

manufacturers and other stakeholders on how TIC are being used in the field. The 

knowledge gained from this workshop and other TIC manufacturing literature on TIC 

applications is listed in Table 1- 1 [Amon 2005]. 

Table 1- 1 TIC Applications 

First Responder Applications for Thermal Imaging Cameras 

Application Description 

Search and Rescue Locate heat sources, such as victims or fallen fire fighters. 

Hazard Assessment Locate and assess the severity of a fire. A TIC can be used 

to find hot spots and a potential threat to adjoining 

structures. 

Building Assessment Analyze the integrity of a structure by identifying hazards 

such as holes in the floor, hanging wires, and the failure of 

load bearing structural elements. 

Navigation Doors, windows, and other escape points can be located for 

quick egress. TIC can distinguish furniture and other objects 

that could block a path. 

Fire Attack 

Directing hose streams

Identify potential flashover or back draft conditions. Find 

ventilation locations, direct hose streams, analyze the 

effectiveness of the hose stream and access the severity of 

the upper layer temperature. 

Over-haul Quickly scan for remaining hot spots and embers that lead to 

rekindling. Over-haul can be carried out more rapidly and 

with minimal damage to the structure. 

Wild land Fires TIC can be used on the ground or in the air to locate hot 

spots in vegetation and root systems. Useful for determining 

fire fighting strategies and identifying animals, people, and 

nearby buildings that may be in danger. 

Incident 

Control/Command 

Fire fighter activity can be monitored by sending images 

from TIC back to the incident commander. The images can 

be used to account for fire fighters, as well as make 

decisions as to the tactics used to extinguish the fire. This 

application can be particularly helpful in high-rise building 

fires where fire fighter coordination is more difficult. 

Hazardous Materials Help identify the level of liquid in hazardous material 
9 

containers and track the movement of hazardous material 

after spillages. Fire fighters can make more accurate 

decisions as to where barriers may need to be positioned, 

how much hazardous material has been spilled, and the 

potential risks to the nearby area. 

Post-incident 

Investigation 

Identify the source of a fire and how the fire spreads. A TIC 

can capture images of a scene while a fire is occurring. The 

images can later be used as evidence for understanding and 

verifying the progress of the fire situation. 

The applications listed in Table 1- 1 demonstrate the exposure of TIC to a variety of 

thermal targets and operating temperatures. As more fire departments are equipped with 

TIC and the technologies become more advance, additional ways to utilize a TIC will be 

discovered. The knowledge gained from the BFRL workshop was incorporated into the 

design of the images used in this study to represent a typical TIC operating environment. 

1.3 Development of NFPA 1801

1.3.1 NIST Involvement

The National Fire Protection Association (NFPA) Technical Committee of Electronic 

Safety Equipment is developing a standard to govern the design, performance, testing, 

and certification requirements for TIC used by first responders. The standard is currently 

being created by NIST in collaboration with committees formed by users, manufacturers, 

technical experts, and the public. NIST provides unbiased science-based research and 

experience in fire testing including the evaluation of fire fighter personal protective 

equipment. The suggestions made about the content of the standard provided by NIST 

will be taken into consideration by the NFPA for use in NFPA 1801, Standard on 

Thermal Imagers for the Fire Service. 
10 

The research at NIST, headed by Dr. Francine Amon in the Fire Fighting Technology 

Group in BFRL, is focused on TIC overall system performance requirements, specifically 

the output of the display screens. The requirements specified in NFPA 1801, Section 7.1, 

Thermal Imager Performance Requirements, include a range of performance testing on 

ingress protection, electromagnetic emissions and immunity, resistance to vibration, 

impact-acceleration resistance, corrosion resistance, viewing surface abrasion resistance, 

resistance to heat and flame, product label durability, cable pullout test, and most 

importantly, display image quality. 

The performance test methods designed by NIST treat the TIC as a “black box” to focus 

on the entire system as the TIC would be used by the fire service and not the various 

components separately. The display quality is of upmost importance because it is the 

primary mechanism for relaying information to the user. The display image of a TIC is 

influenced by a large number of factors due to the number of components involved in 

converting IR radiation into a formidable image on the display screen. There are 

numerous component packages available on commercial TIC which includes a variety of 

detector technologies, signal processing algorithms, gain settings, optics, electronics, and 

displays. However, there are very few manual adjustments to the display image that can 

be performed by the user. Typically, there is only an on/off switch and maybe one more 

specialty button depending on the brand of TIC. All adjustments to focus, gain, 

sensitivity and other image enhancements are all automatically done by the interior 

functions of the TIC. Each manufacturer has complex (and secret) algorithms to post 

process the signal output of the detector array to the image formed on the display screen. 
11 

Every manufacturer has different techniques to improve the quality of the image and 

testing each subsystem of every camera would be cumbersome and unnecessary. 

Section 7.2, Imaging Performance Requirements, of NFPA 1801 applies specifically to 

the quality of the display image. The test methods designed by NIST measure various 

aspects of the display image quality including contrast, overall brightness, spatial 

resolution, and image nonuniformity (noise). For a more detailed description of display 

measurement techniques refer to the Video Electronics Standards Association (VESA) 

Flat Panel Display Measurements Standard [VESA 2001] 

1.3.2 Bench-Scale Test Methods Developed by NIST

The methods described in NFPA 1801, Section 8.1.6, Spatial Resolution Procedure, 

incorporate measurements of image contrast, overall brightness, and spatial resolution. 

The procedures require the TIC under testing to be centered one meter (the minimum 

focusing distance of a TIC) from a spatial resolution target, shown in Figure 1- 2. The 

TIC is required to have a line of sight perpendicular to the target. 
12 

Figure 1- 2 Spatial Resolution Source Target, NFPA 1801-F09-ROP 

The target design was an adaptation from a portion of the ISO 12233 test chart (ISO 

12233). The target and a black backdrop are required to fill the TIC field of view (FOV). 

The spatial resolution target is set to 28 C ± 0.5 C. A black shroud is placed over the 

view path of the camera to block out any glare incident on display. 

A calibrated luminance meter is positioned as close as possible to the TIC to capture the 

FOV of the display screen. A minimum of 100 uncompressed images at a minimum 16-

bit depth are captured with the luminance meter. 
13 

Using the captured images, contrast, brightness, and spatial resolution calculations are 

performed at each baseline index (shown in Figure 1- 2) which corresponds to a specific 

spatial frequency. The contrast is calculated according to NFPA 1801 Section 8.1.6.11 at 

each indexed baseline using the standard deviation of an equal amount of pixel intensities 

from the heated target and backdrop. Brightness is calculated in NFPA 1801 according 

to section 8.1.5.13a as the mean pixel intensity over the same region. The spatial 

resolution is measured using the Modulation Transfer Function (MTF) which is 

calculated using a Contrast Threshold Function (CTF) as described in the NFPA 1801 

Section 8.1.6.10. The spatial resolution target utilizes essentially a square bar target to 

represent spatial frequencies instead of a sinusoidal target because it is easier to 

manufacturer. The CTF is defined in Equation 1-4 as 

max min

max min

I I CTF

I I

−

=

+

 1-4 

where I is the pixel intensity at a point of interest. The CTF is defined by the ratio of the 

difference between the maximum and minimum pixel intensities. The MTF and CTF can 

be related mathematically through the square and sine wave relationship. 

4

MTF CTF π= 1-5 

A more detailed description of the MTF is described in Chapter 2 of this work. 

The nonuniformity is calculated using the procedure described in Section 8.1.5 of NFPA 

1801. The TIC is positioned near the nonuniformity target to fill the entire FOV of the 

TIC. The nonuniformity target is a blackbody required to stabilize at a temperature 

within 0.02 C at temperatures below 160 C and 0.05 at temperature up to 260 C. The 

luminance meter is positioned again so that the TIC display fills the FOV and placed 
14 

under a black shroud to eliminate glare from surrounding light sources. A minimum of 

100 uncompressed images are taken with the nonuniformity target at set point 

temperatures of 1 C, 30 C, 100 C, 160 C, and 260 C. The standard deviation and mean 

pixel intensity are calculating according NFPA 1801 Equation 8.1.5.13a and 8.1.5.13b. 

The nonuniformity is defined as the ratio of the standard deviation of the pixel intensities 

over the mean. 

Nonuniformity σ

μ

= 1-6 

The maximum nonuniformity at any of the set point temperatures is deemed the 

nonuniformity of the imaging system as a conservative estimate. 

The calculations for contrast, brightness, spatial resolution, at each baseline index and the 

maximum nonuniformity are then used as the image quality input parameters for the 

logistic regression model created by the work done in this study to predict if the TIC 

meets standard requirements for image quality. A complete detailed description of the 

model is outlined in Chapter 4 of this work. 

1. 4 Project Goals

The goal of this study was to determine the effect TIC display image quality has a fire 

fighter’s ability to perform a task typically accomplished using a TIC and complement 

the image quality performance test methods established at NIST by creating a model to 

predict the probability of identifying a fire hazard based on the following image quality 

parameters: contrast, brightness, spatial resolution, and nonuniformity (noise). 
15 

To accomplish the goals of this study, a perception experiment was conducted where test 

subjects, who were a representative group of fire fighters that regularly use TIC, were 

given a task to identify a fire hazard by observing IR images. Although there are a wide 

range of tasks a fire fighter could potentially encounter and the type of images that are 

displayed on the TIC could vary dramatically, hazard recognition is among the most 

important TIC application and therefore was the focus of this study. 

 
16 

Chapter 2: Image Processing

2. 1 Introduction to Image Processing

Image processing includes a collection of techniques used to manipulate the visual 

appearance of an image. The fundamentals needed to execute these tools to enhance or 

degrade the quality of images are the focus of this chapter. Image processing can be 

accomplished in both the spatial and frequency domains. Although many of the 

processes are equivalent, processing in both domains will be discussed because there is 

sometimes value for choosing one over the other. Color will not be included because 

most TIC display images are composed of only grayscale values. In addition, color is not 

accounted for in the TIC performance test methods at NIST. 

2.2 Histograms

Image histograms are valuable for image processing because they display the distribution 

of graylevels within an image. Histograms are essentially bar charts that show the 

number of pixels of an image that have a particular pixel intensity or brightness value. 

For an 8-bit image, there are 256 different possible pixel values that are usually displayed 

on the x-axis of a histogram. Each pixel of an image is then placed in one of the 256 

categories also known as bins. Peaks in a histogram indicate common pixel intensities 

within the image while valleys show less common values. Histograms are useful for 

enhancing the brightness and contrast of an image through a technique called histogram 

equalization as discussed in Section 2.4.1.2 Histogram Equalization. 
17 

2. 3 Image Quality Characteristics

Contrast and brightness are closely related concepts because by definition they are 

associated directly to the graylevel intensity value of the pixels of an image and have 

common image processing techniques. It is easiest to explain these concepts visually 

with images and their corresponding histograms as well as quantitatively in their 

definition. For this discussion, consider an 8-bit infrared image of an office work station 

shown in Figure 2- 1. 

Figure 2- 1 IR image of an office work station 
18 

Figure 2- 2 Image histogram of Figure 2- 1 

The histogram shown in Figure 2- 2 illustrates the image utilizes the full range of 

graylevels of an 8-bit image from 0 to 255. 

2.3.1 Contrast 

The contrast of an image is the range of graylevels used to represent the scene. There are 

a possible 256 shades of gray for an 8-bit imaging system. Typically, the more 

graylevels an imaging system uses the higher the contrast. For a TIC, insufficient 

contrast within a display image reduces the details of objects that have very similar 

emitted or reflected IR radiation. In a low contrast image, more pixels in the display 

image are using the same graylevel to depict different levels of radiation in a 

corresponding object. Consider Figure 2- 3 and the corresponding graylevel histogram in 

Figure 2- 4. 
19 

Figure 2- 3 Image with low contrast 

Figure 2- 4 Image histogram of Figure 2- 3. 

Figure 2- 3 has a lower contrast than Figure 2- 1 because fewer graylevels are being 

utilized. The total number of pixels has been spread over a smaller range of graylevels. 

As a result, some of the details such as the power cords and other small items on the desk 

that are visible in Figure 2- 1, are indistinguishable in Figure 2- 3. 
20 

An image with perfect contrast is subjective and dependent on the scene the imaging 

system is representing. There is no one value used to define the perfect contrast for an 

image but there are several methods of quantifying the overall contrast of an image. One 

method is to measure the average variation in graylevels otherwise known as the standard 

deviation of graylevels [Weeks 1996]. For an N x M image, the contrast is 

[ ]

1 1

2

0 0

1

( , )

M N

y x

contrast I x y B

NM

− −

= =

= − ∑ ∑ 2-1 

where B is the average pixel intensity. The highest possible contrast for an 8-bit image 

for example, is half the number of total graylevels or 128. 

Another common method of defining contrast is 

max min

max min

I I

contrast

I I

−

=

+

 2-2 

where the overall maximum and minimum pixel intensity of the entire image are used. 

This definition of contrast is normalized from 0 to 1. 

Equation 2-1 is a better definition for the contrast of an entire image than Equation 2-2. 

Using Equation 2-2, two images by definition could have the same contrast but appear 

very different. An 8-bit image with one pixel at a graylevel intensity of 255 and one pixel 

at 0 would yield a perfect contrast of 1 even if every other pixel within the image was 

128. A second image with many pixels at 0 and 255 would also yield a contrast of 1 but 

a different perceived look. Equation 2-2 is a well know definition for the CTF 

calculation at a specific frequency and is typically used as a measure of spatial resolution 

as described in Section 1.3.2 Bench-Scale Test Methods Developed by NIST 
21 

2.3.2 Brightness 

Brightness is the overall perceived darkness or lightness of an image. For an 8-bit image, 

0 and 255 correspond to black and white and every other pixel intensity corresponds to 

some shade of gray. For an N x M image I(x,y), brightness is simply defined as the 

average pixel intensity within the image [Weeks 1996]. 

1 1

0 0

1

( , )

M N

y x

brightness B I x y

NM

− −

= =

= = ∑ ∑ 2-3 

Compare Figure 2- 5 with an overall brightness value of 198 to the original image in 

Figure 2- 1 with a brightness of 107. As the brightness increases or decreases the pixels 

saturate at a 0 or 255 intensity as evident by the loss of details of the computer shown in 

the lower left corner of Figure 2- 5. 

Figure 2- 5 Image of office with high brightness 
22 

Figure 2- 6 Histogram of Figure 2- 5 

Figure 2- 7 has a brightness value of 22. The image is saturated at 0 as shown in the 

histogram in Figure 2- 8. 

Figure 2- 7 Image with low brightness 
23 

Figure 2- 8 Histogram of Figure 2- 7 

2.3.3 Spatial Resolution 

The resolution of an imaging system is defined as the separation of two discrete targets 

necessary to discern these targets on a display image. A classical method of quantifying 

the spatial resolution of an imaging system is the Modulation Transfer Function (MTF). 

The MTF is a measure of the ability of an imaging system to recreate the modulation of a 

target to an image for a range of spatial frequencies. The overall system MTF is the 

result of many subsystems such as the optics, scanners, detectors, electronics, signal 

processors, and displays. MTF also applies to any one of these subsystems individual 

such as display luminance value or the voltage signal of the detector array from an 

infrared camera [Boreman 2001]. The NIST test methods treat the TIC as a “black box” 

and focus on the evaluation of the display screen, the final product of the entire system. 

Modulation is defined in Equation 2-4 as the amplitude of the pixel intensity variations 

normalized by the bias level at a given frequency [Boreman 2001]. 
24 

max min

max min

I I Modulation M

I I

−

= =

+

 2-4 

The MTF is the ratio of modulation in the image to the object as a function of spatial 

frequency described in Equation 2-5. 

( )

( )

( )

image

object

M

MTF

M

γ

γ

γ

= 2-5 

Due to the inherent limitation in TIC system components such as the resolution of the 

display and the detector cell spacing and fill factor, the reduction in the modulation of a 

signal is frequency dependent. As the spatial frequency of an object increases, the 

modulation depth of the image decreases and therefore the MTF decreases. Figure 2- 9 

illustrates the concept of MTF for a generic imaging system. 

 
25 

Figure 2- 9 MTF for a generic imaging system 

 

Object 

Intensity

Position

Image 

Intensity

Position

0

1

MTF

Spatial Frequency
26 

At high spatial frequencies as the MTF approaches zero, the modulation is typically no 

longer due to the imaging of the target but the random modulation of random in pixel 

output, known as a type of noise. The noise-equivalent modulation (NEM) characterizes 

the noise in a TIC in terms of the MTF and is defined as the amount of image modulation 

necessary to yield a signal to noise ratio (SNR) of unity [Boreman 2001]. This value is 

also measured using the Nonuniformity calculation shown in Section 8.1.5 of NFPA 1801 

[NFPA 1801 2008]. 

The limiting resolution of an imaging system is the location where the NEM dominates 

the MTF. Any point on the MTF curve greater than the intersection of these two points is 

a corrupted signal and not a testament to the resolution of the imaging system. 

While the MTF provides a more complete description of image quality at all spatial 

frequencies it is common to specify a single value for spatial resolution. A common 

definition of the overall spatial resolution of an imaging system is integration of the MTF 

curve between 0 and the spatial frequency at the intersection between the NEM and MTF 

known as the MTF area (MTFA). A larger MTFA indicate better spatial resolution. 

Figure 2- 10 illustrates the definition of spatial resolution. 
27 

Figure 2- 10 Generic MTFA 

The fundamental difficulty in defining spatial resolution using the MTFA is that two 

imaging systems with the same MTFA but different NEM could have a very different 

performance in a particular range of spatial frequencies. Consider the two imaging 

systems MTF curves in Figure 2- 11. Both imagers have the same MTFA but different 

responses to spatial frequencies. 
28 

Figure 2- 11 Generic Comparison of MTF curves 

TIC A has a higher MTF in the lower frequencies than Imager B. In the mid-range 

spatial frequencies TIC B is better than TIC A 

2.3.4 Nonuniformity and Noise 

An undesired deviation from an ideal signal is defined as noise. Noise is typically either 

a constant amplitude over all signal levels or increases with signal level resulting in more 

noise in brighter areas than darker areas of an image [Smith 2007]. Noise is inherent in 

all electro-optical imaging systems in all processes from the optics used to capture the 

scene to the production of the display image. Detector sensors, amplifiers and cabling are 

a few of the system processes sources of noise. A wide range of external factors also 

influence noise, including environmental conditions, radiation, and the instability of a 

light source. The most common noise that occurs in all imaging systems is detector noise 

from the counting statistics of the incident photons on a detector pixel due to the discrete 

nature of radiation [Russ 2002]. 
29 

Noise is generally thought of in two main categories: uncorrelated (independent) noise 

and correlated (dependent) noise. Uncorrelated noise is defined as the random graylevel 

variations within an image that have no dependency on the graylevels of neighboring 

pixels [Weeks 1997]. Noise is generated in images as both additive and multiplicative 

noise. Our discussion is limited to uncorrelated additive noise where a recorded image 

R i,( j) can be defined as 

R i j T i j n i j ( , ) ( , ) ( , ) = + 2-6 

where ) T i,( j is the pixel intensities of the noise free image and ) n i,( j is the intensity of 

the noise. 

Noise is generally classified by the probability distribution or the discrete histogram for 

digitalized images in terms of the mean, M, and the variance σ

2

. The mean is defined as 

max

0

G

i

i

mean M i n

=

= = • ∑ 2-7 

where i

n is the probability of the noise at each graylevel i from 0 to Gmax. The variance is 

defined as 

max

2 2 2

0

G

i

i

σ i n M

=

= ∗ − ∑ 2-8 

 The standard deviation can be obtained from the variance as 

max

1/2

2 2

0

G

i

i

σ i n M

=

 

= ∗ −     ∑ 2-9 

A uniform distribution of noise produces random noise values with equal probability in a 

range of pixel intensities. 
30 

1

,

( )

0,

for K i J

n i J K

otherwise



≤ ≤  − = 





 2-10 

Figure 2- 12 displays a uniform noise histogram. 

Figure 2- 12 Probability Distribution Histogram of Uniform Noise 

Additive uniform noise is then the summation of the random noise value with the original 

pixel value only for pixel values from J → K . 

Noise is often modeled by an additive Gaussian distributed noise because by the central 

limit theorem, a large number of additive independent noise sources approaches a 

Gaussian distribution [Smith 2007]. The Gaussian distribution also describes detector 

noise which is one of the largest sources of noise in electro-optical imaging systems due 

to the nature of radiation and the limited time and space for the detector arrays to count 

the incident photons [Russ 2002]. 
31 

Gaussian noise is expressed as 

2

2

( )

2

( )

2

i M

e

n i

σ

σ π

− −

= 2-11 

 

and by the probability distribution histogram as 

Figure 2- 13 Probability Distribution Histogram of Gaussian Distributed Noise 

which has a peak at the mean. Most Gaussian distributed noise is applied to images with 

a mean of 0. In other words, the highest probability of an occurrence of Gaussian noise 

has a noise value of zero. The probability of the Gaussian noise decreases as the intensity 

of the noise increases the farther the graylevels are from the mean. As with any statistical 

Gaussian or normal distribution, 68% of the noise values lie within one standard 
32 

deviation, 95% within two, and 99.7% within three standard deviations. The variance 

specifies the thickness of the bell shaped curve. A higher variance would create a greater 

magnitude in noise intensity for more pixels. 

Another common form of noise in electro-optical systems is salt-and-pepper noise where 

the noise values are generally outliers that deviate far from the expected pixel intensity. 

In electronic cameras, errors in data transmission generally produce saturated pixels or 

white and black graylevel intensities. Salt-and-pepper noise can also occur from dust or 

lint on the optics of the camera during data acquisition. Generally, salt-and-pepper noise 

takes on two discrete values and occurs at a percentage of the total pixels within the 

image as defined in Equation 2-12. 

( )

( ) ( )

0

p pepper i J

n i p salt i K

otherwise



=





= = 







 2-12 

The histogram of salt-and-pepper noise is 
33 

Figure 2- 14 Probability Distribution Histogram of Salt and Pepper Noise 

where the probably is equal of having two discrete noise intensity value J and K. Saltand-pepper noise is quantified by the percentage of pixels that are corrupted. 

Figure 2- 15 and Figure 2- 17 display examples of images corrupt by additive Gaussian 

and salt-and-pepper noise, respectively. The Gaussian noise was added with a mean of 0 

and a variance of 290. 

Figure 2- 15 Image degraded by Gaussian distributed noise 
34 

Figure 2- 16 Image histogram 

Notice the histogram for the image corrupted with Gaussian noise in Figure 2- 16. The 

first and last bins of the histogram are higher than would be predicted by the Gaussian 

distribution because digitized images have only a finite range of pixel intensities and the 

Gaussian distribution extends to infinity. The summation of the noise and original image 

pixel values exceed the graylevel range of the image and therefore saturation occurs at 

the highest or lowest possible pixel value. 

The salt-and-pepper noise had a 10% corruption rate. In other words, 5% of the original 

pixel values were converted to white and 5% were converted to black. 
35 

Figure 2- 17 Image degraded by salt and pepper noise 

Figure 2- 18 Image histogram 
36 

The histogram for the salt-and-pepper noise corrupted image is as expected. The first and 

last bins are higher than the original image histogram because 10% of the pixels were 

converted to black and white. 

The impact of noise within an image is often defined by the signal to noise ratio. For 

most applications of SNR, the signal is a distinct or known value, like a DC voltage, with 

respect to time. The noise is the random unwanted fluctuations in that signal. For this 

discussion, the SNR is the ratio of the noise free image pixel intensities over the intensity 

due to noise as function of pixel location within the image. The SNR is quantified as the 

ratio of the standard deviation over all the pixels in an image such that 

T

N

SNR σ

σ

= 2-13 

whereσ T

is the standard deviation of the pixel intensities of the noise-free image and σ N

is the standard deviation of the noise [Fisher 2003]. A high SNR would indicate that the 

pixel intensities of the noise free image dominate the noise intensities causing very little 

degradation to the corrupted image. In the same way, a low SNR would indicate the 

noise values of the corrupted image dominate those of the original image. As the SNR 

decreases the noise begins to dominate over the signal and the original image is lost. 

2.4 Image Processing Techniques

2.4.1. Processing in the Spatial Domain 

Processing images in the spatial domain implies modifications or operations are 

performed directly to the pixel intensity values of each pixel location of the original 

image. These modifications are made to each pixel value independently, known as local 
37 

or point processing, or these adjustments can depend on the combination or comparison 

of a pixel location with its surrounding pixels, known as neighborhood processing. 

Image processing in the spatial domain is less computationally demanding than 

processing in the frequency domain because the images are not transformed into 

frequency space and therefore advanced mathematics or processing programs are not 

required. Modifications are applied directly to the image by scanning each pixel value 

and performing some operation. 

2.4.1.1 Point Processing 

Contrast and brightness are two images characteristics that are processed in the spatial 

domain by the manipulation of an image’s graylevels. Some transfer function, linear or 

non-linear, is applied to the original pixel graylevel values to map these values to a new 

set of graylevels. 

Linear transfer functions include addition (subtraction) and multiplication (division). 

Each original pixel within an image is multiplied and/or added to a constant value to 

create a new pixel value. Generally, these two functions can be combined as described in 

Equation 2-14. 

P m O d k k = ∗ + 2-14 

In Equation 2-14, m describes the slope and d describes the offset. Each original pixel, 

Okis then modified by this transfer function to create a new pixel value, Pkfor all image 

pixels, k . Figure 2- 19 illustrates the concept of linear mapping. 
38 

Figure 2- 19 Linear Mapping 

The linear mapping of graylevels to new values is only valid within the range of the 

graylevel scale which is based on the bit depth of the image. An output value exceeding 

the range of the grayscale is set to the limits of that scale. For an 8-bit image, an output 

value of greater than 255 would be mapped to 255 and an output value less than 0 would 

be mapped to 0. The linear transfer function in Figure 2- 19 created a saturation line at 

the maximum possible graylevel. 

The slope of the linear transfer function in Equation 2-14 changes both the contrast and 

the brightness of an image and the offset alters only the brightness. To separate the 

adjustments for contrast and brightness, Equation 2-14 is rewritten as 

( ) ( ) P m O B B d k k = ∗ + + 2-15 

where B is the average brightness of the image as defined in Equation 2-3. The variable 

m changes only the contrast and the offset d changes only the brightness [Weeks 1996]. 
39 

A slope of one and an offset of 0 in the transfer function would take each original pixel 

value and map it to the same value in the modified image. If the transfer function had a 

slope value greater than one than a smaller range of graylevels in the original image is 

linearly spread over a larger range of graylevels in the modified image known as contrast 

expansion. This is used for image enhancement to expand an image that does not utilize 

the full range of graylevels available for a particular bit depth to the full range of 

graylevels. This greatly improves the contrast of an image and enhances detail. 

Similarly, a slope value of less than one can be used to degrade the contrast of an image. 

A slope of less than one linearly decreases the amount of graylevels in the output image 

that are utilized in the original image. A positive offset value would increase the overall 

brightness of an image and a negative value would produce a darker image. Figure 2- 20 

illustrates the use of Equation 2-15 to modify the brightness and contrast of an image 

using point processing. A slope, m , value of 0.3 and an offset, d , value of 80 was used. 

Figure 2- 20 Image degraded using point processing 
40 

Figure 2- 21 Image Histogram 

Figure 2- 20 essentially has a contrast of 30% of the original image shown in Figure 2- 1 

and an average overall brightness 80 graylevels higher than the original image. 

Non-linear transfer functions operate in a similar fashion to linear functions with the 

exception that the output pixel value will be dependent on the value of the input pixel. 

Non-linear functions are typically used to enhance dark or light regions of an image that 

are of interest to an observer. A non-linear transfer function can expand some portions of 

grayscale range while compressing others depending on an observer’s needs. Several of 

the most common types of non-linear transfer functions are the exponential and 

logarithmic among others presented in Figure 2- 22. 
41 

Figure 2- 22 Point processing using nonlinear transfer functions 

Figure 2- 22 displays the original image pixel value on the x-axis and the modified pixel 

value on the y-axis after the application of a transfer function. The exponential or 

squared transfer function increases the contrast of the light areas of an image while 

reducing the contrast of dark areas. The logarithmic and square root transfer function 

have the opposite effect. The inverse function reverses the pixel values and the identity 

function leaves the image unchanged. 

Transfer functions, either linear or non-linear, are an important part of image processing 

because a reproducible quantitative modification can be applied to a series of images and 

to create the same effect. 

2.4.1.2 Histogram Equalization 

Histogram equalization is used to modify the contrast and brightness of an image by 

modifying the image histogram. The goal is to redistribute the graylevels of an image so 
42 

each graylevel has an equal probability of occurring while retaining the brightness order 

of the pixels (See Figure 2- 26). In other words, the new histogram has uniformly 

distributed pixel intensities but relative intensities remain in the same order as the 

original image. Peaks in the histogram are spread out over a larger range of graylevels 

while the valleys are compressed into fewer graylevels creating visibility in minor pixel 

variations for a greater number of pixels. 

For a discrete image, the process of histogram equalization can be described as 

0

j

i

i

N

k

= T

= ∑ 2-16 

where the sum counts the total number of pixels within an image with original brightness 

equal to or less than, j, and T is the total number of pixels [Russ 2002]. For each 

original brightness level, j, the new assigned value is k.

Figure 2- 23 show an original image with its histogram as well as an image using 

histogram equalization. After histogram equalization, some features in the new image 

became more apparent and other details were lost. 
43 

Figure 2- 23 Original Image 

Figure 2- 24 Image histogram of Figure 2- 23 

Figure 2- 25 Image after histogram equalization 
44 

Figure 2- 26 Image histogram after equalization 

The surge protector located in the center of the floor, the rim of the trash can, and the 

table legs had pixel intensity values at a peak in the spectrum in Figure 2- 24. As a result 

of histogram equalization, the details in these objects are more noticeable. On the other 

hand, other details were lost such as the variation in color of the computer monitor. The 

monitor pixel intensities were located in a valley in Figure 2- 24 and therefore the 

graylevels in this region were compressed. 

In practice, after applying histogram equalization, the new histogram does not produce an 

image with an equal distribution of graylevels. The reason is because histogram 

equalization assumes the graylevels continuously vary between the minimum and 

maximum graylevels. Since digitalized images have only a discrete number of graylevels 

the solution is only an approximation [Weeks 1996].

2.4.1.3 Convolution in the Spatial Domain 

Convolution is a common image processing technique used in the spatial domain to filter 

noise and adjust the spatial resolution of an image by the manipulation of the image 
45 

graylevels. Convolution is the replacement of a pixel value with a weighted average of 

itself and the neighboring pixels using an array of integer weights known as a kernel. A 

kernel is essentially a filter with an impulse response given by the kernel weights that is 

applied pixel by pixel to an entire image. Each location in the kernel array corresponds 

to a pixel location relative to the pixel being processed. The integer weights in the kernel 

are multiplied by their corresponding pixel value and the average of these values is used 

to replace the original pixel value. A kernel is typically square with odd dimensions 

(3x3, 5x5, 7x7, etc.) so it can be symmetrical about a central pixel. To illustrate, consider 

an original image with a pixel location ) f (x, y and a 3 x 3 filter kernel ) h(x, y with 

weights wk

. 

Figure 2- 27 Schematic of kernel operations 

The center of the kernel is defined by the coordinate (0, 0) and exists over the range

x, y ∈ − 1,0,1 . The new pixel value ) g(x, y after convolution by ) h(x, y with weights Wk

can be described as 
46 

2 2

( 3 )

0 0

2 2

( 3 )

0 0

( 1 , 1 )

( , )

W j i

i j

W j i

i j

f x j y i h

g x y

h

+

= =

+

= =

− + − + ⋅

=

∑∑

∑ ∑

 2-17 

The summation of the central and neighborhood pixels multiplied by the kernel weight 

and then normalized by the sum of the weights produces the new pixel value. 

Applying a kernel around a central pixel creates a problem at the border of an image. At 

pixel location )0,0( f in Figure 2- 27, five of the nine kernel weights do not apply to any 

neighboring pixel. There are several approaches to deal with this problem. The first 

approach is to simply not process the edges of the images where some kernel weights 

would not exist. This is not a major limitation for small kernel sizes because typically 

edges do not contain the most important details of an image. A second approach is to 

mirror the edge pixels as if they extended beyond the image. Finally, the kernel could 

wrap around the image and take the pixel values from the opposite size of the image as if 

they image was continuous. When using small kernels this problem is not a major 

limitation. However, when dealing with larger kernel sizes the problem could be 

significant. The convolution process would not be uniform throughout the image. 

The impulse response (the values of the kernel weights) and the size of the kernel dictate 

the effect of convolution on the image. The most common convolution process is a 

simple neighborhood averaging kernel where the weight of each location within the 

kernel is equal. This type of filter is beneficial for reducing noise by removing high 
47 

frequencies from an image. Figure 2- 28 illustrates a 3 x 3 kernel array for simple 

neighborhood averaging. 

Figure 2- 28 Neighborhood averaging kernel 

The random noise pixel values are reduced because of the contribution of true image 

pixel values from neighborhood pixels. In general, the larger the kernel size, the more 

noise is filtered out of an image. Convolution also reduces the spatial resolution by 

blurring edges and boundaries of objects in the image. In fact, convolution in the spatial 

domain can be a useful tool not only for reducing noise but also for image degradation to 

reduce the spatial resolution of an image. 

To reduce the amount of blurring for a desired amount of noise reduction, the weight 

values of the kernel can be adjusted to add a greater emphasis on the original pixel value 

and the contribution of neighborhood pixels diminishes the farther away from the central 

pixel. The weight values could be chosen somewhat arbitrarily depending on an 

observer’s opinion when the convolution process has created a desired result. However, 

it is useful to use standardized numbers for weight values so the same kernel can be 

applied to multiple images for comparison. 
48 

The most common weighted kernel is the Gaussian kernel. This type of kernel is an 

approximation of the Gaussian function along every row, column, and diagonal through 

the center of the kernel [Russ 2002]. The actual numbers used in the kernel vary 

particularly in the smaller kernels because discrete values are used to approximate a 

smooth continuous function. The Gaussian kernel is typically described by the standard 

deviation which is defined as the radius (in pixels) from the center of the filter containing 

68% of the integrated magnitude of the coefficients [Russ 2002]. Consider Figure 2- 29 

of an image corrupted with noise. 

Figure 2- 29 Image corrupt with noise 

Figure 2- 30 shows the convolution of Figure 2- 29 using several size Gaussian kernels. 

Kernel size increases with standard deviation. 
49 

Figure 2- 30 Image processed using associated kernel shown in Figure 2- 31 

Figure 2- 31 Gaussian kernel (3x3) 

 

Figure 2- 32 Image processing used associated kernel shown in Figure 2- 33 
50 

Figure 2- 33 Gaussian Kernel (9 x 9) 

Figure 2- 34 Image processing used Gaussian kernel shown in Figure 2- 35 

Figure 2- 35 Gaussian Kernel (15 x 15) 
51 

As the Gaussian kernel size increases, the visibility of the noise present in the image 

decreases but the sharpness of the image also decreases. 

The use of neighborhood averaging kernels such as the Gaussian kernel in a convolution 

process reduces the blurring effect for a given amount of noise reduction but does not 

completely eliminate the reduction in spatial resolution. Neighborhood averaging kernels 

operate based on the assumption that every pixel within the kernel size belongs to the 

same feature in the image. Because this is not true at edges and boundaries there will 

always be some reduction in the spatial resolution of an image. 

To sharpen a blurry image, negative weight values can be given to a kernel for the 

neighborhood pixels and a positive weight to the central pixels. The intensity of the 

central pixel is magnified, sharpening edges and creating greater contrast. The process is 

limited to images with small amounts of noise; otherwise, noise pixels would be 

magnified and defeat the purpose of sharpening edges. 

2.4.2 Image Processing in Frequency Domain 

2.4.2.1 Fourier Transforms 

The Fourier transform is the most common transform used for image processing in the 

frequency domain because of the availability of an efficient algorithm for computing it, 

known as the fast Fourier Transform [Cooley and Tukey, 1965; Bracewell, 1989]. 

Performing image measurements and processing operations in the frequency domain 

offers some advantage over the kernel operations in the spatial domain. In many cases, it 

is desired to filter out a particular spatial frequency of an image such as the removal of a 
52 

periodic noise that modulates at a known frequency. It is difficult to know the kernel 

weights to create an impulse response that would produce the desired effect on a 

particular frequency. Additionally, the computational cost of performing operations such 

as convolution using extremely large kernel sizes in the spatial domain can be 

significantly greater than the calculation of the Fourier transforms needed for the same 

operations in the frequency domain. 

Other transforms such as the Hadamard, Walsh, and discrete cosine transform are 

typically used for image compression [Weeks 1997]. Most image characteristics are 

defined in the lower spatial frequencies and therefore eliminating high frequency 

components reduces the necessary storage for an image with minimal impact on image 

quality. The conversion of an image in the spatial domain to the frequency domain using 

the Fourier transform will provide the framework for filtering operations used to adjust 

noise and spatial resolution discussed in the following sections. 

4.2.4.1.1 The 1-D Fourier Transform

Consider a continuous function f(x) such as spatially-varying image brightness where x is 

the distance in one direction across an image. Fourier’s theorem states that a onedimensional continuous function f(x) can be decomposed into a summation of a series of 

sine and cosine terms of increasing frequency known as the forward Fourier transform, 

denoted F[f(x)] and written as: 

2

( ) ( ) iux F u f x e dx π

∞ −

−∞

= ∫ 2-18 
53 

where i = −1 . Using Euler’s formula to expand Equation 2-18, the Fourier transform, 

F(u), can be separated into real and imaginary components. 

F u R u iI u ( ) ( ) ( ) = + 2-19 

where ) R(u is the real part of ) F(u and is defined as 

R u f x ux dx ( ) ( )cos(2 ) π

∞

−∞

= ∫ 2-20 

and ) I(u is the imaginary part of ) F(u

I u f x ux dx ( ) ( )sin(2 ) π

∞

−∞

= − ∫ 2-21 

Each sinusoidal term in the Fourier series corresponds to a spatial frequency or 

specifically for this demonstration, a frequency where the brightness of the image 

modulates. The Fourier frequency components can be written in terms of magnitude 

otherwise known as the magnitude spectrum, 

2 2 F u R u I u ( ) ( ) ( ) = + 2-22 

and phase also known as the phase spectrum, 

1

( ) ( ) tan

( )

I u

u

R u

φ

−

 

=     2-23 

The magnitude is essentially the amplitude of the brightness modulation and the phase 

represents the shift in the sinusoid relative to the origin [Weeks 1996]. 

The Fourier Transform encodes a series of sinusoids for a range of spatial frequencies 

from zero or no modulation (the average brightness of the image) to the highest spatial 
54 

frequency. Up until now we have considered a continuous function and the highest 

spatial frequency would be dependent on the function f(x). However, digital images have 

discrete brightness values at each pixel location. The integrals shown in Equations 2-20 

and 2-21 are evaluated from minus to plus infinity. The discrete forward Fourier 

transform for a digital image would be limited by the finite spacing of the pixels and can 

be written as 

1

2 /

0

1

( ) ( )

N

i ux N

x

F u f x e

N

π

−

=

= ⋅ ∑ 2-24 

where N depends on the number of pixels in the X-direction. The summation is 

performed over terms up to one-half the dimension of the image in pixels. The final 

frequency term is known as the nyquist frequency and is defined as the highest spatial 

frequency that can be encoded in a digital image. The nyquist frequency is one half the 

total pixels in a dimension because it requires a minimum of two pixel brightness values 

to define a frequency. Because each frequency component has a real and imaginary part, 

the total number of values produced by the Fourier Transform is the same as the total 

number of pixels in the x-direction [Russ 2002]. 

One of the most important aspects of the Fourier Transform is that given ) F(u , the 

original spatial domain function f(x) can be recovered using the same technique. 

2

( ) ( ) iux f x F u e du π

∞ −

−∞

= ∫ 2-25 

or in the discrete case 

1

2 /

0

( ) ( )

N

i ux N

u

f x F u e π

−

=

= ⋅ ∑ 2-26 
55 

This property of Fourier transform is extremely important when using linear filtering 

techniques to modification the spatial frequencies present within an image. 

4.2.4.1.2 The 2-D Fourier Transform

Expanding the properties of the one-dimensional Fourier transform into two-dimensions, 

entire images can be decomposed into frequency space where each pixel corresponds to a 

complex value representing a magnitude and phase component. The 2-dimensional 

Fourier Transform is 

1 2 ( ) ( , ) ( , ) i vx wy F v w f x y e dxdy

NM

π

∞

− +

−∞

= ∫ ∫ 2-27 

and its inverse as 

1 2 ( ) ( , ) ( , ) i vx wy f x y F v w e dvdw

NM

π

∞

− +

−∞

= ∫ ∫ 2-28 

where v and w are the frequencies in the x and y directions. For an N x M finite size 

image the discrete 2-dimensional Fourier transform is 

1 1

2 ( / / )

0 0

1

( , ) ( , )

M N

j nx N my M

y x

F n m f x y e

NM

π

− −

− +

= =

= ⋅ ∑ ∑ 2-29 

and its inverse as 

1 1

2 ( / / )

0 0

( , ) ( , )

M N

j nx N my M

m n

f x y F n m e π

− −

+

= =

= ⋅ ∑ ∑ 2-30 

The terms in the Fourier series are independent of each other. Most of the image 

characteristics are described in the first few terms of the series. Adding higher and higher 

frequency terms improves the quality of the image, sharpening edges and providing the 
56 

fine details. Performing the transform at higher and higher frequencies does not alter the 

previous terms. 

Images in frequency space are commonly represented based on only the magnitude 

values of the sinusoids called the magnitude spectrum. Sometimes the square of the 

magnitude or the power is used. An image is created from the magnitude spectrum by 

simply scaling the values to coincide with the graylevel range based on the bit depth of 

the image (0 to 255 for an 8-bit image). The distance from the origin of the magnitude 

spectrum corresponds to an increase in spatial frequency. The origin is the zero 

frequency component otherwise known as the DC level (no modulation or the average 

pixel intensity). The magnitude spectrum is commonly represented with the origin in the 

center and increasing frequency with the radius. The orientation depends on the angle. 

Figure 2- 36 and Figure 2- 38 are real images of two shapes. Figure 2- 37 and Figure 2- 

39 are the representations of the corresponding magnitude spectrum. 

Figure 2- 36 Image of a circle 
57 

Figure 2- 37 Frequency Magnitude Spectrum of Figure 2- 36 

Figure 2- 38 Image of square 

Figure 2- 39 Frequency Magnitude Spectrum of Figure 2- 38 

Notice most of the image in frequency space is located near the origin or at the lowest 

spatial frequencies. The magnitudes of the lowest frequencies are high creating bright 
58 

pixels in the magnitude spectrum. At higher frequencies, the magnitudes become smaller 

representing gray to black values in the magnitude spectrum. 

2.4.2.2 Spatial Frequency Filtering 

The decomposition of an image into a series of frequency terms using the Fourier 

transform is the basis for filtering images in the frequency domain. The modification of a 

particular spatial frequency term has no effect on any other spatial frequencies because 

each term in the series is independent. The effect of filtering in the frequency domain is 

exactly the same as convolution in the spatial domain. In the spatial domain, a filter with 

a given impulse response determined by the weights of the kernel, was applied to each 

image pixel. Filtering in the frequency domain is accomplished by multiplying the 

Fourier transform of both the image and the filter’s impulse response as shown in 2-31. 

G n m F n m H n m ( , ) ( , )* ( , ) = 2-31 

where n and m are the spatial frequencies in the x and y direction and ) H(n,m , ) F(n,m , 

and ) G(n,m are the Fourier components of the impulse response h(x, y) , the original 

image ) f (x, y , and the filtered image ) g(x, y . The reverse Fourier transform is then 

used to convert the frequency components back into the image as outlined in Figure 2- 

40. 
59 

Figure 2- 40 Flow chart of frequency filtering of images 

The Fourier transform of the impulse response of a filter is a function ) H(n,m used to 

modify an image’s frequency components. However, it is not necessary to know the 

impulse response directly (although it can be found by taking the inverse Fourier 

transform of the frequency response of the filter). Instead an arbitrary function can be 

used to modify the spatial frequencies directly without knowing the impulse response. 

This is advantageous because typically the effect the impulse response of a filter has on 

the spatial frequencies is unknown and it is the spatial frequencies that are important to 

manipulate. 

A common way to make a filter is to create a function in one dimension with respect to 

spatial frequency from the center of the magnitude spectrum of the Fourier transform of 

an image and then expand the function into two dimensions. Each spatial frequency has a 

designated location or radius from the origin (DC component) located at the center of the 

magnitude spectrum. The one-dimensional filter ) H(n,m is rotated 360 degrees based on 

the radius from the center shown in Equation 2-32 and Equation 2-33 . 
60 

H n m H ( , ) ( ) = ρ 2-32 

where 

2 2 2 ρ = + n m 2-33 

to create a circular filter. The phase components of the frequency terms must be 

preserved in order to ensure an inverse Fourier transform can transform the image in the 

frequency domain back to the spatial domain. The only requirement to be a phase 

preserving filter is that the values of ) H(n,m must be real. The filter values are 

multiplied by both the real and imaginary parts of the Fourier Transform corresponding 

to spatial frequency component. The circular property of the filter ensures that the same 

filter value is applied to all phase components at a given spatial frequency. 

The filter function typically ranges from 0 to 1 over the range of spatial frequencies 

present in the image (DC component or zero frequency to the Nyquist frequency). If the 

filter function has a value of zero, this essentially changes the magnitude at the 

corresponding spatial frequency to zero or no modulation. If the filter function has a 

value of 1, the modified magnitude at the corresponding frequency is equal to the original 

magnitude. 

2.4.2.2.1 Filtering Techniques

The most common filters are low-pass, high-pass, and band-pass. A low-pass filter 

attenuates high frequencies while passing low frequencies. The effect of low-pass filters 

is the same as convolution in the spatial domain with simple averaging kernel weights. 

The image loses sharp edges and fine details and essentially blurs the image because the 

higher frequency information is subtracted from the image. The most common filter is 
61 

the ideal low-pass filter where frequencies below a cutoff frequency cf are allowed to 

pass and the frequencies above cf are blocked. The ideal low-pass filter has no transition 

period from passing to attenuation of frequencies and can be described for the one and 

two dimensional cases in Equation 2-34. 

2 2

2 2

1 1

( ) ( , )

0 0

c c

c c

for f f for n m f

H f H n m

for f f for n m f

    ≤ + ≤

= → =  

    > + >

 2-34 

Figure 2- 41 shows the magnitude spectrum of a one dimensional ideal low-pass filter 

and Figure 2- 42 shows the one dimensional filter rotated 360 degrees about n and m in 

the x and y directions to create a two dimensional filter for an image size of 640 x 480. 

Figure 2- 41 One-dimensional low pass filter 

Figure 2- 42 Two-dimensional low pass filter 
62 

The magnitude spectrum of the two dimensional filter is designed to coincide with the 

magnitude spectrum of Fourier transform of the image which is commonly displayed 

with the DC component in the center and distance from the center corresponding to an 

increase in spatial frequency. The ideal low-pass filter starts at 1 at the lowest frequency 

and drops to 0 at a desired frequency cf . 

Ideal low-pass filters create a finite discontinuity in the magnitude spectrum and therefore 

create a finite discontinuity in the Fourier transformed image. The truncation of the 

Fourier spectral components at the cutoff frequency introduce artifacts commonly called 

ringing when the filtered image is transformed back into the spatial domain [Weeks 

1997]. To illustrate the concept of ringing an ideal low pass filter was applied to Figure 

2- 1 to create Figure 2- 43. 

Figure 2- 43 Example of ringing artifacts 

An ideal low pass filter was applied to Figure 2- 1 to produce the artifacts that appear in 

Figure 2- 43. 
63 

To circumvent the effect of ringing at sharp discontinuities a smooth edge can be applied 

at the transition point of the low-pass filter. There are several common filter functions 

used in digital image processing such as a parabolic or cosine function. The most 

appropriate function is the Gaussian shape because the filter never drops to zero but 

leaves a long tail beyond the cutoff frequency. The inverse Fourier transform of the 

Gaussian filter is another Gaussian filter which would eliminate the effect of ringing. It 

is also common to use the discrete approximation to the Gaussian filter known as the 

Butterworth filter to produce the same effect. It is important to note that only the 

magnitude spectrums of these filters can be used in image processing due to the phase 

preserving requirements. 

The magnitude of the Butterworth filter is described by Equation 2-35: 

1

2

( ) 1

n

c

D

H D C

D

−

   

= +           2-35 

where D is the distance from the center of the filter or the zero frequency to a particular 

frequency and Dc is the distance to the nominal filter cutoff value cf . Again, ultimately 

this distance corresponds to a specific spatial frequency. The constant C is commonly set 

to 1 or 0.414 to set the magnitude of the filter at the nominal filter cutoff value to 50% or 

2

1 respectively. The integer n is the order of the filter commonly 1 or 2. The higher 

the function order, the steeper the filter profile. Figure 2- 44 displays three Butterworth 

filter curves with common cutoff distances (frequencies) and Figure 2- 45 displays 

different function orders. 
64 

Figure 2- 44 Butterworth filter curves with varying cutoff frequencies 

Figure 2- 45 Butterworth filter curves with varying function orders 

Figure 2- 45 shows three Butterworth filters with different cutoff distances but the same 

function order. The best function to use would depend on the image and the desired 

effect on the image. At the least, the order should be chosen to eliminate the ringing 

effect at sharp edges. The two dimensional representation of the Butterworth filter is 

displayed in the magnitude spectrum shown in Figure 2- 46. Figure 2- 47 and Figure 2- 

48 show the original and filtered image respectively. Notice the ringing effect evident in 

Figure 2- 43 using the ideal low-pass filter is eliminated. 
65 

Figure 2- 46 Magnitude spectrum of 2-D Butterworth filter 

Figure 2- 47 Original Image 
66 

Figure 2- 48 Image modified using Butterworth filter 

High-pass filters pass high frequency information and attenuate low frequency 

information. The filters previously discussed for low-pass can be modified to create high 

pass filters. When applying a high-pass filter, the edges of image features are retained 

but the overall detail of the image is lost. To illustrate the effect of a high-pass filter, 

consider a high-pass Butterworth filter described by Equation 2-36. 

1

2

( ) 1

n

Dc H D C

D

−

   

= +          

 2-36 

and represented in two dimensions in Figure 2- 49. 
67 

Figure 2- 49 High Pass 2-D Butterworth filter 

The result of applying this filter to Figure 2- 47 is shown in Figure 2- 50. 

Figure 2- 50 Image processed with high pass Butterworth filter 

Notice the edges at sharp brightness differences are retained in the filtered images shown 

by the outline in components such as the computer screen, PCU, and the lamp. It is 
68 

important to note that when using high pass filters the average overall brightness of an 

image is usually kept the same. Therefore the filter magnitude at the DC level is left 

unchanged. 

Finally, band-pass filters are used to attenuate or pass a particular band of spatial 

frequencies of interest. A common procedure for noise removal is to analyze the 

magnitude spectrum for peaks at frequencies where there is periodic or unwanted noise. 

These frequencies can simply be subtracted from an image by applying a filter function 

that equals zero at these frequencies. The filter functions used for band-pass filters are 

equivalent to those used for low and high pass filters. The edges of the bands can be 

sharp like the ideal filter or smooth like Gaussian or Butterworth filter. 

 
69 

Chapter 3: Human Perception Experimental Design

3.1 Approach

To understand the effect TIC display quality has on human perception, fire fighters were 

given a typical TIC task: identifying a fire hazard by observing an IR image. A series of 

images were presented to the test subjects, which were a representative sample of fire 

fighters that regularly use TIC, on well-characterized computer screens in an 

ergonomically designed perception laboratory. The images were adjusted to 

quantitatively degrade image contrast, brightness, noise level, and spatial resolution. 

These image quality parameters were labeled the primary factors. Robustness factors, 

such as the amount of thermal clutter, the type of thermal scene, the shape and relative 

location of the fire hazards within the image were added to the image test matrix to 

control for variables that could potentially affect the results. The matrix of images 

presented to the test subjects was statistically constructed using a Taguichi experimental 

design so that it was possible to deconvolve the results to understand the interactions of 

the primary factors and their weighted effect on perception. Using the results of this 

study, a model was developed to predict a fire fighter’s probability of successfully 

completing the recognition task given the key primary factors. A pilot study, using NIST 

personnel, was conducted as a proof of concept and to aid in the design of the full scale 

test. 

The project was investigated through the collaboration between the National Institute of 

Standards and Technology (NIST), the Fire Protection Engineering Program at the 

University of Maryland, and the Army’s Night Vision Laboratory (NVL). 
70 

3.2 Night Vision Laboratory (NVL)

NVL is a military laboratory at Fort Belvoir in Virginia that is dedicated to the research 

and development of night vision technology for military applications. As part of NVL’s 

mission, a perception lab is devoted to testing soldiers’ ability to identify and recognize 

targets based on the information gained from a thermal image. NVL evaluates military 

tasks such as recognizing and identifying ships, weapons, explosives and video clips of 

threatening human movements based on thermal imaging of the scenario. 

Because of NVL’s experience in human testing and data collection methods, NVL’s 

ergonomically designed perception lab was an ideal environment to conduct the testing 

on fire fighter task performance. The lab included ten test stations with 12-bit cathode 

ray tube (CRT) monitors that differentiate 4096 levels of gray, far greater than a standard 

monitor that distinguish only 256 gray levels. The CRT grid was also more fine then the 

grid of the TIC system. Therefore the CRT grid adequately sampled the image and 

therefore any impact of resolution was not due to the screens at NVL but the resolution of 

the imaging system. Sampling is critical to avoid aliasing artifacts. For a more detailed 

discussion of the sampling of system resolution refer to work done by Boreman 

[Boreman 2001]. 

Each station was equipped with sufficient lighting, comfortable chairs and temperature 

control to create an ideal comfortable atmosphere and windowless to avoid glare issues. 
71 

3.3 Image Production

3.3.1 Hazards 

The study was designed to investigate the ability to identify fire hazards in office and 

living room scenes that fire fighters are trained to understand and accustomed to viewing 

with a TIC. Hazards such as hotspots in walls, overheated electrical equipment, hot 

wires, and buried hot spots in furniture were used to simulate a smoldering or flaming fire 

in early stages where there would be no visual evidence of a flame or the origin of smoke. 

According to fire fighters trained in TIC, one of the most common reasons fire 

department are called to a scene is because building occupants smell smoke but cannot 

determine the origin. Fire fighters use TIC to scan the room. 

One hazard type that was used for this study was a faulty connection in an electrical 

system that caused a low-resistance connection such as a wire, to carry a large amount of 

current to a source not equipped to handle the voltage. Figure 3- 1 displays infrared 

images of overheated electrical outlets. 

Figure 3- 1 Overheated electrical outlets 
72 

Overheated wiring or devices could occur for various reasons such as lightning strikes 

sending current through an electrical system, poor connections, or uninsulated wiring. 

Another common occurrence of overheated wires occurs when a table or desk leg crushes 

a wire and causes a considerable amount of resistance heating as shown Figure 3- 2. 

Figure 3- 2 Crushed wire under table leg 

Other hazards used for this study included buried hot spots in trash cans and furniture as 

shown in Figure 3- 3. 

Figure 3- 3 Buried hotspot in chair 
73 

Buried hazards were used to represent a cigarette or match that was thrown away or 

dropped which has the potential to be slow developing and could elude a building 

occupant of the origin of the burning. 

Although this experiment focused on one of the most common applications of TIC, it is 

important to note that TIC are used in a dynamic range of environments and applications. 

Due to a number of limiting factors, other scenarios and uses of TIC were beyond the 

scope of this work. 

As an alternative to physically creating wall fires, buried hazards and short circuiting 

electrical devices, external heat sources were used to simulate the effect the radiation 

from the actual hazards would have on the TIC detectors. Heat rope and heat tape, which 

are essentially high resistance wires, were used to reproduce over heated wires and 

receptacles. To reproduce a generic hot spot, a high intensity halogen lamp and heat guns 

were used. The intent of this work was only to replicate the radiation emitted from a real 

hazard on a TIC display screen and not to reproduce the hazards. 

A balance between the realism of the hazards and a controlled experiment was necessary. 

Fire fighters must be able to positively identify realistic fire hazards and at the same time 

create controlled images to focus the experiment on image quality parameters and 

conditions that could influence detection probability. To ensure the validity of the 

thermal images and the type of hazards, the images were sent to fire fighters who train 

others on the applications and techniques used for TIC in the field. In addition, the 
74 

feedback from the pilot study images was used to tweak the types of images used for the 

real perception experiment. 

3.3.2 Scene 

A small one compartment structure was constructed to be a representative room or office 

a fire fighter could encounter. A 12’ by 12’ room was built from gypsum wallboard 

backed by 2 x 4 constructional lumber at 16” on center spacing. Electrical outlets, 

overhead lights, wall lamps, and carpet were installed in the room. 

The room was furnished with living room furniture on two walls and office equipment on 

the other two walls to capture two scenes with one room to reduce construction costs. 

Figure 3- 4 and Figure 3- 5 displays the living room scene assembled on two walls and 

Figure 3- 6 and Figure 3- 7 displays the office work station. 
75 

Figure 3- 4 Living room scene 
76 

Figure 3- 5 Living room scene 

Figure 3- 6 Office scene 
77 

Figure 3- 7 Office scene 

Common living furniture such as tables, chairs, and standing lamps were added to the 

living room scene. Other items such as candles, lamps, plants, coffee cups, etc were also 

added as thermal clutter. The office work station included desks and computer chairs as 

well as computers, monitors, coffee makers, surge protectors, battery chargers among 

other electronic equipment. 

3.3.3 Image Capturing 

The images were captured using a FLIR Systems ThermaCam P640 commercial infrared 

camera. The display image quality of the FLIR P640 was chosen because it had far better 

display image quality than any fire fighting TIC available on the market. Most 

commercial fire fighting TIC have detectors with 320 x 240 or 160 x 120 pixel arrays. 
78 

The ThermaCam P640 has a detector pixel array of 640 x 480, four times the resolution 

of fire fighting TIC. Each detector pixel can distinguish 16-bit of information. In other 

words, the image produced on the display considers 65536 different intensity values or 

graylevels to create the image. A fire fighting TIC typically uses an 8-bit or 256 

graylevel scale. 

3.4 Defining the Scenario Criteria

3.4.1 Robustness Factors 

Robustness factors were included in the test design to ensure the conclusions of the study 

would apply to a broad range of scenarios. There were a total of four robustness factors 

that included, hazard position, hazard type, thermal clutter, and scene type which were 

considered the most important factors that may influence the results according to pilot 

study results. The number of levels associated with each hazard and the definition of 

these levels are shown in Table 3- 1 . 

 
Robustness Factor

1 Target Position 

2 Hazard Type 

3 Amount of Clutter

4 Scene 

 

One hazard type was used in each image (except for images with no hazard) in one of 

five locations as shown in

79 

Table 3- 1 Robustness Definitions 

Robustness Factor Number 

of Levels Level Definition

6 Center 

Upper Left 

Upper Right 

Lower Left 

Lower Right 

No Target 

5 1 Overheated receptacle

2 Overheated wire 

3 Buried hotspot in furniture/ trash 

can 

4 Small hotspot in wall

5 Large hotspot in wall

2 Small: 2-5 thermal objects

Large: 8-10 thermal objects

2 Office work station 

Living room 

One hazard type was used in each image (except for images with no hazard) in one of 

locations as shown in Figure 3- 8. 

Figure 3- 8 Hazard location divisions 

Level Definition

1 Overheated receptacle

3 Buried hotspot in furniture/ trash 

wall

5 Large hotspot in wall

5 thermal objects

10 thermal objects

One hazard type was used in each image (except for images with no hazard) in one of 
80 

In addition to the hazard, thermal clutter was added to the image. Clutter was defined as 

an object that emits or reflects enough radiation operating in normal operating conditions 

to create a hot spot on a TIC. Clutter was used to make the images challenging and force 

the test subject to distinguish hazards from other objects. Figure 3- 9 displays several 

objects that were used as thermal clutter. 

Figure 3- 9 Thermal clutter 

The robustness factors were also used to ensure test subjects would not become too 

familiarized with images. A preconceived notion of the location and type of objects in 

the scene would simplify the task of identifying the location of the hazard on the image. 

3.4.2 Primary Factors 

The main focus of the study was to investigate display image quality in terms of four 

characteristic or primary factors; contrast, brightness, spatial resolution, and noise. The 

primary factors and definitions were chosen to understand their impact on a user’s 

probability of successfully completing a hazard recognition task. The primary factors, 

definitions, and ranges are shown in Table 3- 2. 
81 

Table 3- 2 Primary Factor Definitions 

Image 

Characteristic 

Definition Range 

Min Max 

Contrast Contrast = σ lu min ance 0 ∞

Brightness Brightness = μ lu min ance 0 ∞

Spatial 

Resolution 

( )

0

SR MTF NEM

A

= curve − ∫

where A= intersection of 

MTF and NEM

0 pixel

cycles f

nyquist = 5.0

Noise 

μ

σ noise Nonuniformity = 0 ∞

The results of this study must have a connection to the NIST test methods to establish the 

minimum requirements for the image quality parameters in NFPA 1801, Standard for 

Thermal Imagers for the Fire Service. Conceptually, the perception experiment was 

designed to find the minimum image quality for a user to perform a task and the NIST 

test methods evaluate a TIC ability to reproduce an equivalent image quality. The 

definitions used to quantify image quality in terms of contrast, brightness, spatial 

resolution, and noise are equivalent in both cases but these parameters are evaluated on 

dissimilar images. However, conceptually we are still evaluating the same principal; the 

ability of a TIC to distinguish relatively hot and cold objects and the ability of a user to 

distinguish relatively light and dark objects. 

 

As discussed in Section 1.3.2 Bench-Scale Test Methods Developed by NIST, contrast, 

brightness, and spatial resolution are evaluated using a controlled thermal image of a 

heated bar target over an ambient background. In the perception experiment, the 

parameters are evaluated over images of heated realistic objects in an ambient scene. In a 

similar fashion, nonuniformity is evaluated in the NIST test method as the random 
82 

fluxuations of pixel intensities from a uniform blackbody. In the perception experiment, 

random fluxuations were simply added to the images to produce similar false variations 

in pixel intensity. The perception experiment makes the connection between the user and 

the image while the NIST test methods make the connection from the image to the TIC 

resulting in a relationship between the user and the TIC. 

3.5 Defining the Image Set

3.5.1 Restrictions 

An image matrix was methodically constructed to ensure that each image contained a 

combination of the primary and robustness factors and so that statistically it was possible 

to extract the interactions between the factors and determine the weighted effect of each 

factor on detection probability. The number of observations that could be completed in 

one day was deemed to be 1250 according to recommendations made by the staff at NVL 

that have experience conducting similar experiments that took a period of days. 1250 

observations per day minimized the fatigue and boredom, human factors that could 

influence test results. The total number of images or “observations” was restricted to 

5,000 so that the test could be completed in four day window (1250 observations per day 

* 4 days) to maximum the number of fire fighters and thus increasing the sample size for 

more valid statistical data. 

3.5.2 Pristine Image Set 

All combinations of the robustness factors were considered in a full factorial matrix to 

create a “pristine” image set that did not include image degradation from the primary 
83 

factors. From Table 3- 1, multiplying the number of levels for each robustness factor 

leads to 6 x 5 x 2 x 2 or 120 settings. In addition to a full factorial, one half of the images 

were “replicated”, for a total of 180 images. Replication for this experiment did not 

mean identical images but rather the replicated images had the same robustness settings. 

The 180 pristine images were created from the FLIR ThermaCam. The detailed image 

set is shown in Appendix A. 

3.5.3 Primary Factor Design Points 

A subset of an mk Factorial Grid was driven by a Taguchi L25 Orthogonal Design to 

create the combinations (design points) of primary factors. A total of approximately 27 

design points were possibly to satisfy the 5,000 image constraint (5000 total images / 180 

pristine images~ 27 design points). A 54

 grid design or five levels at each of the four 

primary factors consists of 625 design points. The Taguichi L25 Orthogonal subset of 

the grid consists of only 25 design points, meeting the 27 point restriction while retaining 

orthogonality. Orthogonality is important to ensure no correlation between any two 

factors and therefore each design point is independent providing different information 

improving the efficiency of the results (Sanchez 2007). 

The 25 design points are shown in Table 3- 3. 

 
84 

Table 3- 3 Design Points 

Factor Settings 

Design 

Point Contrast Brightness 

Spatial 

Resolution Noise 

1 0.4000 0.5015 0.0284 0.3333

2 0.4000 3.6339 0.0522 0.2000

3 0.4000 6.7696 0.0760 0.1429

4 0.4000 9.9021 0.0998 0.1111

5 0.4000 13.0346 0.1234 0.0909

6 0.9330 0.5015 0.0522 0.1429

7 0.9330 3.6339 0.0760 0.1111

8 0.9330 6.7696 0.0998 0.0909

9 0.9330 9.9021 0.1234 0.3333

10 0.9330 13.0346 0.0284 0.2000

11 1.4669 0.5015 0.0760 0.0909

12 1.4669 3.6339 0.0998 0.3333

13 1.4669 6.7696 0.1234 0.2000

14 1.4669 9.9021 0.0284 0.1429

15 1.4669 13.0346 0.0522 0.1111

16 1.9993 0.5015 0.0998 0.2000

17 1.9993 3.6339 0.1234 0.1429

18 1.9993 6.7696 0.0284 0.1111

19 1.9993 9.9021 0.0522 0.0909

20 1.9993 13.0346 0.0760 0.3333

21 2.5317 0.5015 0.1234 0.1111

22 2.5317 3.6339 0.0284 0.0909

23 2.5317 6.7696 0.0522 0.3333

24 2.5317 9.9021 0.0760 0.2000

25 2.5317 13.0346 0.0998 0.1429

A pilot study was conducted using NIST personnel to get an idea of the amount of image 

degradation in terms of the four primary factors was necessary to impact the hazard 

detection probability. The TIC display quality test methods in NFPA 1801 require the 

TIC to produce an image that would yield a detection probability of 95% [NFPA 1801]. 

Using the results of the pilot study, the 25 design points were chosen to fine tune the 

settings of the images to capture a high probability of hazard detection ranging between 
85 

50-95%. Using a focused range of image settings, more data could be collected within 

the range of interest. 

3.5.4 Calculations 

3.5.4.1 Contrast and Brightness 

Contrast is the standard deviation of the 640 x 480 2-D luminance array of the image 

captured with the FLIR Thermacam corresponding to the image as it would be seen on 

the monitors at NVL. 

[ ]

1 1

2

0 0

1

( , )

M N

y x

contrast c f x y B

NM

− −

= =

= = − ∑ ∑ 3-1 

where B is the brightness or mean luminance as 

1 1

0 0

1

( , )

M N

y x

brightness B f x y

NM

− −

= =

= = ∑ ∑ 3-2 

and N and M are 640 and 480 respectively. 

3.5.4.2 Spatial Resolution 

The spatial resolution of an imaging system over all spatial frequencies from 0 (DC or 

zero modulation) to the nyquist frequency (the highest spatial frequency that can encoded 

in a digital image) is defined by the MTF as described in Chapter 2 Section 

2.3.3 Spatial Resolution. The MTFA, a single number value to describe the spatial 

resolution of an imaging system is found by integrating the area under the MTF curve 

between the MTF and the NEM of the imaging system. 
86 

To generate an MTF or a known frequency response for the images used in this study, a 

low-pass Butterworth filter (a discrete approximation to the Gaussian filter) was applied 

to the 2-D Fourier Transforms of the pristine images. The Butterworth filter was chosen 

because it offered the ability to control the attenuation rate of the filter for increasing 

frequency components. In addition, the filter changes from the pass band to the 

attenuation band without producing ringing artifacts in the filter image as common in 

other filters such as the ideal lowpass filter. 

The Butterworth filter reduces the modulation depth at increasing spatial frequencies of 

each pristine image according to specified slope properties as described in 

Section2.4.2.2.1 Filtering Techniques. The design points for spatial resolution used for 

this study were dependent on the nominal cutoff frequency (Dc) of the low-pass 

Butterworth filter. For design points 1, 10, 14, 18 and 22 the nominal cutoff frequency 

was set to 0.02 

	
  . The constant C was set to 1 to adjust the magnitude of the 

filter at the nominal filter cutoff value to 50%. The integer n was set to 2. The 

magnitude of the Butterworth filter H(D) which when multiplied by the pristine image to 

create the MTF of the degraded image is shown in Equation 3-3. 

1

2 1

4

( ) 1 ( ) 1

0.02

n

c

D f H D C MTF f

D

− −

       

= + → = +                     3-3 

To calculate the MTFA, the NEM is also required. The NEM was calculated using the 

methods described in NFPA 1801 section 8.1.5 specifically for the FLIR camera used to 

capture the IR images in this study. The dimensionless value is 0.02861. The final step 
87 

is to define the bounds of the integration for the MTFA by calculating the intersection of 

the MTF and the line created by the NEM as described in Section 

2.3.3 Spatial Resolution. To find the intersection, both equations were set to be equal to 

each other and solved for the frequency. 

1

4

1 0.02861 0.048278

0.02

f cycles f

pixel

−

      + = → =        

 3-4 

The MTFA is then 

1

0.048278 4

0

1

0.048278 0.048278 4

0 0

( ) 1 0.02861

0.02

1 0.02861 0.0203

0.02

f

MTFA f

f cycles

pixel

−

−

   

= + − =          

      + − =        

∫

∫ ∫

 3-5 

The MTFA must then be converted from cycles/pixel to a universal unit of frequency, 

cycles/mrad because cycles/pixel is dependent on the imaging system’s detector array. 

The detector array typically does not fill the enter cell or pixel area. The ratio of the 

active detector element to the actual cell is known as the fill factor. A finite fill factor 

affects the resolution of the imaging system [Lloyd 1979]. If the frequency of target is 

high enough to fit between the active detector elements there will be no output from the 

imaging system. 

 

Although cycles/mrad is a universal frequency unit, the conversion factor from 

cycles/pixel to cycles/mrad is unique to a specific camera at a specific distance away 

from the target. To calculate the conversion factor for the FLIR camera used for this 
88 

study, a path length of one meter was used to position a blackbody of known dimensions 

from the lens of the TIC to yield a conversion factor of 

 1 0.7147 pixel mrad = 3-6 

 

One meter was chosen as the pathlength because it is the distance specified for the 

performance test methods in the NFPA 1801. 

The final value for the MTFA is 

0.0203 1 0.0284 0.7147

cycles pixel cycles

pixel mrad mrad ∗ = 3-7 

3.5.4.3 Noise and Nonuniformity 

To quantify the amount of noise added to the images used in this study the inverse of a 

signal to noise ratio otherwise called Nonuniformity was used. Nonuniformity is a 

classical measurement in optical systems and is defined in section 8.1.5.13 of NFPA 1801 

as 

noise Nonuniformity σ

μ

= 3-8 

The amount of noise added to each image was dependent on the mean pixel intensity to 

obtain a constant nonuniformity for each design point. 

TIC nonuniformity patterns can vary dramatically and no one type of nonuniformity is 

evident in all TIC. For a more complete discussion of nonuniformity measurements in 

TIC refer to work done by Amon et al [Amon 2008]. Due to limitation in the number of 
89 

images and factors that could be included in this study, all types of nonuniformity where 

not investigated. A Gaussian distributed noise was added to the pristine image to act as a 

general nonuniformity. 

A Gaussian distribution was chosen because it was the most common type of electronic 

noise present in cameras and sensors (Weeks 1996). It is often also used to model 

unknown additive noise sources from different parts of the image system. By the central 

limit theorem, the sum of a large number of independent noise sources approaches 

Gaussian distributed noise [Smith 2007]. 

3.6 Image Processing

Due to the interactions of the image degradation techniques used to manipulate each of 

the primary factors to create an image with specific values for contrast, brightness, spatial 

resolution and noise, the order of image processing was critical. Image processing is 

typically used to improve not degrade the quality of images. Techniques such as 

frequency filtering effect many image characteristics, specifically contrast and noise. 

While a low-pass filter such as the Butterworth was used in this study to reduce and 

remove the higher frequency components to blur the images and generate a frequency 

response (MTF) of the image, the filter also decreased the contrast and adjusted the noise 

of an image. 

Low pass filtering limits the span of graylevels used to create the image. Blurring 

reduces sharp edges and therefore the contrast [Russ 2002]. Sharp distinctions in 

graylevels between objects in an image correspond to a high contrast. As the image 
90 

becomes blurry due to a low pass filter, the span of graylevels used to create the objects 

in the images shrink, reducing contrast. 

To circumvent the interactions of contrast and filtering for this study an iterative 

approach was use to find a balance that would create an image that met the design points 

for both the contrast and spatial resolution as shown in Figure 3- 10. The contrast and 

brightness of the images were adjusted first to meet their design points. The low pass 

Butterworth filter was then applied to the image to adjust the MTF of the image. The 

contrast and brightness were then readjusted so that at the end of the process each 

primary factor met the desired design point. Up until this point in the image processing 

program, noise was not introduced into the image. 

The quantity of noise in the final images was assumed to only be a result of the additive 

Gaussian noise. Although all images have noise, the amount of noise present in the 

images before the application of noise was assumed to be negligible to the amount of 

desired Gaussian noise added. Noise is hard to quantify unless there are obvious spikes 

in the magnitude spectrum of the Fourier transform of the image that do not contribute to 

the quality of the image but random fluxuations in the image signal. 

To further justify this assumption, the application of the low-pass Butterworth filter 

removed the high frequency signal components. At higher spatial frequencies the 

magnitude of the frequency response is not due to the quality of the camera but the 

random pixel to pixel variations associated with noise [Russ 2002]. The Butterworth 
91 

filter eliminated the high frequencies in particular the frequencies above the intersection 

of the MTF and the NEM. Any frequency response of the image above the NEM is due 

to noise and not the quality of the image. For these reasons, noise was the last 

component added to the image set. A flow chart of the image processing is shown in 

Figure 3- 10. 
92 

Figure 3- 10 Flowchart of image processing 
93 

To implement the degradation process outlined in Figure 3- 10, Matlab R2006b Version 

7.3.0 was used to write a program to manipulate the pristine images to meet each of the 

25 design points. The complete custom made program can be found in Appendix B 

Image Processing Program. An example of how this program manipulated one of the 

images from the pristine image set to meet each of the 25 design points can be found in 

Appendix D. 

 
94 

Chapter 4: Modeling Human Perception 

4.1 Objective

Create a model to predict the probability of a fire fighter successfully completing a 

hazard recognition task with the aid of only an IR image. 

4.2 Test Subjects

A group of sixteen TIC users of varying age, fire fighting experience, TIC experience and 

skill level were used to capture data from a representative portion of the fire fighting 

community to help identify any bias in the test results that could link test subject 

performance with experience. A list of fire fighter backgrounds can be seen in Appendix 

C Test Subject Background. 

The test subjects were required to attend an informative session which included a Power 

Point presentation followed by a hazard training exercise on the NVL testing program. 

The Power Point presentation described the project goals as well as the types of scenes, 

thermal clutter, and hazards that would be seen in the images. Because of the diversity of 

the fire fighter’s training backgrounds, to avoid possible confusion, test subjects were 

given a training exercise that included pristine images similar to the types of scenes that 

would be seen in the actual study. The test subjects were required to select the hazard in 

each of the training images. Only test subjects who scored a 100% on the training 

exercise were allowed to proceed to the real study to ensure any wrong answers could be 

attributed to the image quality and not the definition of a hazard. The training program 
95 

also familiarized the test subjects on how to navigate through the images and select the 

hazards using NVL’s testing program. 

4.3 Experiment

The test was conducted in NVL’s ergonomically designed perception laboratory using 

their testing system as well their procedures to avoid any impact on a test subject’s 

performance that could not be attributed to the image quality. The experiment included 

4500 images split up into 25 sessions containing 180 images each. The images were 

presented in a strategic order by progressively improving the quality of the images to 

minimize the effect of learning during the tests. The ranking of design point order was 

chosen based on pilot study results. 

Time limitation was not a variable. Each image was presented on the screen for an 

unlimited amount of time until a selection was made. A five minute break was required 

between each of the sessions to avoid fatigue and boredom which could potentially 

influence their alertness and performance on the study. 

The test subjects were asked to view each of the images and located the hazard via a 

mouse click on the screen. A “No Hazard” selection box was also incorporated on the 

test screen for images without a hazard. The user’s mouse click location was compared 

to the actual hazard location. If the mouse click was within the coordinates of the hazard 

a correct answer was registered by NVL’s program. A ‘1’ indicated a correct answer and 

a ‘0’ represented incorrect. The program automatically consolidated each test subject’s 

test results in a comma delimited text file that included the test subject ID, the mouse 
96 

click coordinates on the screen, the result of the selection, and the time to make the 

decision. 

4. 4 Data

Several of the 16 user’s were unable to complete the entire test, therefore, rather than 

4,500 x 16 = 72,000 data points, only 54,540 points were recorded. These data points 

were binary; either a 1 for correct response or 0 for incorrect response. Each data point 

corresponded to a design point (1-25) for contrast, brightness, spatial resolution, and 

nonuniformity. The average probability of successfully identifying a fire hazard for each 

design points is summarized in Figure 4- 1. 

Figure 4- 1 Average response for design points 

 It is important to note that the design points were not ranked based on difficulty. 

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Design Point/Image Setting

0.0

0.2

0.4

0.6

0.8

1.0

Average Response
97 

4. 5 Logistic Regression Model

When the response variable is binary, the response function often follows the shape of a 

logistic regression function. This model is typically sigmoidal and monotonic having a 

stretched “S” (increasing) or reverse “S” (decreasing) shaped response with asymptotes at 

0 and 1 and takes on the following form (Agresti, 1990). 

exp( ' )

1 exp( ' )

X

p

X

β

β

∧

=

+

 4-1 

The probability of success is predicted based on X which can be any number of input 

parameters. X in this study corresponded to the primary factors to define image quality: 

contrast, brightness, spatial resolution, and nonuniformity. Several versions of the model 

were considered including the primary factors only, the primary factors plus two terms 

interactions, and primary factors plus all interactions. The primary factors are shown in 

Table 4- 1. 

Table 4- 1Primary Factors 

Variable Description

X1 Contrast

X2 Brightness

X3 Spatial Resolution

X4 Nonuniformity (noise)

Based on the diagnostics discussed later in this section, a modification to the primary 

factors plus two term interaction multiple logistic regression model was chosen. The 

coefficients of each parameter, β , are regression coefficients typically calculated using 

computer-intensive numerical search procedures. For a more detailed description of how 
98 

the coefficient values are produced refer to work done by Neter et al (Neter, Kutner, 

Nachtsheim, &Wasserman, 1996). The calculated regression coefficients are shown in 

Table 4- 2. 

Table 4- 2 Multiple logistic regression coefficients 

Coefficient Description Value Std. Error t-value

β0

Intercept -1.030 0.140 -7.346 

β1 Contrast 0.076 0.040 1.929 

β2 Brightness -0.172 0.008 -20.220 

β3 Spatial Resolution 0.991 0.343 2.893 

β4 Noise 44.510 2.238 19.885 

β5 Contrast-Brightness Interaction 0.169 0.005 36.195 

β6 Contrast-Noise Interaction -12.350 0.708 -17.449 

β7 Brightness-Spatial Resolution Interaction -0.216 0.027 -7.975 

β8 Brightness-Noise Interaction -1.597 0.108 -14.753 

β9 Spatial Resolution-Noise Interaction -16.935 3.947 -4.291 

Expanding Equation 4-1 to account for two term interactions 

1 2 3 4

1 2 1 4 2 3 2 4 3 4

1 2 3 4

1 2 1 4 2 3 2 4 3 4

exp( 1.030 0.076 0.172 0.991 44.510

0.169 12.350 0.216 1.597 16.935 )

1 exp( 1.030 0.076 0.172 0.991 44.510

0.169 12.350 0.216 1.597 16.935 )

X X X X

X X X X X X X X X X

p

X X X X

X X X X X X X X X X

∧

− + − + +

+ − − − −

=

+ − + − + +

+ − − − −

 4-2 

Given constant values for the primary factors X1, X2, X3, and X4, the probability of 

successfully identifying the target in the images is predicted by p

∧

. 

4.6 Cross Validation

A cross validation study was used to compare the performance of various versions of the 

logistic regression model. From the original dataset of 54,540 points, two thirds of the 

records from each image set was randomly selected to create the modeling dataset, and 
99 

the remaining one third of the records from each design point was used as a validation 

dataset. The process is displayed in Figure 4- 2. 

Figure 4- 2 Formation of modeling and validating datasets 

Using the modeling dataset, several model structures were considered including primary 

factors only, primary factors with two term interactions minus the contrast-spatial 

resolution, primary factors with all two term interactions, and primary factors with all 

interactions. Each model was used to get an estimate of the probability of successfully 

completing the recognition task of the validating dataset. The difference between the 

empirical value and the predicted values are calculated at each image setting. The 

process was repeated 100 times and the results are shown in Figure 4- 3 through Figure 4- 

6 and summarized in Figure 4- 7. 
100 

Figure 4- 3 Main effects only 

Figure 4- 4 Main effects + all two term interactions 

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0 5 10 15 20 25

Empirical Value - Predicted Value

Image Setting

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0 5 10 15 20 25

Empirical Value - Predicted Value

Image Setting
101 

Figure 4- 5 Main effects + all two term interactions - contrast/spatial resolution 

interaction 

Figure 4- 6 Main effects +all two term interactions

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0 5 10 15 20 25

Empirical Value - Predicted Value

Image Setting

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0 5 10 15 20 25

Empirical Value - Predicted Value

Image Setting
102 

Figure 4- 7 Average deviation from observed values 

The main effect plus 2 term interactions as well as subsequent models with additional 

parameters show significant improvement upon the main effect only model. The average 

greatest deviation over 100 trials from the observed data and the model incorporating 

main effects plus two term interactions was 11.3%. The data also shows that the main 

effect plus all interaction model had an average greatest deviation of 10.8%. Since the 

model with additional terms did not offer a substantial gain over models with less 

parameters, it was discarded. 

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0 5 10 15 20 25

Average ( Empirical Value - Predicted Value)

Image Setting

Main Effects Only

Main Effect + 2 term int

Main Effect + 2 term int - contrast/spatial res

Main Effect + all ints
103 

4.7 Model Deviance and Partial Deviance

When creating a logistical regression model, the model deviance and partial deviance can 

be informative tests in determining the number factors contributing to the model fit. The 

deviance of a fitted model determines the relationship of the fitted model to the model 

that fits all n observations perfectly, otherwise known as the saturated model (Neter, 

Kutner, Nachtsheim, & Wasserman, 1996). The partial deviance is the difference 

between the model deviances for two fitted models and is used to determine if a reduced 

fitted model is comparable to a larger model. When the partial deviance is small, the 

reduced parameter model provides a similar fit to that of the larger model (Neter, Kutner, 

Nachtsheim, & Wasserman, 1996). When the number of data points, n, is reasonably 

large, as in our case, the partial deviance follows approximately a chi-squared distribution 

with p-q degrees of freedom; where p is the number of parameters in the larger model, 

and q the number of parameters in the subset model. 

The first test is to determine if the any of the primary factors Xi

, do not contribute to the 

model fit; or in other words, do βq = βq+1 = ... = βp-1 = 0? A partial deviance test was 

conducted between the null model, a model that simply relies on a constant, to the 

expanded modeling incorporating the primary factors. 

The selected model, shown in Equation 4-2, incorporated all the primary factors plus two 

term interactions less contrast- spatial resolution interactions. 


,  , ... , 

 = 68,979.70
104 

Comparing this model deviance, in a partial deviance test, to that of the null model where 




 = 73,057.14, we can see a significant improvement to the model fit. 


 , ... , |

 = 73,057.14 − 68,979.70 = 4,077.44

With a chi-square critical value of %.&;

( = 16.92, we can strongly reject the null 

hypothesis that β1 = β2 = ... = β9 = 0. 

A further look at the partial deviance between the model with primary factors plus all two 

term interactions versus the subset model used in this study shows the additional contrastspatial resolution interaction term, corresponding to the coefficient β10 , does not provide 

additional improvement on the model fit. 


|,  , ... , 

 = 68,979.70 − 68,979.70 = 0

With a chi-square critical value of %.&;

( = 3.84, we can accept the null hypothesis that 

β10 =0. 

4.8 Informal Goodness of Fit Test

For a fitted multiple logistic regression model to be appropriate, the shape of the 

estimated response function must be monotonic and sigmoidal; key properties of a 

logistic response function. To perform an Informal Goodness of Fit Examination records 

with similar fitted values,π

∧

, are grouped into a number of classes (typically between 5 

and 10) with approximately the same number of n observations. Within each class, the 

estimated proportion of 1s, denoted by pj, is calculated for all n. These values are then 

plotted against the midpoint of the fitted values for each class. Table 4- 3 and Figure 4- 8 
105 

display the Informal Goodness of Fit data, using five classes, for the selected human 

perception model. 

Table 4- 3 Informal Goodness of Fit Test with 5 Classes 

Class j *+ Interval Midpoint nj pj

1 0.222 , 0.507 0.364 10912 0.409

2 0.507 , 0.562 0.534 10904 0.532

3 0.562 , 0.671 0.617 10908 0.612

4 0.671 , 0.724 0.698 10916 0.736

5 0.724 , 0.779 0.751 10900 0.749

Figure 4- 8 Diagnostic plot of estimated proportions with 5 classes 

Figure 4- 8 clearly indicates the model is monotonic, and sigmoidal in nature. Expanding 

the Informal Goodness of Fit Test to seven classes yields the following result shown in 

Table 4- 4 and Figure 4- 9. 

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0

p

Fitted Value
106 

Table 4- 4 Informal Goodness of Fit Test using 7 Classes 

Class j *+ Interval Midpoint nj pj

1 0.222 , 0.486 0.354 7798 0.380 

2 0.486 , 0.546 0.516 7790 0.522 

3 0.546 , 0.570 0.558 7792 0.536 

4 0.570 , 0.671 0.621 7796 0.593 

5 0.671 , 0.719 0.695 7784 0.735 

6 0.719 , 0.736 0.727 7792 0.738 

7 0.736 , 0.779 0.757 7788 0.750 

Figure 4- 9 Diagnostic plot of estimated proportions using 7 classes 

Again, Figure 4- 9 suggests that a monotonic, sigmoidal relationship is tenable. 

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.800

0.900

1.000

0.000 0.200 0.400 0.600 0.800 1.000

p

Fitted Values
107 

4.9 Chi-Square Goodness of Fit Test

The Informal Goodness of Fit Test can be extended into a formal Chi-Square Goodness 

of Fit Test provided the observations are independent and the sample size is large. This 

test provides the ability to detect large departures from the logistic response function. 

Similarly, to the Informal Goodness of Fit Test, the records are again divided into classes 

of approximately equal size with similar fitted values,π

∧

. The number of observed 

successes (1’s) and failures (0’s) are denoted by Oj1 and Oj0, respectively. If the logistic 

response function is appropriate, the expected number of successes within a class will be 

equal to the sum of the fitted values for that class; likewise, the number of failures will be 

equal to the sum of 1 − ,-. This leads to the Chi-Square Goodness of Fit Test statistic: 

( )

2

1

2

1 0

c

jk jk

i k jk

O E

E

χ

= =

−

= ∑ ∑ 4-3 

with decision rules: 

If 

( ≤ %(

1 − /;  − 2, conclude H0 , logistic response appropriate

If 

( > %(

1 − /;  − 2, conclude Ha , logistic response not appropriate 

The classes, observed and expected number of successes and failures for the calculation 

of the test statistic are displayed in Table 4- 5. 
108 

Table 4- 5 Goodness of Fit Test 

Class 

j

*+ Interval nj

Number of Failures Number of Successes

Observed

Oj0

Expected

12 − *+

Observed

Oj1

Expected

1*+

1 0.222 , 0.507 10912 6447 6426.54 4465 4485.46 

2 0.507 , 0.562 10904 5101 5004.68 5803 5899.32 

3 0.562 , 0.671 10908 4230 4098.98 6678 6809.02 

4 0.671 , 0.724 10916 2878 3139.85 8038 7776.16 

5 0.724 , 0.779 10900 2739 2724.96 8161 8175.04 

The test statistic for the selected human perception model is calculated as: 



( =

6447 − 6426.54

(

6426.54 +

4465 − 4485.46

(

4485.46 + ∙∙∙ +

2739 − 2724.96

(

2724.96

+

8161 − 8175.04

(

8175.04 = 41.04 

The critical value is found to be %.&;5

( = 7.81, thus the null hypothesis of the logistic 

response function being appropriate is rejected. The associated p-value with this test is 

6.40 x 10-9. 

4.10 Deviance Goodness of Fit Test

Given a large sample size, n, the model deviance, 
6,  , ... , 789, will follow 

approximately a chi-square distribution with n – p degrees of freedom if the logistic 

response function is correct. The decision rules for the deviance goodness of fit test are: 

If 
6,  , ... , 789 ≤ %(

1 − /; : − , conclude H0 , logistic response 

appropriate
109 

If 
6,  , ... , 789 > %(

1 − /; : − , conclude Ha , logistic response not 

appropriate 

The deviance of the selected human perception model is found to be: 


,  , ... , 

 = 68,979.7

With n = 54540 and p = 10, the critical value is found to be %.&;&;&5

( = 55,074.33, and 

thus the null hypothesis of the logistic response function being appropriate is rejected. 

4.11 Fitted Values and Confidence Intervals

Given the estimated parameters for the selected model, the estimated logistic response 

function can be expressed as: 

Using the logistic regression model found in Equation 4-2, p

∧

 is the estimate of the 

probability a user will successfully complete a recognition task given an image’s values 

of contrast (x1), brightness (x2), spatial resolution (x3), and nonuniformity (x4). As an 

example, consider an image with a contrast x1 = 0.40, brightness x2 = 0.50, spatial 

resolution x3 = 0.33, and nonuniformity x4 = 0.03. p

∧

is calculated as: 

 

exp( 1.03 0.076*0.4 0.172*0.5 0.991*0.33 44.51*0.03

0.169*0.4*0.5 12.35*0.4*0.3 0.216*0.5*0.33 1.597*0.5*0.03

16.935*0.3*0.03)

1 exp( 1.03 0.076*0.4 0.1720.5 0.991*0.33 44.51*0.03

0.169*0.4*0.5 12.3

p

∧

=

− + − + + +

− − −

−

+ − + − + + +

− 5*0.4*0.3 0.216*0.5*0.33 1.597*0.5*0.03

16.935*0.3*0.03)

0.545

− −

−

=
110 

With an estimated regression function there is uncertainty in the parameters. This 

uncertainty leads to uncertainty in the fitted value, p

∧

. One way to capture this 

uncertainty is in the form of a confidence interval about the fitted value. The lower, L, 

and upper, U, (1 – α)% confidence interval values for p

∧

 are found by: 

{ }

{ }

' ' 2

(1 /2)

' ' 2

(1 /2)

exp( )

1 exp( )

b X z X s b X

L

b X z X s b X

α

α

−

−

−

=

+ −

 4-4 

{ }

{ }

' ' 2

(1 /2)

' ' 2

(1 /2)

exp( )

1 exp( )

b X z X s b X

U

b X z X s b X

α

α

−

−

+

=

+ +

 4-5 

where b is the vector of regression coefficients provided in Table 4- 2; 

X is the vector of predictor variable terms, to include interactions terms: 

 {1, x1, x2, x3, x4, x1x2, x1x4, x2x3, x2x4, x3x4, }; 

z68=

(

 9

 is the inverse of the standard normal cumulative distribution at 61 −

α

2

 9%; 

 and @

A

BCD is the variance-covariance matrix for the regression parameters found 

to be: 

@

A

BCD =

0.020 -0.004 -0.001 -0.041 -0.280 0.000 0.082 0.001 0.011 0.370 

-0.004 0.002 0.000 0.008 0.051 0.000 -0.020 0.000 -0.001 -0.068 

-0.001 0.000 0.000 0.001 0.002 0.000 0.000 0.000 0.000 0.003 

-0.041 0.008 0.001 0.117 0.521 0.000 -0.135 -0.003 -0.018 -1.038 

-0.280 0.051 0.002 0.521 5.010 0.008 -1.472 0.000 -0.207 -6.288 

0.000 0.000 0.000 0.000 0.008 0.000 -0.002 0.000 0.000 -0.006 

0.082 -0.020 0.000 -0.135 -1.472 -0.002 0.501 0.001 0.058 1.510 

0.001 0.000 0.000 -0.003 0.000 0.000 0.001 0.001 0.000 -0.030 

0.011 -0.001 0.000 -0.018 -0.207 0.000 0.058 0.000 0.012 0.173 

0.370 -0.068 0.003 -1.038 -6.288 -0.006 1.510 -0.030 0.173 15.577 
111 

The variance-covariance matrix is calculated using statistical computer programs and will 

not be discussed further here. Please refer to work by Neter et al (Neter, Kutner, 

Nachtsheim, &Wasserman, 1996). 

For the considered example of contrast x1 = 0.40, brightness x2 = 0.50, spatial resolution 

x3 = 0.33, and nonuniformity x4 = 0.03, the lower and upper 95% confidence bounds for 

p

∧

= 0.545 can be calculated as: 

C

EF = 

G

H

H

H

H

H

H

H

H

I

−1.03

0.076

−0.172

0.991

44.510

0.169

−12.350

−0.216

−1.597

−16.935J

K

K

K

K

K

K

K

K

L

E

G

H

H

H

H

H

H

H

H

I

1

0.40

0.50

0.33

0.03

0.20

0.01

0.17

0.01

0.01J

K

K

K

K

K

K

K

K

L

= 0.1835; F

E

@

A

BCDF =

G

H

H

H

H

H

H

H

H

I

1

0.40

0.50

0.33

0.03

0.20

0.01

0.17

0.01

0.01J

K

K

K

K

K

K

K

K

L

E

@

A

BCD

G

H

H

H

H

H

H

H

H

I

1

0.40

0.50

0.33

0.03

0.20

0.01

0.17

0.01

0.01J

K

K

K

K

K

K

K

K

L

= 0.0015;

z68.&

(

 9 = z.M& = 1.96;

Hence: 

N =

exp60.1835 − 1.96√0.00159

1 + exp60.1835 − 1.96√0.00159

= 0.526 and 

V =

exp60.1835 + 1.96√0.00159

1 + exp60.1835 + 1.96√0.00159

= 0.565
112 

Chapter 5: Summary and Conclusions 

5.1 Summary of Model Fit

The chosen model function to estimate the probability of successfully identifying the 

target utilizes the main effects (contrast, brightness, spatial resolution, and noise) plus 

two term interactions less the spatial resolution/contrast interaction term. Through a 

cross validation study, this model’s prediction never deviated more than approximately 

11% from the observed data. A more complex model, utilizing all interaction terms, only 

improved the model fit by less than 1%. 

Of all the models compared in this study, the selected model was chosen because it was 

the simplest form (least amount of terms) while offering the most accurate results. The 

selected function showed significant improvement over a constant model as indicated by 

the partial deviance test. In addition, the Informal Goodness of Fit test suggests that the 

response function follows a sigmoidal and monotonic shape, key indicators of the validity 

of using a logistic response function to model binary response data. Although further 

diagnostic testing, using the Chi-Squared Goodness of Fit Test and the Deviance 

Goodness of Fit test, debunk the use of a logistic response function to characterize the 

data, there is no one statistical test that offers concrete evidence. With the use of 

confidence intervals, the uncertainty in the model can be characterized and therefore the 

failed goodness of fit tests should not be justification to eliminate the model. 

5.2 Recommendation for Model Use in NFPA 1801

One of the most important findings of this study was that the interactions between 

contrast, spatial resolution, brightness, and noise in an image have a greater effect on 
113 

human perception than any one variable by itself. When considering test methods to 

adequately characterize the ability of a TIC to produce a quality image, interactions must 

be accounted for. 

The predictions made by the fitted model will be more conservative when using the 

lowest primary factors measurements in the NIST test methods. As discussed in 1.3.2 

Bench-Scale Test Methods Developed by NIST, contrast, brightness, spatial resolution, 

and nonuniformity (noise) are calculated from many images captured, from thermal 

targets over a range of temperatures, and the measurements will vary. Since the test 

methods are designed to investigate temperatures indicative of actual scenarios, the TIC 

must be required to provide adequate image quality over the entire range. The method by 

which the model should be used is outlined below. For additional details on these 

procedures refer to the draft of NFPA 1801 [NFPA 1801 2008]. 

1. Perform Image Recognition Test (spatial resolution). Calculate the contrast and 

CTF at each numbered step (predetermined bar frequency), from lowest to highest 

step number, on the spatial resolution target shown in Figure 1- 2. Also, calculate 

the average brightness of the pixels used in the contrast calculation. 

a. The contrast calculated at step 2 is X1 and is held constant. 

b. The brightness calculated at step 2 is X2 and is held constant. 

c. Convert the CTF measurement, using the bar frequency at each step, to the 

MTF as defined by the procedures outlined in this work in Table 3- 2. The 

result is the spatial resolution, X3 and will vary in value from step to step. 
114 

2. The nonuniformity test is independent. It is calculated over a temperature range 

from 0 to 260C. The maximum nonuniformity at any of the set point 

temperatures is deemed the nonuniformity of the imaging system as a 

conservative estimate for X4 in the model. This value is held constant. 

3. For the above data collected at each numbered step on the Image Recognition 

Test target, plug in the values for contrast (X1), brightness (X2), spatial resolution 

(X3), and noise (X4). 

a. Use the model to calculate p

∧

 at each numbered step. 

4. Note that the Nonuniformity Test in step 2 need be conducted only one time. The 

noise value (X4), can be used in all further image quality testing. 

These procedures, as outlined in the draft form of NFPA 1801, are conducted over a 

range of temperatures. NIST and the NFPA technical committee will have to make a 

decision as to what value for p

∧

 indicates acceptable performance by a TIC. 

5.3 Future Work

This study was the first attempt at trying to model the relationship between TIC image 

quality and fire fighter task performance and therefore there is an extensive list of future 

possibilities to further improve the model. One suggestion would be to create a more 

diverse set of images expanding further into the TIC applications such as images 

incorporating flames, water mist, steam, and smoke. Expanding from still images, three 

dimensional images of a scene could provide a user interactive test offering the ability of 

the test subjects to scan a 3-D image. Incorporating dynamic motion videos, could 

further the realism of the imagery set. 
115 

The statistical analysis of the dataset could also be expanded. The logistic regression 

model used to fit the data found in the perception experiment is a class of generalized 

linear models. This approach transforms the response by use of a link function, which 

relates the linear combination of the predictor variables to the mean response. One may 

consider an approach using a generalized additive model. The generalized additive 

model also considers a link function, but rather than a linear combination of the predictor 

values, it considers a linear combination of functions of the predictor values. 

Although the user and robustness factors were not considered in the creation of this 

model, as they cannot be controlled in real-world scenarios, their impact and the 

improvement they may bring to the model could be investigated. Such an investigation 

may lead to insights and improvements in system use and training. 
116 

Appendices 

Appendix A

Robustness Factors - (Levels) 

Pristine 

ID 

Target Position 

(6) 

Hazard 

Type (5) Clutter (2) Scene (2) 

1 Center (C) 1 Small Office 

2 Upper Left (UL) 1 Small Office 

3 Upper Right (UR) 1 Small Office 

4 Lower Left (LL) 1 Small Office 

5 Lower Right (LR) 1 Small Office 

6 No Target (N) 1 Small Office 

7 Center (C) 2 Small Office 

8 Upper Left (UL) 2 Small Office 

9 Upper Right (UR) 2 Small Office 

10 Lower Left (LL) 2 Small Office 

11 Lower Right (LR) 2 Small Office 

12 No Target (N) 2 Small Office 

13 Center (C) 3 Small Office 

14 Upper Left (UL) 3 Small Office 

15 Upper Right (UR) 3 Small Office 

16 Lower Left (LL) 3 Small Office 

17 Lower Right (LR) 3 Small Office 

18 No Target (N) 3 Small Office 

19 Center (C) 4 Small Office 

20 Upper Left (UL) 4 Small Office 

21 Upper Right (UR) 4 Small Office 

22 Lower Left (LL) 4 Small Office 

23 Lower Right (LR) 4 Small Office 

24 No Target (N) 4 Small Office 

25 Center (C) 5 Small Office 

26 Upper Left (UL) 5 Small Office 

27 Upper Right (UR) 5 Small Office 

28 Lower Left (LL) 5 Small Office 

29 Lower Right (LR) 5 Small Office 

30 No Target (N) 5 Small Office 

31 Center (C) 1 Large Office 

32 Upper Left (UL) 1 Large Office 

33 Upper Right (UR) 1 Large Office 

34 Lower Left (LL) 1 Large Office 

35 Lower Right (LR) 1 Large Office 

36 No Target (N) 1 Large Office 

37 Center (C) 2 Large Office 
117 

38 Upper Left (UL) 2 Large Office 

39 Upper Right (UR) 2 Large Office 

40 Lower Left (LL) 2 Large Office 

41 Lower Right (LR) 2 Large Office 

42 No Target (N) 2 Large Office 

43 Center (C) 3 Large Office 

44 Upper Left (UL) 3 Large Office 

45 Upper Right (UR) 3 Large Office 

46 Lower Left (LL) 3 Large Office 

47 Lower Right (LR) 3 Large Office 

48 No Target (N) 3 Large Office 

49 Center (C) 4 Large Office 

50 Upper Left (UL) 4 Large Office 

51 Upper Right (UR) 4 Large Office 

52 Lower Left (LL) 4 Large Office 

53 Lower Right (LR) 4 Large Office 

54 No Target (N) 4 Large Office 

55 Center (C) 5 Large Office 

56 Upper Left (UL) 5 Large Office 

57 Upper Right (UR) 5 Large Office 

58 Lower Left (LL) 5 Large Office 

59 Lower Right (LR) 5 Large Office 

60 No Target (N) 5 Large Office 

61 Center (C) 1 Small Living 

62 Upper Left (UL) 1 Small Living 

63 Upper Right (UR) 1 Small Living 

64 Lower Left (LL) 1 Small Living 

65 Lower Right (LR) 1 Small Living 

66 No Target (N) 1 Small Living 

67 Center (C) 2 Small Living 

68 Upper Left (UL) 2 Small Living 

69 Upper Right (UR) 2 Small Living 

70 Lower Left (LL) 2 Small Living 

71 Lower Right (LR) 2 Small Living 

72 No Target (N) 2 Small Living 

73 Center (C) 3 Small Living 

74 Upper Left (UL) 3 Small Living 

75 Upper Right (UR) 3 Small Living 

76 Lower Left (LL) 3 Small Living 

77 Lower Right (LR) 3 Small Living 

78 No Target (N) 3 Small Living 

79 Center (C) 4 Small Living 

80 Upper Left (UL) 4 Small Living 

81 Upper Right (UR) 4 Small Living 

82 Lower Left (LL) 4 Small Living 

83 Lower Right (LR) 4 Small Living 
118 

84 No Target (N) 4 Small Living 

85 Center (C) 5 Small Living 

86 Upper Left (UL) 5 Small Living 

87 Upper Right (UR) 5 Small Living 

88 Lower Left (LL) 5 Small Living 

89 Lower Right (LR) 5 Small Living 

90 No Target (N) 5 Small Living 

91 Center (C) 1 Large Living 

92 Upper Left (UL) 1 Large Living 

93 Upper Right (UR) 1 Large Living 

94 Lower Left (LL) 1 Large Living 

95 Lower Right (LR) 1 Large Living 

96 No Target (N) 1 Large Living 

97 Center (C) 2 Large Living 

98 Upper Left (UL) 2 Large Living 

99 Upper Right (UR) 2 Large Living 

100 Lower Left (LL) 2 Large Living 

101 Lower Right (LR) 2 Large Living 

102 No Target (N) 2 Large Living 

103 Center (C) 3 Large Living 

104 Upper Left (UL) 3 Large Living 

105 Upper Right (UR) 3 Large Living 

106 Lower Left (LL) 3 Large Living 

107 Lower Right (LR) 3 Large Living 

108 No Target (N) 3 Large Living 

109 Center (C) 4 Large Living 

110 Upper Left (UL) 4 Large Living 

111 Upper Right (UR) 4 Large Living 

112 Lower Left (LL) 4 Large Living 

113 Lower Right (LR) 4 Large Living 

114 No Target (N) 4 Large Living 

115 Center (C) 5 Large Living 

116 Upper Left (UL) 5 Large Living 

117 Upper Right (UR) 5 Large Living 

118 Lower Left (LL) 5 Large Living 

119 Lower Right (LR) 5 Large Living 

120 No Target (N) 5 Large Living 

121 Upper Left (UL) 1 Small Office 

122 Upper Right (UR) 1 Small Office 

123 Lower Right (LR) 1 Small Office 

124 Center (C) 2 Small Office 

125 Upper Left (UL) 2 Small Office 

126 Lower Left (LL) 2 Small Office 

127 Center (C) 3 Small Office 

128 Lower Right (LR) 3 Small Office 

129 No Target (N) 3 Small Office 
119 

130 Center (C) 4 Small Office 

131 Lower Left (LL) 4 Small Office 

132 No Target (N) 4 Small Office 

133 Upper Left (UL) 5 Small Office 

134 Upper Right (UR) 5 Small Office 

135 Lower Right (LR) 5 Small Office 

136 Center (C) 1 Large Office 

137 Lower Left (LL) 1 Large Office 

138 No Target (N) 1 Large Office 

139 Upper Right (UR) 2 Large Office 

140 Lower Right (LR) 2 Large Office 

141 No Target (N) 2 Large Office 

142 Upper Left (UL) 3 Large Office 

143 Upper Right (UR) 3 Large Office 

144 Lower Left (LL) 3 Large Office 

145 Upper Left (UL) 4 Large Office 

146 Upper Right (UR) 4 Large Office 

147 Lower Right (LR) 4 Large Office 

148 Center (C) 5 Large Office 

149 Lower Left (LL) 5 Large Office 

150 No Target (N) 5 Large Office 

151 Center (C) 1 Small Living 

152 Lower Left (LL) 1 Small Living 

153 No Target (N) 1 Small Living 

154 Upper Right (UR) 2 Small Living 

155 Lower Right (LR) 2 Small Living 

156 No Target (N) 2 Small Living 

157 Upper Left (UL) 3 Small Living 

158 Upper Right (UR) 3 Small Living 

159 Lower Left (LL) 3 Small Living 

160 Upper Left (UL) 4 Small Living 

161 Upper Right (UR) 4 Small Living 

162 Lower Right (LR) 4 Small Living 

163 Center (C) 5 Small Living 

164 Lower Left (LL) 5 Small Living 

165 No Target (N) 5 Small Living 

166 Upper Left (UL) 1 Large Living 

167 Upper Right (UR) 1 Large Living 

168 Lower Right (LR) 1 Large Living 

169 Center (C) 2 Large Living 

170 Upper Left (UL) 2 Large Living 

171 Lower Left (LL) 2 Large Living 

172 Center (C) 3 Large Living 

173 Lower Right (LR) 3 Large Living 

174 No Target (N) 3 Large Living 

175 Center (C) 4 Large Living 
120 

176 Lower Left (LL) 4 Large Living 

177 No Target (N) 4 Large Living 

178 Upper Left (UL) 5 Large Living 

179 Upper Right (UR) 5 Large Living 

180 Lower Right (LR) 5 Large Living 

 
121 

Appendix B Image Processing Program

Main Programs 

%This program converts the temperature output (.mat) file from the 

%FLIR ThermaCam P640 to a 16-bit uncompressed image

close all

clear all

%Input a .mat file into Matlab

im=input('What file would you like to load?\n');

im1=strcat(im,'.mat');

load(im1);

im2=input('What image you want to convert?No file extension\n');

%Find image size

[ymax xmax]=size(im2);

%Find minimum and maximum temperature in file

minimum=min(im2);

minval=min(minimum);

maximum=max(im2);

maxval=max(maximum);

%Enter temperature range that produces best quality image

temp1=input('What is the minimum temp\n');

temp2=input('What is the max temp\n');

image1=zeros(ymax, xmax);

%Normalize temperature data

for i=1:xmax

 for j=1:ymax

 image1(j,i)=(im2(j,i)-minval)/(maxval-minval);

 end

end

image2=zeros(ymax,xmax);

%Create a 16-bit grayscale with temperature data

for q=1:i

 for r=1:j

 image2(r,q)=image1(r,q)*65535;

 end

end

%Solve for variables needed to adjust image to correct grayscale

p=((temp1+273.15)-minval)/(maxval-minval);

xkcd=0;

if p<0

 p=0;

 xkcd=(minval-(273.15+temp1))/(temp2-temp1);

end
122 

z=((temp2+273.15)-minval)/(maxval-minval);

%Create 16 bit image from temperature data

image3=uint16(image2);

%Adjust image to match desired gray-scale

image4=imadjust(image3,[p,z],[xkcd,1]);

%Verify image is appropriate

imshow(image4)

%Create filename

filename = strcat(im,'.png');

%Save image as 16-bit uncompressed .png file

imwrite(image4,filename,'png','BitDepth',16)

%------------------------------------------------------------------- 

%ImagePro is an image processing program to adjust the contrast,

%brightness, spatial resolution, and noise of an image to meet the 

% 25 design points

clear all

close all

fprintf('Beginning LumImageProLoop')

%Image Counter

ii=1;

%Design Point Counter

iii=1;

%Allocate memory

conarray=zeros(4500,1);

brightarray=zeros(4500,1);

spatialarray=zeros(4500,1);

noisearray=zeros(4500,1);

%Start outerloop to loop through 180 pristine images (image filenames 

are

%numerical labeled from 1 to 180)

while ii<=180

%Input Image 

name=num2str(ii);

name1=strcat('image',name,'.png');

im = imread(name1);

%Convert the image to an array of numbers to manipulate

im2=double(im);

%Find the size of the array

[M N]=size(im2);

%Create an array of luminance data to describe the image as it will 

appear
123 

%on the test monitors at NVL

lumimage=zeros(M,N);

for j=1:M

 for k=1:N

 if im2(j,k)>8192

 lumimage(j,k)=((1*10^-8)*((im2(j,k))^2))-

(0.0002*(im2(j,k)))+1.6159;

 elseif im2(j,k)<=8192

 lumimage(j,k) = (3*(10^(-05)))*im2(j,k)+0.0266;

 else

 fprintf('ERROR\n')

 end

 end

end

%Find the brightness of the original image in pixel intensity

bright = round(mean(mean(im2)));

%Find the corresponding luminance on NVL displays

lumbright=round(mean(mean(lumimage)));

%Find the contrast of the original image in pixel intensity

values=zeros(M,N);

for j=1:M

 for k=1:N

 values(j,k)=((im2(j,k)-bright)^2); 

 end

end

contrast=sqrt(mean(mean(values)));

%Find the corresponding contrast on NVL display 

lumvalues=zeros(M,N);

for j=1:M

 for k=1:N

 lumvalues(j,k)=((lumimage(j,k)-lumbright)^2);

 end

end

lumcontrast=sqrt(mean(mean(lumvalues)));

%Loop through all 25 design points

counter=1;

while counter<=25 

%Input design point parameters

if counter==1

 stdcon=900;

 lumstdcon=0.4;

 newbright=12800;

 lumnewbright=0.5015;

 Wn=0.02;

 SNR=15.0;

 LumSNR=3.0;

 

elseif counter==2

 stdcon=900;

 lumstdcon=0.4;

 newbright=27200;

 lumnewbright=3.6339;
124 

 Wn=0.0366;

 SNR=20.0;

 LumSNR=5.0;

 

elseif counter==3

 stdcon=900;

 lumstdcon=0.4;

 newbright=33600;

 lumnewbright=6.7696;

 Wn=0.0533;

 SNR=25.0;

 LumSNR=7.0;

elseif counter ==4

 stdcon=900;

 lumstdcon=0.4;

 newbright=40000;

 lumnewbright=9.9021;

 Wn=0.07;

 SNR=30.0;

 LumSNR=9.0;

elseif counter ==5

 stdcon=900;

 lumstdcon=0.4;

 newbright=43200;

 lumnewbright=13.0346;

 Wn=0.0866;

 SNR=35.0;

 LumSNR=11.0;

elseif counter ==6

 stdcon=1500;

 lumstdcon=0.933;

 newbright=12800;

 lumnewbright=0.5015;

 Wn=0.0366;

 SNR=25.0;

 LumSNR=7.0;

elseif counter ==7

 stdcon=1500;

 lumstdcon=0.933;

 newbright=27200;

 lumnewbright=3.6339;

 Wn=0.0533;

 SNR=30.0;

 LumSNR=9.0;

elseif counter ==8

 stdcon=1500;

 lumstdcon=0.933;

 newbright=33600;

 lumnewbright=6.7696;

 Wn=0.07;

 SNR=35.0;

 LumSNR=11.0;

elseif counter ==9

 stdcon=1500;

 lumstdcon=0.933;

 newbright=40000;

 lumnewbright=9.9021;
125 

 Wn=0.0866;

 SNR=15.0;

 LumSNR=3.0;

elseif counter ==10

 stdcon=1500;

 lumstdcon=0.933;

 newbright=43200;

 lumnewbright=13.0346;

 Wn=0.02;

 SNR=20.0;

 LumSNR=5.0;

elseif counter ==11

 stdcon=2000;

 lumstdcon=1.4669;

 newbright=12800;

 lumnewbright=0.5015;

 Wn=0.0533;

 SNR=35.0;

 LumSNR=11.0;

elseif counter ==12

 stdcon=2000;

 lumstdcon=1.4669;

 newbright=27200;

 lumnewbright=3.6339;

 Wn=0.07;

 SNR=15.0;

 LumSNR=3.0;

elseif counter ==13

 stdcon=2000;

 lumstdcon=1.4669;

 newbright=33600;

 lumnewbright=6.7696;

 Wn=0.0866;

 SNR=20.0;

 LumSNR=5.0;

elseif counter ==14

 stdcon=2000;

 lumstdcon=1.4669;

 newbright=40000;

 lumnewbright=9.9021;

 Wn=0.02;

 SNR=25.0;

 LumSNR=7.0;

elseif counter ==15

 stdcon=2000;

 lumstdcon=1.4669;

 newbright=43200;

 lumnewbright=13.0346;

 Wn=0.0366;

 SNR=30.0;

 LumSNR=9.0;

elseif counter ==16

 stdcon=2500;

 lumstdcon=1.9993;

 newbright=12800;

 lumnewbright=0.5015;

 Wn=0.07;
126 

 SNR=20.0;

 LumSNR=5.0;

elseif counter ==17

 stdcon=2500;

 lumstdcon=1.9993;

 newbright=27200;

 lumnewbright=3.6339;

 Wn=0.0866;

 SNR=25.0;

 LumSNR=7.0;

elseif counter ==18

 stdcon=2500;

 lumstdcon=1.9993;

 newbright=33600;

 lumnewbright=6.7696;

 Wn=0.02;

 SNR=30.0;

 LumSNR=9.0;

elseif counter ==19

 stdcon=2500;

 lumstdcon=1.9993;

 newbright=40000;

 lumnewbright=9.9021;

 Wn=0.0366;

 SNR=35.0;

 LumSNR=11.0;

elseif counter ==20

 stdcon=2500;

 lumstdcon=1.9993;

 newbright=43200;

 lumnewbright=13.0346;

 Wn=0.0533;

 SNR=15.0;

 LumSNR=3.0;

elseif counter ==21

 stdcon=3000;

 lumstdcon=2.5317;

 newbright=12800;

 lumnewbright=0.5015;

 Wn=0.0866;

 SNR=30.0;

 LumSNR=9.0;

elseif counter ==22

 stdcon=3000;

 lumstdcon=2.5317;

 newbright=27200;

 lumnewbright=3.6339;

 Wn=0.02;

 SNR=35.0;

 LumSNR=11.0;

elseif counter ==23

 stdcon=3000;

 lumstdcon=2.5317;

 newbright=33600;

 lumnewbright=6.7696;

 Wn=0.0366;

 SNR=15.0;
127 

 LumSNR=3.0;

elseif counter ==24

 stdcon=3000;

 lumstdcon=2.5317;

 newbright=40000;

 lumnewbright=9.9021;

 Wn=0.0533;

 SNR=20.0;

 LumSNR=5.0;

elseif counter ==25

 stdcon=3000;

 lumstdcon=2.5317;

 newbright=43200;

 lumnewbright=13.0346;

 Wn=0.07; 

 SNR=25.0;

 LumSNR=7.0;

end

%Finding an initial guess for slope of linear point processing for 

contrast

slope=stdcon/contrast;

%Finding the y-intercept d as initial guess for the amount of increase 

in 

%brightness

d=newbright-bright;

%Wn is the nominal cutoff frequency used in a butterworth filter 

Wn = Wn*sqrt(M.^2+N.^2);

%n defines the order of the butterworth equation of the slope of the 

filter

n=2; 

countername=num2str(counter);

%fminsearch varies the values for the slope and d so that after the 

spatial

%resolution test all three parameters of the degraded image are as 

desired

slopei = slope;

%Initial guess for point processing of contrast and brightness

X0 = [slopei,d];

options=optimset('TolX',1e+00,'Tolfun',1e+00);

X = fminsearch(@Lumsearchfile, X0, options, im2, newbright, Wn, n, 

contrast, bright,stdcon,lumbright,lumcontrast,lumstdcon,lumnewbright);

%Final slope and intercept values for contrast and brightness

slope=X(1);

d=X(2);

%......................................................................

...
128 

%ConBrighta manipulates contrast/brightness 

[contrastimage]= LumConbrighta(im2,slope,d,bright);

%Spatialresa adjusts the spatial resolution of the image using a 

butterworth

%filter in the frequency domain.

[freqimage,Fplot,Gplot,newbright3,SR,contrastf, lumnewbright3, 

lumcontrastf, Dmax]=LumSpatialresa(contrastimage,im2,Wn,n);

%fprintf('Your adjusted image has the following parameters\n')

%fprintf('Your new contrast is %g\n',2*lumcontrastf/32.562)

%fprintf('Your new brightness is %g\n',lumnewbright3/32.562)

%fprintf('Your spatial resolution is %g\n', SR)

%Getting the desired nonuniformity by adding noise

%Find the amount of noise necessary to create the desired nonuniformity

%Based on brightness

DevVar1=newbright3/SNR;

LumDevVar1=lumnewbright3/LumSNR;

%First guess

Vari = 0.01;

X0 = [Vari];

options=optimset('Tolfun',1e-06,'TolX',1e-06);

X = fminbnd(@LumNoisesearch,0,0.1,options, 

freqimage,DevVar1,LumDevVar1);

%Var is the final variance needed to reach the desired nonuniformity

Var=X(1);

[noiseimage,lumDevNoise,lumnoisy]=LumNoise(freqimage,Var);

%Final Nonuniformity

LumSNR1=lumnewbright3/lumDevNoise;

% fprintf('You deviation of noise is %g\n',DevNoise)

%Minor adjustment to get image back to 640x 480

%Add one more col and row

noiseimage1=double(noiseimage);

[q,p]=size(noiseimage1);

toprow = noiseimage1(1,:);

finalimage1 = [toprow;noiseimage1];

[q,p]=size(finalimage1);

lastcol = finalimage1(:,p);

finalimage = [finalimage1, lastcol];

%Put numbers back into 16-bit image

finalimage=uint16(finalimage);
129 

%Variable Output Names

Wn1=num2str(Wn/sqrt(M.^2+N.^2));

n1=num2str(n);

Lumnewbright31=num2str(lumnewbright3);

SR1=num2str(SR);

LumDevNoise1=num2str(lumDevNoise);

Lumcontrastf1=num2str(lumcontrastf);

finalimage(:,:,2) = finalimage(:,:);

finalimage(:,:,3) = finalimage(:,:,1);

%Write the file as a .tif 16-bit gray scale image with NO Compression

 imwrite(finalimage,finalname,'tif','Compression','none')

 conarray(iii,1)=(2*lumcontrastf)/32.562;

 brightarray(iii,1)=lumnewbright3/32.562;

 spatialarray(iii,1)=SR;

 noisearray(iii,1)=LumSNR1;

 iii=iii+1;

 counter=counter+1;

end

ii=ii+1;

fprintf('Image %g\n',ii)

end

%------------------------------------------------------------------- 

%Find slope and intercept values needed to adjust contrast and 

brightness

%to desired levels

function Y = Lumsearchfile(X, im2,newbright, Wn, n, contrast, bright, 

stdcon, lumbright, lumcontrast, lumstdcon, lumnewbright)

slope = X(1);

d = X(2);

%Manipulates contrast/brightness 

[contrastimage]= LumConbrighta(im2,slope,d,bright);

%Adjusts the spatial resolution of the image using a butterworth 

filter.

[freqimage,Fplot,Gplot,newbright3,SR,contrastf, lumnewbright3, 

lumcontrastf, Dmax]=LumSpatialresa(contrastimage,im2,Wn,n);

%Calculate error and minimize with fminsearch

Y = (lumcontrastf-lumstdcon)^2 + (lumnewbright - lumnewbright3)^2;
130 

end

%------------------------------------------------------------------- 

%Use linear point processing to adjust contrast and brightness

function [contrastimage]= LumConbrighta(im2,slope,d,bright)

%Adjust contrast and brightness and output image

[M N]=size(im2);

im3=zeros(M,N);

for j=1:M

 for k=1:N

 im3(j,k)=(slope*(im2(j,k)-bright))+(bright+d); 

 end

end

%Convert contrast/brightness adjusted pixels back into an image

contrastimage=uint16(im3);

%------------------------------------------------------------------- 

%Butterworth filter is multiplied by the forward Fourier Transform of 

image

function [freqimage,Fplot,Gplot,newbright3,SR,contrastf, lumnewbright3, 

lumcontrastf, Dmax]=LumSpatialresa(contrastimage,im2,Wn,n)

%Convert image to grayscale numbers

im5 = double(contrastimage);

%Find size of image

[M1,N1] = size(im5);

%Subtrast 1 row and 1 column to create 2-d array with odd dimensions

Mlogic = ceil(M1/2);

Nlogic = ceil(N1/2);

if Mlogic==M1/2

 im5 = im5(1:M1-1,:);

end

if Nlogic==N1/2

 im5 = im5(:,1:N1-1);

end

%Find size of new image

[M,N] = size(im5);

%Take 2-D fourier transform of the image

F = fft2(im5); 

% Rearrange the quadrants so zero frequency is located at the center

% Need for plotting magnitude spectrum and applying filter

F1=fftshift(F);

%Plot magnitude spectrum of frequencies

Fplot = uint16(F1);

%Create a array of numbers for mapping 2-d space for applying filter
131 

u = 0:(M-1); % Create a vector u from zero to M-1

v = 0:(N-1); % Create a vector v from zero to N-1

%The fourier transform is symmetrical about the nyquist frequency, or 

M/2

%the second half is often considered to be the response of negative

%frequencies, thus the following steps create these negative values

idx=find(u>M/2); % Create a vector that is the index(position) of the 

second half of the vector u

u(idx)=u(idx)-(M-1); % Replace the second half of u with negative 

values 

idy=find(v>N/2); % create a vector that is the index of the second half 

of the vector v

v(idy)=v(idy)-(N-1); % Replace the second half of v with negative 

values

% Create a 2-D map of all possible combinations of u and v.

%This map of numbers will be used to identify the distance from the 

zero

%frequency to apply filter

[V,U]=meshgrid(v,u); 

% Solve for D which is essentially the radius of a point in the fourier

% transform

D=sqrt(U.^2+V.^2); 

Dmax=max(max(D));

%Create filter

H = 1./(1+(D./Wn).^(2*n)); 

%Apply filter by multiplying by fourier transform of image

G = H.*F;

%Calculate the MTFA of the butterworth filter

SR = quad(@(x)Lumfiltercurve(x,Wn,n),0,Dmax)./(2*Dmax);

%Find inverse fourier transform of image

image=real(ifft2(double(G)));

%convert the filtered fourier back into an image

freqimage=uint16(image); 

%Plot magnitude spectrum of filtered image

G1=fftshift(G);

Gplot=uint16(G1);

newfreq=double(freqimage);

%Create Luminance array to recalculate contrast and brightness

lumnewfreq=zeros(M,N);

 

for j=1:M

 for k=1:N
132 

 if newfreq(j,k)>8192

 lumnewfreq(j,k)=((1*10^-8)*((newfreq(j,k))^2))-

(0.0002*(newfreq(j,k)))+1.6159;

 elseif newfreq(j,k)<=8192

 lumnewfreq(j,k) = (3*(10^(-05)))*newfreq(j,k)+0.0266;

 else

 fprintf('ERROR\n')

 end

 end

end

%Repeat contrast and brightness measurements

newbright3=mean(mean(newfreq));

lumnewbright3=mean(mean(lumnewfreq));

values=zeros(M,N);

for j=1:M

 for k=1:N

 values(j,k)=((newfreq(j,k)-newbright3)^2); 

 end

end

contrastf=sqrt(mean(mean(values)));

lumvalues=zeros(M,N);

for j=1:M

 for k=1:N

 lumvalues(j,k)=((lumnewfreq(j,k)-lumnewbright3)^2); 

 end

end

lumcontrastf=sqrt(mean(mean(lumvalues)));

%------------------------------------------------------------------- 

%Function finds the amount of noise needed to create desired 

nonuniformity

function Y = LumNoisesearch(X, freqimage,DevVar1, LumDevVar1)

Var = X(1);

[noiseimage,LumDevNoise,noisy]=LumNoise(freqimage,Var);

Y = (LumDevNoise-LumDevVar1)^2; 

end

%-------------------------------------------------------------------

%Adds noise to image

function [noiseimage,LumDevNoise,lumnoisy]=LumNoise(freqimage,Var)

[X,Z] = size(freqimage);

freqimage1=double(freqimage);

lumfreqimage1=zeros(X,Z);

%Calculate luminance array as seen on NVL displays
133 

for j=1:X

 for k=1:Z

 if freqimage1(j,k)>8192

 lumfreqimage1(j,k)=((1*10^-8)*((freqimage1(j,k))^2))-

(0.0002*(freqimage1(j,k)))+1.6159;

 elseif freqimage1(j,k)<=8192

 lumfreqimage1(j,k) = (3*(10^(-05)))*freqimage1(j,k)+0.0266;

 else

 fprintf('ERROR\n')

 end

 end

end

%Add Noise to the contrast/brightness/spatial resolution adjusted image

noiseimage=imnoise(freqimage,'Gaussian',0,Var);

noiseimage1=double(noiseimage);

lumnoiseimage1=zeros(X,Z);

for j=1:X

 for k=1:Z

 if noiseimage1(j,k)>8192

 lumnoiseimage1(j,k)=((1*10^-8)*((noiseimage1(j,k))^2))-

(0.0002*(noiseimage1(j,k)))+1.6159;

 elseif noiseimage1(j,k)<=8192

 lumnoiseimage1(j,k) = (3*(10^(-

05)))*noiseimage1(j,k)+0.0266;

 else

 fprintf('ERROR\n')

 end

 end

end

%Calculating the noise added

lumnoisy=zeros(X,Z); 

for j=1:X

 for k=1:Z

lumnoisy(j,k)=(lumfreqimage1(j,k)-lumnoiseimage1(j,k));

 end

end

%Calculating actual standard deviation of noise

fullarray = [];

for i = 1:Z

 fullarray = [fullarray;lumnoisy(:,i)];

end

LumDevNoise = std(fullarray,1);

%------------------------------------------------------------------- 

%Integration of butterworth filter

function y = Lumfiltercurve(x,Wn, n)

y =1./(1+(x./Wn).^(2*n));

%------------------------------------------------------------------- 
134 

%tif2arf 

%This script takes 16-bit tiff images and converts them to 12-bit 

ARF's. It

%reads in all tiff files in a driectory and writes them out to a new

%directory with the same filename but different extension.

tifDir = 'F:\Images\'; %Directory containing the tiff files

newDir = 'F:\Thesis\PerceptionExp_08\TIC_PerceptionTest_08\Images\'; 

%Directory to write the new images to

tifFiles = dir([tifDir '*.tif']);

index = size(tifFiles,1);

for ii=1:index

 filename = tifFiles(ii).name;

 pathname = [tifDir filename];

 outfile = [newDir filename(1:end-4) '.arf'];

 

 %Read in the tiff image and shift it so that the mean is at 2048 

(4096/2)

 tifImg = imread(pathname,'tif');

 tifImg = tifImg(:,:,1);

 sizeImg = size(tifImg);

 

 

imagetif=double(tifImg);

[M,N]=size(imagetif);

for j=1:M

 for k=1:N

 if imagetif(j,k)>65520

 imagetif(j,k)=65520;

 end

 end

end

shiftedImage= round(imagetif/16);

%-------------------------------------------------------------------

 
135 

Appendix C Test Subject Background

Person Age 

Years using 

TIC Eyesight 

A 49 8 20/20 

B 51 3 20/20 

C 21 3 20/20 

D 43 18 20/20 

E 51 4 20/70 

F 24 3.5 20/20 

G 41 8 20/20 

H 37 9 20/20 

I 45 15 20/20 

J 44 7 20/30 
Appendix D Example of Design Point

Design Point 1

Design Point 3

Design Point 5

136 

Example of Design Point

Design Point 1 Design Point 2

Design Point 3 Design Point 4

Design Point 5 Design Point 6

Design Point 2

Design Point 4

Design Point 6
Design Point 7

Design Point 9

Design Point 11

137 

 Design Point 8

Design Point 9 Design Point 10

Design Point 11 Design Point 12

Design Point 8

Design Point 10

Design Point 12
Design Point 13

Design Point 15

Design Point 17

138 

 Design Point 14

Design Point 15 Design Point 16

Design Point 17 Design Point 18

Design Point 14

Design Point 16

Design Point 18
Design Point 19

Design Point 21

Design Point 23

139 

 Design Point 20

Design Point 21 Design Point 22

Design Point 23 Design Point 24

Design Point 20

nt 22
Design Point 25

140 

Design Point 25
141 

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