New AUTOMATED DETECTION AND TRACKING OF SHOCK WAVES: … · 2018. 3. 5. · AUTOMATED DETECTION AND TRACKING OF SHOCK WAVES: APPLICATIONS TO SWIFT IMAGERY BY Christopher J. Trujillo,

AUTOMATED DETECTION AND TRACKING OF SHOCK WAVES:

APPLICATIONS TO SWIFT IMAGERY

BY

Christopher J. Trujillo, B.S.E.E.

A thesis submitted to the Graduate School

in partial fulfillment of the requirements

for the degree

Master of Science

Major Subject: Electrical Engineering

New Mexico State University

Las Cruces, New Mexico

May 2017

“Automated Detection and Tracking of Shock Waves: Applications To SWIFT

Imagery,” a thesis prepared by Christopher Trujillo in partial fulfillment of the

requirements for the degree, Master of Science, has been approved and accepted

by the following:

Louí-Vicente ReyesDean of the Graduate School

Laura BoucheronChair of the Examining Committee

Date

Committee in charge:

Dr. Laura Boucheron, Chair

Dr. Charles Creusere

Dr. Joseph Lakey

ii

DEDICATION

This dissertation is dedicated to the memory of my late father, Gerald F.

Trujillo, for the never ending love and joy he brought to my life. I miss him every

day, but I am glad to know that we only part to one day meet again. A special

feeling of gratitude to my parents, Samuel Garcia and Maria De La Torre Garcia,

for all their unconditional love, guidance, and support they have given me. I will

always appreciate all they have done.

iii

ACKNOWLEDGMENTS

Chiefly, I would like to express my an earnest appreciation to my advisor Prof.

Laura E. Boucheron for the support she has given to me during my research and

academic studies at NMSU. I couldn’t have had a better advisor. I’d also like to

extend my thanks to the rest of my committee members: Charles Creusere and

Joseph Lakey, for their encouragement and insightful thoughts. A sincere thanks

to the Michael Murphy at Los Alamos National Laboratory for the collaboration

needed for my research. A special thanks to the group Detonator Technology

(Q-6), at Los Alamos National Laboratory, for their support. Without them this

opportunity would not have been made possible.

iv

VITA

December 02, 1993 Born in Los Alamos, New Mexico

2012-2016 B.S.E.E., New Mexico State University,Las Cruces, New Mexico.

2013-2017 Engineering Student Intern,Detonator Technology (Q-6),Los Alamos National Laboratory,Los Alamos, New Mexico.

PUBLICATIONS [or Papers Presented]

1. C. J. Trujillo, ”Automated Detection and Tracking of Shock Waves:

Applications to SWIFT Imagery” in preparation Proc. 20th Biennial

International Conference on Shock Compression of Condensed Matter, 2017.

2. C. J. Trujillo,”Fireset and Cable Design for Support of Detonator

Diagnostic Development,” in preparation Proc. 20th Biennial International

Conference on Shock Compression of Condensed Matter, 2017.

FIELD OF STUDY

Major Field: Electrical Engineering

Area of Specialty: Digital Signal Processing and Power Systems

v

ABSTRACT

Automated Detection and Tracking of Shock Waves:

Applications To SWIFT Imagery

BY

Christopher Trujillo, B.S.E.E.

MASTER OF SCIENCE

New Mexico State University

Las Cruces, New Mexico, 2017

Dr. Laura E. Boucheron, Chair

Accurately tracking the position of explosive-induced shock waves is a critical

method for characterizing high explosive (HE) performance. The application of

the shock wave image framing technique (SWIFT) has proven to be a successful

diagnostic tool that utilizes ultra-high-speed imaging to capture time series images

of explosively-driven shock waves propagating through transparent media. The

use of common edge-detection algorithms, including Sobel, Canny, and Prewitt,

tend to be susceptible to background noise and require noise reduction prepro-

cessing that can alter the position of edge boundaries. We present results of the

application of active contours without edges and robust image corner detection

based on the chord-to-point distance accumulation technique for automated de-

tection and tracking of shock waves. We used a full SWIFT test series conducted

vi

at Los Alamos National Laboratory (LANL) to test the proposed algorithm. The

proposed method can accurately detect the temporal and spatial evolution of shock

waves propagating from detonation events observed by SWIFT. The obtained re-

sults are validated using manually predetermined results carefully produced by

scientist Michael Murphy, the SWIFT experiment developer, and published ve-

locity measurements characteristic to the explosives used to drive the shock waves.

The application of advanced image-processing techniques to experimental SWIFT

data show that shock wave position can accurately be detected and tracked, while

also maintaining robustness to background image noise and efficiency for data

analysis.

vii

CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii

1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 SWIFT for Shack Wave Propagation . . . . . . . . . . . . . . . . 1

1.2 Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Active Contour Models . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1 Classical Snakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Active Contours Without Edges (ACWE): . . . . . . . . . . . . . 6

2.3 Advantages of ACWE over Classical Snakes . . . . . . . . . . . . 8

2.4 Applications of ACWE to Image Segmentation . . . . . . . . . . . 9

3 Robust Image Corner Detection . . . . . . . . . . . . . . . . . . . 11

3.1 Robust Image Corner Detection Through Curvature Scale Space . 11

3.2 Disadvantages of the Curvature Scale Space Technique . . . . . . 14

3.3 Robust Image Corner Detection Based on the Chord-to-Point Dis-

tance Accumulation Technique . . . . . . . . . . . . . . . . . . . . 15

3.4 Applications of CPDA to Image Corner Detection . . . . . . . . . 17

4 Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.1 SWIFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.1.1 XTX-8004 High Explosive . . . . . . . . . . . . . . . . . . 19

4.1.2 Dynamic Witness Plates . . . . . . . . . . . . . . . . . . . 20

4.1.3 Specialized Imaging . . . . . . . . . . . . . . . . . . . . . . 20

viii

4.2 Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

5 Application of ACWE . . . . . . . . . . . . . . . . . . . . . . . . 27

5.1 Pre-Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

5.2 Initialization by Thresholding . . . . . . . . . . . . . . . . . . . . 27

5.3 Parameter Selection . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5.4 Stopping Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5.5 Segmentation Results . . . . . . . . . . . . . . . . . . . . . . . . . 33

6 Application of CPDA . . . . . . . . . . . . . . . . . . . . . . . . . 40

6.1 Pre-Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

6.2 Application of the Algorithm . . . . . . . . . . . . . . . . . . . . . 41

6.2.1 Curve Extraction and Smoothing . . . . . . . . . . . . . . 41

6.3 Curvature Estimation . . . . . . . . . . . . . . . . . . . . . . . . . 42

6.4 Corner Refinement . . . . . . . . . . . . . . . . . . . . . . . . . . 43

6.5 Parameter Selection . . . . . . . . . . . . . . . . . . . . . . . . . . 43

6.6 Corner Detection Results . . . . . . . . . . . . . . . . . . . . . . . 44

7 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

7.1 Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

7.2 Algorithm Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

7.2.1 Contour Extraction Comparison . . . . . . . . . . . . . . . 57

7.3 Intermediate Dataset Results . . . . . . . . . . . . . . . . . . . . 61

7.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

8 CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

9 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

ix

LIST OF TABLES

1 Manually Selected Corner Results: 2.0 mm XTX 8004 Charge Di-

ameter. yLeft & yRight represented as pixel locations. . . . . . . . 52

2 Manually Selected Corner Results: 6.5 mm XTX 8004 Charge Di-

ameter. yLeft & yRight represented as pixel locations. . . . . . . . 53

3 Detonation Velocity: XTX 8004 Charge Diameter from [1]. . . . . 54

4 Automated Corner Results: 2.0 mm XTX 8004 Charge Diameter.

yLeft & yRight are represented as pixel locations. . . . . . . . . . . 57



6 Fit Error: 2.0 mm XTX 8004 Charge Diameter. % are normalized

with respect to their fitted velocities (υ). . . . . . . . . . . . . . . 58

7 Fit Error: 6.5 mm XTX 8004 Charge Diameter. % are normalized

with respect to their fitted velocities (υ). . . . . . . . . . . . . . . 59

8 Automated Corner Results without Canny Edge Detector: 2.0 mm

XTX 8004 Charge Diameter. yLeft & yRight are represented as pixel

locations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

9 Automated Corner Results w/o Canny Edge Detector: 6.5 mm

XTX 8004 Charge Diameter. yLeft & yRight are represented as pixel

locations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

x

10 Averaged (left and right interface) detonation velocities for interme-

diate dataset’s: XTX 8004 charge diameters compared to nearest

published values in [1]. Percent Errors normalized with respect to

the nearest published values. For published detonation velocities,

refer to Table 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

















xi

LIST OF FIGURES

1 SWIFT system consisting of model SIMD16 Ultra High Speed Fram-

ing Camera coupled with Schlieren optics and a spoiled-coherence

laser backlighting. Image taken from [2]. . . . . . . . . . . . . . . 2

2 Example of curve C propagating in normal direction, from [3]. . . 7

3 Intrinsic definition of curvature, from [4]. . . . . . . . . . . . . . . 13

4 Chord-to-point distance accumulation technique for a chord CL of

length L, from [4]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

5 Detonator and cylindrical column of XTX-8004 fully embedded

within the machined PMMA. . . . . . . . . . . . . . . . . . . . . 22

6 SWIFT images of the flow in PMMA resulting from the detonation

of a 2.0 mm HE column of XTX 8004 and a 0.19 μs time between

each frame. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24



each frame. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

8 HE/PMMA interface along propagating shock wave. . . . . . . . . 26

9 Histogram example of single data image. . . . . . . . . . . . . . . 29

10 (a) 8th time series image from the 2.0 mm HE Column of XTX

8004 dataset. (b) Mask generated by applying threshold of 241 to

the sub-figure in (a). (c) 16th time series image from the 2.0 mm

HE Column of XTX 8004 dataset. (d) Mask generated by applying

threshold of 241 to the sub-figure in (c). . . . . . . . . . . . . . . 30

xii

11 (a) 8th time series image from the 6.5 mm HE Column of XTX

8004 dataset. (b) Mask generated by applying threshold of 241 to

the sub-figure in (a). (c) 16th time series image from the 6.5 mm

HE Column of XTX 8004 dataset. (d) Mask generated by applying

threshold of 241 to the sub-figure in (c). . . . . . . . . . . . . . . 31

12 Time series segmented images from the 2.0 mm HE Column of XTX

8004 dataset. The yellow contour overlaid on the SWIFT images

is the final converged ACWE contour. . . . . . . . . . . . . . . . . 34




14 Corner detection results corresponding to left and right subimages

taken from the images of Figure 12. . . . . . . . . . . . . . . . . . 45



16 Evolution of the shock wave resulting from the detonation of a 2.0

mm HE column of XTX 8004. . . . . . . . . . . . . . . . . . . . . 55





each frame. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69



each frame. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

xiii



each frame. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71



each frame. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72



each frame. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73



each frame. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74



each frame. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75



each frame. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76







xiv

























xv

























xvi



xvii

1 INTRODUCTION

Throughout the world, scientists and engineers such as those at Los Alamos

National Laboratory perform research and testing aimed towards advancing tech-

nology and understanding the nature of materials. With this testing comes a

need for advanced methods of data acquisition and most importantly a means of

analyzing and extracting the necessary information from such acquired data.

1.1 SWIFT for Shack Wave Propagation

At Los Alamos National Laboratory (LANL), the Detonator Technology (Q-6)

group has a strong foundation in both research and design. Detonator Tech-

nology currently operates a unique detonator test laboratory which utilizes high

speed diagnostics and further supports other Los Alamos explosive test facilities

with designing, deploying, and maintaining timing, firing, and integrated safety

systems, as well as providing technical detonator support in fielding and executing

integrated weapon experiments.

Ongoing research is aimed at understanding high explosive materials (HE)

and characterizing their performance. This research is conducted using various

techniques including high speed diagnostics. One specific technique is known

as the Shock Wave Image Framing Technique (SWIFT), and was designed by

Ph.D Michael Murphy, a Research & Design (R&D) Engineer at LANL. This

technique involves using a model SIMD16 Ultra High Speed Framing Camera

coupled with Schlieren optics and a spoiled-coherence laser backlighting to image

explosive output within transparent media with high image quality and multi-

1

frame resolution [5] (see Figure 1). More details on this imaging technology is

described in Chapter 4. This technique is used to perform observations of the

temporal and spatial evolution of shock waves propagating from detonation events

confined within transparent media and displayed as sequence of visualizations [2].

The ability to conduct such observations using an ultra-high-speed device allows

for quantitative information such as two-dimensional shock position, displacement,

and velocity to be obtained from the characterization of two-dimensional shock-

front geometries using SWIFT images. The primary goal of this thesis is to

introduce methods for an automated edge detection and feature point extraction

as a means for quantifying information within datasets produced by SWIFT.

Figure 1: SWIFT system consisting of model SIMD16 Ultra High Speed FramingCamera coupled with Schlieren optics and a spoiled-coherence laser backlighting.Image taken from [2].

1.2 Previous Work

Current techniques employed to analyze datasets produced by SWIFT have proven

to be rudimentary. These techniques require the manual location of shock prop-

agation edges and manual location of points of interest for every image within

the dataset. This method has proven to be time-consuming, undesirable, and can

produce a degree of inconsistent results from person to person. Previous attempts

2

to employ common edge detection methods such as the Canny edge detector [6]

to SWIFT datasets has proven unsuccessful. Many common edge detectors are

highly susceptible to background noise and require preprocessing techniques that

can alter the precision and accuracy of measurements from the data.

In this thesis, we aim to produce an automated method implementing advanced

image processing techniques and tools to analyze SWIFT image datasets for Det-

onator Technology at LANL. Such an effective method for edge detection and

point extraction can prove to be advantageous in analyzing such unique datasets

and provide for consistency in producing results. To the best of our knowledge,

this is the first systematic application of advanced image processing techniques

for automated analysis of SWIFT images.

1.3 Outline

The rest of this thesis is organized as follows. Chapter 2 provides the necessary

background to understand active contour techniques, by first introducing classical

snakes and then providing an overview of active contours without edges and its

advantages over the classical snakes model for applications of segmenting shock

waves. Chapter 3 introduces robust image corner detection through curvature

scale space (CSS), which is a technique used for detection of corners with rounded

characteristics, and then gives an overview of robust image corner detection based

on the chord-to-point distance accumulation technique, which provides advantages

over the CSS corner detector.

In Chapter 4, we discuss the novel shock wave image framing technique and the

instruments and data used in this study. Chapters 5 & 6 present the application

of ACWE and robust image corner detection for analyzing the SWIFT dataset,

3

as well as the intermediate results obtained. Chapter 7 presents the final results

and discusses their validation. We discuss conclusions in Chapter 8 and future

work in Chapter 9.

4

2 Active Contour Models

This chapter provides brief discussions of the background information relevant

to the concept of active contour models by first introducing classical snakes and

proceeding to active contours without edges.

2.1 Classical Snakes

A snake is defined as an energy-minimizing spline guided by external constraint

forces and influenced by image forces that pull it toward features such as lines

and edges [7]. The basic snake model is a controlled continuity spline [8] that is

propagated under the influence of both image forces and external constraint forces.

The image forces move the snake towards prominent image features such as edges,

lines, and contours, while the external constraint forces are responsible for placing

the snake towards the local minimum of the image object. Essentially, an edge

detector is used to stop the evolving curve on the object’s boundary by analyzing

the gradient of the image. The snake model is formulated as the following energy

functional with a position that is parameterized by v(s) = (x(s), y(s)):

E∗snake =∫ 1

0

Esnake(v(s))ds =∫ 1

0

Eint(v(s)) + Eimage(v(s)) + Econ(v(s))ds (1)

Within this functional, Eint represents the internal energy of the spline due to

bending, Eimage gives rise to the image forces, and Econ gives rise to the external

constraint forces [7]. Note that by minimizing the energy (1), we are trying to

locate the curve at the points of maxima (i.e., image gradients), acting as an edge-

detector, while keeping smoothness in the curvature of the object boundary [3].

5

Since the classical snake model relies on an edge detector that uses the image

gradient to stop curve evolution, this model is then unique only to detecting

objects with boundaries defined by a strong gradient. Applied implementation is

difficult with raw images containing significant amounts of noise. Such a noisy

image requires a smoothing filter to be applied, which in turn can smooth object

edges making the curve evolution process difficult to stop, as it may pass directly

through the object’s edge. Therefore, a model that is not based on the gradient of

an image in order to stop curve evolution is proposed as the method of choice for

analyzing datasets from SWIFT. One such method is known as Active Contours

Without Edges [3].

2.2 Active Contours Without Edges (ACWE):

The model ACWE [3] does not contain a stopping edge-function like the classical

snakes model. In other words, the model is not based on the gradient of the image

to stop curve evolution on the desired boundary. Instead, the stopping term

is derived using segmentation techniques by Mumford—Shah [9]. This model

is considered as a minimization of an energy-based segmentation problem that

requires minimizing over all set boundaries C, where C is composed of closed

curves defining a boundary [10]. This is accomplished by applying the level set

technique established by Osher and Sethian [11].

The formulation attempts to separate the image into various regions based

upon the homogeneity of intensities. The algorithm requires an initialization

curve C, defined by C = {(x, y) : φ(x, y) = 0}, which propagates normally to

the contour with a speed dependent on the energy functional until the energy

functional is minimized. This can be seen in Figure 2 where C is the initial curve,

6

x and y are the coordinates of the curve location, and φ is a signed distance

function [12].

Figure 2: Example of curve C propagating in normal direction, from [3].

The energy functional for the model is defined as:

F (cin, cout, C) = μ · Length(C) + ν · Area(inside(C))

+λin

∫inside(C)

|uin0 (x, y)− cin|2dxdy

+λout

∫outside(C)

|uout0 (x, y)− cout|2dxdy

(2)

where μ ≥ 0, ν ≥ 0, λin, λout > 0 are fixed weighting parameters and u0 is

the image formed by two regions of approximately piecewise-constant intensities

of distinct values uin0 , the intensities inside the desired boundary, and uout0 , the

7

intensities outside the desired boundary. cin and cout are average intensity levels

inside and outside of the contour, respectively, and the parameters μ, ν, λin, and

λout are weighting variables that can be adjusted for different evolving behavior.

The energy functional above is based on the following minimizer:

infC{Fin(C) + Fout(C)} ≈ 0 ≈ Fin(Cfinal) + Fout(Cfinal) (3)

where Cfinal is assumed to be the desired boundary and C is the evolving curve

or the initial curve. Fin(C) is defined as the energy functional inside the curve

while Fout(C) is the energy functional outside the curve. It can be shown that

if the curve C is outside the object, then Fin(C) > 0 and Fout(C) ≈ 0. If the

curve C is inside the object, then Fin(C) ≈ 0 but Fout(C) > 0. If the curve C is

both inside and outside the object, then Fin(C) > 0 and Fout(C) > 0. Finally, the

fitting energy is minimized if C = Cfinal, i.e., if the curve C is on the boundary

of the object [3].

2.3 Advantages of ACWE over Classical Snakes

The ACWE model has prominent advantages over the classical snakes model.

The classical snakes model contains a stopping criterion based on the gradient of

an image, limiting the model to incorporate only edge information and discount

other image characteristics such as color intensity and texture or object boundaries

defined by smoothly varying intensity gradients. The ACWE model is not based

on any sort of edge function to stop the curve evolution on the desired edge

boundaries and can therefore detect contours with or without a gradient in the

image. This includes the ability to detect objects with either discontinuous or

8

very smooth boundaries.

In many images, the presence of undesirable features such as noise or clutter

arises. The classical snakes model requires either preprocessing to smooth the im-

age or initialization to be as close as possible to the boundary of interest such that

the active contour can avoid undesirable features such as noise. However, ACWE

requires no such smoothing of the initial image even if there are high levels of

noise present. The initial curve will propagate in the normal direction and the

locations of object boundaries are very well detected and preserved. This is benefi-

cial because image smoothing can be problematic in situations like SWIFT where

accurate measurements must be made. Preprocessing with a smoothing filter to

remove noise artifacts can consequently smooth edges and affect measurements

such as contour or corner positions.

Finally, the ACWE model can automatically detect any interior contours (i.e.,

“holes”) and change of topology (i.e., “contour splitting or merging”) when starting

with only a single initial curve. This initial curve can be positioned anywhere in

the image and does not have to surround the objects of interest to be detected.

This is primarily because the velocity of the curve evolution has a global depen-

dence and is naturally attracted towards objects.

2.4 Applications of ACWE to Image Segmentation

In the context of image processing, the application of ACWE is slowly developing

popularity due to the advantages the algorithm presents. The medical image

processing field is one particular area which has more widely used the algorithm

in novel ways. More recently, ACWE has also been applied in astronomical image

processing.

9

Maroulis et al. [13] published a paper on computer-aided thyroid nodule detec-

tion in ultrasound images using ACWE. In this work, the authors used ACWE in

a novel way which achieved more accurate delineation of the thyroid nodules in ul-

trasound images and faster convergence as compared to other existing techniques.

Some other medical works using ACWE include semi-automatic cervical cancer

segmentation [14], automatic tooth segmentation [15], and inner iris boundary seg-

mentation [16]. Aside from medical image processing, Valluri [17]and Boucheron

et al. [18] used ACWE as a means for solar image analysis. In [17] and [18],

ACWE is used for the segmentation of coronal holes in solar images. ACWE pro-

vides a tool for researchers to study small boundary flashes possibly associated

with magnetic reconnection events at coronal hole boundaries in large datasets as

well as to validate coronal hole segmentation [17] [18] [19].

10

3 Robust Image Corner Detection

Feature detection and matching are an essential task and fundamental prob-

lem in image processing. There are many applications including object recognition

and motion tracking. However, typical practice is to use a set of representative

features, most commonly corners, to identify transformations in images through

the process of feature matching [20]. A fundamental problem arises when cor-

ners exhibit more gradual curvature features in place of sharp, defined points of

intersection. In this chapter, we present the concept of corner detection within im-

ages that exhibit curvature features by first introducing corner detection through

curvature scale space (CSS) and proceeding to corner detection based on the

chord-to-point distance accumulation technique. These two concepts stem from

highly cited technical papers on robust corner detection techniques.

3.1 Robust Image Corner Detection Through Curvature Scale Space

A corner is defined by Webster’s dictionary as the point where converging lines,

edges, or sides meet [21]. The corner points of an image are further defined

as the points where the edges within an image have their maxima of absolute

curvature [22]. For proper corner detection, the following set of criteria should be

satisfied:

• Corner points should be well localized.

• All true corners should be detected.

• False corners should not be detected.

11

• Corner detectors should be robust in regards to noise.

• Corner detectors should be efficient.

In a publication by Mokhtarian et al. [22], the authors propose a corner detec-

tion method based on the curvature scale-space (CSS) technique that satisfy the

previously defined set of criteria. Furthermore, this technique is designed for the

detection of curvature features from an image edge contour at a continuum of

scales.

The advantage of using the CSS technique is its ability to retrieve invariant

geometric features, such as extrema points and curvature zero-crossing points, of a

planar curve at various scales. Curvature zero-crossing points are inflection points

of the image edge contours. To compute the CSS technique, we must compute

the curvature at a point P . This curvature κ is represented as the instantaneous

rate of change of the angle ψ between the tangent at point P and the x-axis, with

respect to the arc length s [23] (see Figure 3). This is represented as the following

formulation as described in [22]:

κ =dψ

ds(4)

Let the curve of length n pixels be represented by Γ(t) = (x(t), y(t)), where

x(t) and y(t) denote the x and y positions of each point along the curve with

respect to arbitrary arc length parameter t, 1 ≤ t ≤ n. The curvature can then

be represented as the following:

κ(t) =x(t)y(t)− x(t)y(t)

(x2(t) + y2(t))3/2(5)

12

Figure 3: Intrinsic definition of curvature, from [4].

where x(t) and y(t) are the first order derivatives and x(t) and y(t) are the sec-

ond order derivatives with respect to parameter t. The first and second order

derivatives at any arbitrary point Pi can be represented as:

Pi =Pi+1 − Pi−1

2and Pi =

Pi+1 − Pi−12

. (6)

To reduce the effects of local variation and noise along the planar curve, curve

smoothing is conducted prior to taking the curvature measurement. This smooth-

ing is conducted independently for each coordinate function along the curve, x(t)

and y(t), by convolving with a Gaussian function g(t, σ), where σ denotes the

width of the Gaussian (also known as the smoothing scale parameter). The smooth

13

curve can be represented as the following:

Γs(t, σ) = (xs(t, σ), ys(t, σ)), (7)

and the curvature of the smoothed curve becomes:

κ(t, σ) =xs(t, σ)ys(t, σ)− xs(t, σ)ys(t, σ)

(x2s(t, σ) + y2s(t, σ))3/2

(8)

wherexs(t, σ) = x(t) ∗ g(t, σ), xs(t, σ) = x(t) ∗ g(t, σ),

ys(t, σ) = y(t) ∗ g(t, σ), and ys(t, σ) = y(t) ∗ g(t, σ),(9)

where ∗ denotes the convolution operator.

The CSS technique is used to find the local maxima of the absolute value

of curvature through various scales σ. At a small scale, the number of maxima

defined is large due to the noise present along the contour. However, as the scale

is increased, the noise present is smoothed away resulting in only the maxima

corresponding to the real corners. In this way, the CSS technique can be employed

into a corner detector by locating and tracking corners through varying scales. A

thresholding and tracking step can be used to further improve localization of true

corners and eliminate false corners.

3.2 Disadvantages of the Curvature Scale Space Technique

The CSS corner detector exhibits disadvantages stemming primarily from two

main problems [4]. The foremost problem with the CSS technique is due to the

curvature estimation defined by the instantaneous rate of change of angle ψ. The

curvature estimation technique is highly sensitive to local variation and noise

14

along the contour. Furthermore, this curvature estimation requires higher order

derivatives of curve point locations and can cause errors and instability in the

produced results. By observing the first order derivatives in equation (6), you can

observe that only the first immediate neighbor points on either side of point Pi

are considered in the estimation. The second order derivative only considers the

first two immediate neighbor points on either side. Such a small neighborhood

results in the local variation and noise problem which can lead to the detection of

many weak and false corners.

To prevent the issues stated above, there is a need for using a high-smoothing

scale; however, this presents another issue. The CSS corner detection method

involves the selection of an appropriate Gaussian smoothing-scale to smooth the

curve. As stated, this smoothing reduces local variation and noise in order to

remove weak or false corners. However determining the appropriate factors is

a difficult task itself, the scale factor can vary for each curve, and smoothing

with inappropriate Gaussian scales could result in poor corner detection along the

contour. Furthermore, smoothing shrinks the curve and consequently smooths out

details along the curve with a high scale factor. This can result in less accurate

estimation and localization and therefore an implementation of the chord-to-point

distance accumulation technique is proposed to resolve these issues.

3.3 Robust Image Corner Detection Based on the Chord-to-Point Dis-

tance Accumulation Technique

Maintaining robustness to the presence of noise and producing accurate and con-

sistent results is important when performing data analysis. Awrangjeb et al. [4]

proposed a corner detection algorithm that overcomes the problems associated

15

with the CSS corner detector and offers improved performance. The proposed

technique is based on the chord-to-point distance accumulation (CPDA) for the

curvature estimation [24]. This technique exhibits reduced sensitivity to local

variation and noise on the contour. This technique also eliminates the use of

derivatives and does not have the undesirable effects of the Gaussian smoothing.

The CPDA technique was proposed by Han and Poston [24] for measuring the

discrete curvature, while providing increased reliability. The technique moves a

chord along a curve and sums the perpendicular distances from each point on the

curve to the cord. The sum represents the curvature at that point. In this way,

the CPDA technique is based on Euclidean distance and does not involve any

derivative of the curve-point locations as with the CSS technique.

To measure the CPDA curvature we must consider n points along Γ(t) =

(x(t), y(t)), where x(t) and y(t) denote the x and y positions of each point along

the curve with respect to arbitrary arc length parameter t, 1 ≤ t ≤ n. The

curvature κL(t) is then measured by moving a chord CL, with user defined length

L, on each side of point Pi at most L points while maintaining Pi as an interior

point. According to [24] and shown in Figure 4, the chord length L denotes the

arc-length of the interior curve-segment. In general, the movement begins when

the two end points of the chord are at Pi−L and Pi respectively. From this position,

the perpendicular Euclidean distance di,i−L is then measured between the chord

and point Pi. Following this measurement, the chord is moved one point ahead

resulting in a new position with end points located at Pi−L+1 and Pi+1 respectively.

The perpendicular Euclidean distance di,i−L+1 is once again measured, and the

procedure is continued until the chord’s endpoints are located at Pi and Pi+L

respectively. Once the chord reaches this stopping location, the summation of the

16

accumulated measured distances represents the CPDA discrete curvature at the

point Pi. This summation is represented as the following formulation:

κL(i) =i∑

j=i−Ldi,j (10)

Figure 4: Chord-to-point distance accumulation technique for a chord CL of lengthL, from [4].

Using the above discrete curvature estimation technique as the basis for the

CPDA corner detector, the key problems associated with the CSS corner detector

no longer become an issue. The CPDA corner detector does not suffer from inad-

equate local variation and noise issues and does not require appropriate selection

of a smoothing scale factor σ.

3.4 Applications of CPDA to Image Corner Detection

In the context of image processing, the application of CPDA is slowly develop-

ing popularity as a robust corner detector due to the advantages the algorithm

presents. One particular area that has more widely used the algorithm is in aerial

surveillance. In a study by Sirmacek et al. [25], the CPDA algorithm was used

to detect buildings in aerial and satellite images. Similarly, Awrangjeb et al. [26]

17

applied the CPDA algorithm for automatic extraction of building roofs in LIDAR

data and multispectral imagery. CPDA provides a robust method for applications

involving the need of corner detection.

18

4 Datasets

4.1 SWIFT

In this section, we discuss the experimental setup, including critical components,

that produced the datasets used for the SWIFT segmentation and feature extrac-

tion algorithm. The initial intent behind the experimental setup was to char-

acterize the performance of high explosives. The experiment used a successfully

implemented technique that provides critical visualization of explosive events.

This method employs the current shock wave image framing technique (SWIFT)

developed in Detonator Technology at Los Alamos National Laboratory. SWIFT

combines ultra-high-speed imaging with spoiled-coherence laser backlighting to

directly visualize explosive output aimed into transparent media.

4.1.1 XTX-8004 High Explosive

As stated, the primary intent of the experiment is aimed toward the characteriza-

tion of high explosives. In this experiment the high explosive of choice was XTX-

8004, also commonly known as Extex 8004. XTX-8004 is an extrudable RDX-

based (Research Design Explosive) high explosive coated with low-temperature

vulcanizing silicone resin, Sylgard 182 [1]. The composition by weight is 80%

RDX and 20% Sylgard 182 silicone elastomer. Uncured XTX-8004 is putty-like

in consistency which allows it to be extrudable. When cured, the high explosive

then becomes white and rubbery in consistency.

19

4.1.2 Dynamic Witness Plates

Dynamic witness plates are machined from optical grade Polymethylmethacry-

late (PMMA) to have two parallel opposing surfaces that are each flat and hand

polished to a high-quality finish as well as to have precisely machined cylindrical

cavities. These cavities are loaded with extrudable XTX-8004 that cures within

the confinement forming a cylindrical column of HE. The PMMA is chosen based

on the following beneficial characteristics: optical clarity, mechanical properties,

machinability, and known shock Hugoniot parameters which describes the rela-

tionship between the states on both sides of a shock wave. This transparent solid

media provides direct visualization of shock waves through detonation reaction

with the PMMA.

4.1.3 Specialized Imaging

Data recording is conducted using two critical system components that each di-

rectly affect the quality of the data. The first component is a SIMD-16 ultra-high-

speed framing camera (from Specialised Imaging Inc. [27]) coupled with Schlieren

optics that utilizes eight Charge-Coupled Device (CCD) sensors each operating in

a dual-frame capacity. Schlieren optics allow us to see small changes in the index

of refraction in gases. More information and a video representation of Schlieren

optics can be found at [28]. The dual-frame capacity allows each CCD to capture

two images. The system employs multiple image intensifiers on the sensors that

provide minimalized error due to perspective and channel registration, as well as

a hybrid beamsplitter to overcome parallax and improve resolution. But most

importantly, the system provides ultra-short (5 ns) exposure times. A system

with such a short exposure provides for the visualization of explosive events by

20

first freezing the motion of the supersonic shock waves without blurring the shock

fronts and second by minimizing the light saturation on the sensors due to intense

explosive luminance.

The second system component is a 5 Watt spoiled-coherence continuous-wave

laser customized by Spectra-Physics [29]. The laser is used for backlighting the

experiments with fiber-optic light delivery. This component is critical because the

absence of coherence in the laser light prevents considerable drawbacks introduced

by coherent light into Schlieren applications. Further discussion and study results

can be found in [5, 30, 31]. The resulting backlight is an intense monochromatic

light source of finite-sized aperture suitable for Schlieren applications.

4.2 Datasets

The SWIFT system has the capacity to produce datasets consisting of 16-frame

image sequences at a frame rate up to 16 MHz or 8-frame image sequences at a rate

up to 200 MHz. The datasets represent a simple flow visualization with multi-

frame resolution and high image quality. Each dataset produces 16 interlaced

images with roughly 1.3 Mega-pixel resolution, 12-bit bit depth, 5 ns exposure,

and 195 ns inter-frame recording. Each high-resolution image is 1280×960 pixels

and when interlaced into a 4×4 grid, it is 5120×3840 pixels.

The SWIFT test series consists of ten experiments where the cylindrical HE

charge was varied in diameter from 6.5 mm to 2.0 mm in 0.5 mm decrements. The

HE charge length was kept fixed at 23 mm for all experiments. It is important

to note that conventional wisdom suggests a nominal length-to-diameter ratio to

be greater than or equal to ten (L/d ≥ 10) for a steady detonation wave to occur

within a cylindrical HE charge [32]. However, the L/d ratios for this test, range

21

from 3.5 to 12 by design. This is due to other investigations into the effects of

detonator scaling and its effect on transient development of steady detonation.

The initiation of the columned XTX-8004 is explosively driven by a standard

detonator with HE having a nominal density of 1.5 g/cm3, diameter of 3mm, and

height of 20 mm. A representative image is displayed in Figure 5 displaying both

the detonator and the cylindrical column of XTX-8004 fully embedded within the

machined PMMA.

Figure 5: Detonator and cylindrical column of XTX-8004 fully embedded withinthe machined PMMA.

Through many experiments, scientists have been aiming toward understanding

the detonation parameters of XTX-8004 and few are currently known. One such

parameter is the detonation velocity as a function of charge radius. The published

22

detonation velocity of 1.5 g/cm3 XTX-8004 with a charge diameter of 3.13 mm has

a value of 7.30mm/μs [1]. This measure is to be used as a validation parameter for

analyzing the quantitative results produced by the proposed SWIFT segmentation

and feature extraction method.

We will illustrate the application of automated segmentation and feature ex-

traction on the complete SWIFT test series. Detonation velocities will be pro-

vided in Chapter 7 for the range of diameters and validated using published shock

velocities for varying diameters of cylindrical columns of XTX 8004. Further val-

idation will be conducted on the two extreme (2.0 mm and 6.5 mm cylindrical

charge diameters) datasets with comparitive results manually produced by sci-

entist Michael Murphy. A representation of these two extreme datasets can be

observed in Figures 6 & 7 where you can clearly visualize the detonation and

shock wave propagation as an evolution through time for these extremes. The

shock wave initiates at the detonator and expands outward from the HE column.

From this data, precise measurements of shock position can be made along the

HE/PMMA interface. Observe the interface in example Figure 8. Representations

of the intermediate charge diameter datasets can be observed in Appendix A.

23

Figure 6: SWIFT images of the flow in PMMA resulting from the detonation ofa 2.0 mm HE column of XTX 8004 and a 0.19 μs time between each frame.

24

Figure 7: SWIFT images of the flow in PMMA resulting from the detonation ofa 6.5 mm HE column of XTX 8004 and a 0.19 μs time between each frame.

25

Figure 8: HE/PMMA interface along propagating shock wave.

26

5 Application of ACWE

The ACWE algorithm described in Chapter 2 is applied to SWIFT datasets.

This chapter discusses the steps to obtain the segmented shock wave boundary.

5.1 Pre-Processing

SWIFT datasets are composed of 16 images, each 1280×960 pixels with 24.5

μm/pixel spatial resolution. The system produces this dataset as a single image

file composed of a 4×4 image grid displaying each sub image concatenated along

side each other as a flow representation with respect to the order in which they

were recorded. Because this data set is provided as a single image file, it is

necessary to parse the dataset into 16 individual image files for analysis. We

developed a simple script which takes into account the concatenated 4×4 grid

representation and automatically parses the data into 16 images within a single

image model.

5.2 Initialization by Thresholding

Before applying ACWE to obtain the segmented shock wave boundaries, we must

define an initial curve. This initial curve is the basis from which the curve evolves

per ACWE energies and stops on the desired boundary. An advantage of the

ACWE algorithm is its insensitivity to initialization; however, we want to initialize

the curve to be as close to the desired boundary as possible for computational

efficiency. Furthermore, we want to initialize the contour in such a way that it is

well within the interior of the shock wave boundary thus defining the HE material

27

to be internal to the contour. To do so, a thresholding technique is employed

that initializes the contour to some defined low intensity which we are certain will

result in an initial mask interior to the boundary.

One common characteristic to all SWIFT imagery its trimodal gray level in-

tensity distribution due to the interior and exterior of the shock wave. Exterior to

the shock wave, the intensity is high and white in nature. Interior to the shock,

the intensity is dark gray to black. If you observe the histogram plot in Figure 9,

there are three Gaussian shaped distributions. The Gaussian on the left repre-

sents the black intensities within the column of HE and detonator. The middle

Gaussian represents the gray intensities within the shock wave, and the Gaussian

on the right represents the white intensities within the PMMA external to the

shock wave.

To define an initial mask that lies interior to the shock wave boundary, we

empirically determined a threshold that captures the dark intensities representa-

tive of the column of HE and detonator. Through observations of each datasets’

histogram, it was determined that the data interior to the shock wave consistently

corresponded to the leftmost Gaussian distribution (refer to Figure 9). Therefore,

a threshold value of 241 was hard-coded to capture the pixels representative of

that leftmost Gaussian. In Figures 10 & 11, you can observe the initial masks at

a threshold of 241 for various time series images.

It is important to note that a simple thresholding technique may exhibit ar-

tifacts along the boundary edge as in Figure 11(d). Therefore it is important to

use a sophisticated algorithm like ACWE that is insensitive to initialization.

28

Intensity0

2000

4000

6000

8000

10000

12000

14000

16000

18000#

of p

ixel

s

0 512 1024 1536 2048 2560 3072 3584 4095Intensity

Figure 9: Histogram example of single data image.

5.3 Parameter Selection

In Chapter 2, we discussed the definition of various parameters such as the smooth-

ing factor (μ) and interior and exterior homogeneity (λ1 and λ2), each of which are

essential for curve evolution. The smoothing factor (μ) is the controlling parame-

ter that is measured by the length of the contour. This parameter also penalizes

longer and more discontinuous curves. Alternatively, this parameter can be in-

terpreted as controlling the degree of smoothness or regularity of the boundaries

along the segmented regions [33] [10]. Defining this parameter with higher val-

ues produces smoother region boundaries, but consequently can also smooth out

finer details. Conversely, defining lower values produces less smoothing or more

29

(a) Original 8 (b) MASK 8

(c) Original 16 (d) MASK 16

Figure 10: (a) 8th time series image from the 2.0 mm HE Column of XTX 8004dataset. (b) Mask generated by applying threshold of 241 to the sub-figure in (a).(c) 16th time series image from the 2.0 mm HE Column of XTX 8004 dataset.(d) Mask generated by applying threshold of 241 to the sub-figure in (c).

irregularities in the region boundaries but allows for finer details to be captured.

Due to the nature of the data being processed, it is not desirable to smooth the

contour as it may lead to alteration of vital information that can affect accurate

corner detection.

The lambda (λ1 and λ2) parameters control the direction of movement of

the evolving curve. Definitively, λ1 is a weight parameter that influences the

30

(a) Original 8 (b) MASK 8

(c) Original 16 (d) MASK 16

Figure 11: (a) 8th time series image from the 6.5 mm HE Column of XTX 8004dataset. (b) Mask generated by applying threshold of 241 to the sub-figure in (a).(c) 16th time series image from the 6.5 mm HE Column of XTX 8004 dataset.(d) Mask generated by applying threshold of 241 to the sub-figure in (c).

curve evolution based on the homogeneity of intensities interior to the contour;

whereas the λ2 parameter influences curve evolution based on the homogeneity of

intensities exterior to the contour. Alternatively, there also exists a contraction

bias parameter (ν) that controls the tendency of the contour to grow outwards or

shrink inwards from the initial curve. This is a parameter which constrains the

area inside the curve.

31

In the implementation of the ACWE algorithm, the smoothing factor and the

contraction bias were selected to equal zero (μ = 0, ν = 0). This results in curves

not being penalized for length and no constraints on the force pushing the curve

towards the boundary of interest. The lambda weight parameters are both set

to a value of one (λ1 = 1, λ2 = 1). This implies that there is no bias towards

the homogeneity of intensities outside the curve versus inside the curve. Each of

these parameters have set fixed values as appropriated from the original ACWE

paper [3] and parameter optimization may be considered in future work.

5.4 Stopping Criterion

In ACWE, the stopping criterion consists of two measures, and the evolving curve

stops based on whichever measure is reached first. The first measure is simply

a set number of maximum iterations. This implies that the evolution process

will continue until the set number of maximum iterations has been reached. This

process is rather rudimentary and can have a serious effect on computational

efficiency with excessively large numbers of iterations. In fact, once the evolving

curve has converged to the desired boundary, the resulting segmentation will not

change with increasing numbers of iterations and should therefore be stopped.

The second measure employs a comparative approach. This process takes the

position of the contour at the current iteration and compares it with the most

recent past five iterations. If the current position did not change from one of

those previous five iterations, then the evolution process is completed.

32

5.5 Segmentation Results

This section presents the results obtained by applying the ACWE algorithm for

the two extreme datasets (as discussed in Section 4.2), with a cylindrical charge

diameter of 2.0 mm and 6.5 mm. These results are displayed in Figures 12 & 13.

Appendix B displays ACWE segmentation results for the intermediate charge

diameters.

In the displayed results, we can conclude that the ACWE algorithm detected

the shock wave boundaries as well as the boundary of the columned HE. The

ACWE algoirthm also detected the boundares outlining artifacts within the shock

wave. These artifacts are treated as interior contours by the ACWE algorithm

and can also be referred to as holes. These holes are interior to the shock wave

and do not factor into final analysis. The quantitative accuracy of these results

are presented in Chapter 7.

33

(a) (b)

(c) (d)

(e) (f)

Figure 12: Time series segmented images from the 2.0 mm HE Column of XTX8004 dataset. The yellow contour overlaid on the SWIFT images is the finalconverged ACWE contour.

34

(g) (h)

(i) (j)

(k) (l)

Figure 12: (Cont.) Time series segmented images from the 2.0 mm HE Columnof XTX 8004 dataset. The yellow contour overlaid on the SWIFT images is thefinal converged ACWE contour.

35

(m) (n)

(o) (p)


36

(a) (b)

(c) (d)

(e) (f)

Figure 13: Time series segmented images from the 6.5 mm HE Column of XTX8004 dataset. The yellow contour overlaid on the SWIFT images is the finalconverged ACWE contour.

37

(g) (h)

(i) (j)

(k) (l)


38

(m) (n)

(o) (p)


39

6 Application of CPDA

The image corner detection algorithm based on chord-to-point distance accu-

mulation (CPDA) and described in Chapter 3 is applied to segmented SWIFT

datasets. This chapter discusses the steps to obtain feature detection in order to

track shock wave propagation.

6.1 Pre-Processing

Prior to the application of the corner detection algorithm, SWIFT images are pre-

processed using ACWE. ACWE provides for segmentation of the data such that

the shock wave boundaries can be accurately identified. These images are then

partitioned into two sub-images comprised of the primary features of interest for

analysis using the corner detection algorithm. These features of interest are the

shock wave positions at the HE/PMMA interface. Refer to Figure 8 for visualiza-

tion of the interface. Precise measurements along the left and right interface can

provide for accurate tracking of shock propagation throughout the entire SWIFT

dataset. The sub-images reduce the amount of data to be processed using the

corner detector and therefore provides for further efficiency in computation. In-

stead of processing the full 1280×960 pixel image, computation can be conducted

on two 61×61 pixel images, where each image captures both the left and right

interface regions as seen in Figure 8. To provide for minor user interaction, the

approximate location of the left and right interface are currently interactively de-

fined by the user during data processing and will be automated in future work.

This implementation reduces the processing to less than 1% of the total pixels per

40

image.

6.2 Application of the Algorithm

6.2.1 Curve Extraction and Smoothing

The use of a Canny edge detector was recommended by the authors of [4]. How-

ever, we have elected to also conduct corner detection without the use of the

Canny edge detector and a smoothing kernel for result comparisons. In this case,

the raw contours located in the application of ACWE were simply extracted and

processed using the resulting steps in the corner detection algorithm. The results

of not using the Canny edge detector and Gaussian smoothing are presented in

Chapter 7 along with the results applied directly to the ACWE output.

The sub-images extracted from the segmentation results detailed in the previ-

ous section are each processed using the corner detection algorithm. As described

in [4], the planar curves/contours are extracted from the input image using a

Canny edge detector. This process includes filling any existing gaps along the

contour within a set range of 2 pixels, defining T-junctions and marking them as

T-corners, and defining the status of each edge curve as either ‘loop’ or ‘line’. A

T-junction is any point along an edge that is within two pixels from the end of

another curve. If two ends of a curve are within 5 pixels of each other, then the

status of the edge curve is defined as ‘loop’, otherwise, the status is defined as

‘line’.

Each extracted curve within the image then undergoes smoothing using a small

width Gaussian kernel. The purpose of this smoothing process is to remove quan-

tization noise and any other underlying trivial details that could affect curvature

estimation. The value of σ is typically selected based on the amount of noise

41

present. However, this is unknown and therefore we select a small-scale Gaussian

smoothing to prevent the loss of important features and to minimize the effect on

localization of features.

6.3 Curvature Estimation

After applying Gaussian smoothing, the CPDA technique detailed in Section 3.3 is

then applied to estimate the curvature along the smoothed curve. This technique

uses three chords of different lengths (L1, L2, L3) to calculate three normalized

discrete curvature measurements on each point along the contour. The normalized

discrete curvature function is represented as follows:

h′j =hj(i)

max(hj), for 1 ≤ i ≤ L and 1 ≤ j ≤ 3 (11)

where hj(i) is the curvature function using chord CL with length L and j is

reference to one of the three chords. Note that the normalized discrete curvature

values will be in the range [0, 1].

For each point along the contour, three normalized curvature values are com-

puted and are then multiplied to obtain a single feature value, the estimated

curvature product. This step is represented as the following function:

H(i) = h′1(i) · h′2(i) · h′3(i), for 1 ≤ i ≤ n (12)

This curvature product provides for strong corners to become more distinguishable

from the weak corners, which proves to be advantageous for detection.

42

6.4 Corner Refinement

Candidate corners can be obtained by computing the local maxima of the abso-

lute curvature products (abs(H(i))) along the curve. A local maximum is either

a strong corner, a weak corner, or a false corner. In the implementation of this

algorithm, we want to keep only strong corners. These strong corners will, by

definition, have good localization, high curvature values, and are visually promi-

nent features along curves. To obtain the final corner set, a refinement process

consisting of two steps is necessary to filter out the weak and false corners. The

first step uses a curvature-threshold that eliminates weak corners and the second

step uses an angle threshold that removes the false corners. If any of the local

maxima are below the curvature threshold, then those are to be considered to be

weak corners and are removed from the candidate corner set. The angle threshold

is defined as the maximum angle below which the estimated corner angles are

considered as sharp angles. Lastly; corners, if any, at the ends of a ‘loop’ must

be considered for potential removal as well as T-corners that are far away from

already detected corners.

6.5 Parameter Selection

The selection of various parameters used in the corner detection algorithm is im-

portant to ensure optimum results. Experiments were carried out by the authors

of Robust Image Corner Detection base on the Chord-to-Point Distance Accumu-

lation Technique [4]. These experiments determined the default parameters to be

used for robust corner detection.

Beginning with the Canny edge detector, the threshold values were selected

as low = 0.2 and high = 0.7. It is important to note that in the Canny edge

43

detector, if the low threshold is set too low, then many weak and noisy edges will

be detected, whereas, if the high threshold were set too high, many legitimate

edges could be missed.

The Gaussian width parameter (σ) was determined to be small-scale to prevent

smoothing out important features. For this reason, σ is defined as a variable

parameter based on curve length. For a curve length n ≤ 100 pixels, σ = 1 is

selected; for 100 ≤ n ≤ 200, σ = 2 is selected; and for n ≤ 200, σ = 3 is selected.

It is important to state that the Gaussian small-scale smoothing does not remove

all the weak and false corners, hence the need for the corner refinement process.

Recall that curvature estimation uses three chords of different lengths (L1, L2,

L3) to calculate three normalized discrete curvature measurements on each point

along the contour. The three chords are selected to be of medium lengths and

have values of L1 = 10, L2 = 20, and L3 = 30 irrespective of the curve-length [34].

The two-step refinement process consists of two threshold parameters. The first

is the curvature threshold and second is the angle threshold. Through experiments

in [4] it was determined to select the curvature threshold value Th = 0.2, and the

angle threshold value δ = 157◦. Each of these parameters have set fixed values as

appropriated from the original CPDA paper and parameter optimization for this

SWIFT application may be considered in future work.

6.6 Corner Detection Results

This section presents the results obtained by applying the corner detection algo-

rithm using the CPDA technique for the datasets discussed in Section 4.2, with a

cylindrical charge diameter of 2.0 mm and 6.5 mm. Appendix C displays CPDA

corner detection results for the intermediate charge diameters.

44

By observing the results displayed in Figures 14 & 15 and those in Appendix

C we can conclude that each left and right corner was detected along the HE/P-

MMA interface as desired. Further results concluding the accuracy of the corner

detection are presented in Chapter 7.

Left Output Right Output

(a)


(b)


(c)


(d)


(e)


(f)

Figure 14: Corner detection results corresponding to left and right subimagestaken from the images of Figure 12.

45


(g)


(h)


(i)


(j)


(k)


(l)

Figure 14: (Cont.) Corner detection results corresponding to left and right subim-ages taken from the images of Figure 12.

46


(m)


(n)


(o)


(p)


47


(a)


(b)


(c)


(d)


(e)


(f)

Figure 15: Corner detection results corresponding to left and right subimagestaken from the images of Figure 13.

48


(g)


(h)


(i)


(j)


(k)


(l)


49


(m)


(n)


(o)


(p)


50

7 Results

This chapter presents the results produced by the application of ACWE and

robust image corner detection of SWIFT datasets. The validation of these results

is discussed.

7.1 Previous Work

As discussed in Chapter 1, current techniques require the manual location of

shock propagation edges and manual location of points of interest for every image

within the dataset. This method has proven to be time-consuming, undesirable in

efficiency, and can produce a degree of inconsistent results from person to person.

This section summarizes the previous manual analysis. Results consisting of corner

positions for the 2.0 mm and 6.5 mm experimental datasets presented in Chapter

4 and produced by scientist Michael Murphy are displayed in Tables 1 & 2.

In Table 2, the positions of the corners for the first two time-series images

are represented as zero. This is due to the lack of a defined corner between

the shock wave and the HE/PMMA interface at such early stages of the shock

wave’s propagation from the HE detonator. Therefore, these zero points are not

represented in either Murphy’s results nor those presented in this study.

Using the data from these two experiments, functions representing the position

yLeft(t) and yRight(t) as a function of time t for each shock wave are fit using

a linear least-squares approach. From these equations, the velocities υ of each

shock wave are represented as the slopes of each linear function. To convert

the representations from pixels to millimeters, we must apply the conversion 1

pixel = 24.50 μm. The functions for the 2.0 mm XTX 8004 charge diameter are

51

Table 1: Manually Selected Corner Results: 2.0 mm XTX 8004 Charge Diameter.yLeft & yRight represented as pixel locations.

2.0 mm XTX 8004 Charge DiameterImage Timing (μs) yLeft yRight

1 0.19 93 942 0.38 145 1513 0.57 203 2014 0.76 258 2575 0.95 318 3166 1.14 369 3697 1.33 428 4268 1.52 481 4809 1.71 539 53810 1.90 594 59411 2.09 654 65012 2.28 708 70513 2.47 766 76214 2.66 819 81515 2.85 876 87416 3.04 929 928

represented in the following equations [1]:

yLeft(t) = 7.2252t+ 0.8569 where υ = 7.2252 mm/μs,

yRight(t) = 7.1865t+ 0.8887 where υ = 7.1865 mm/μs,(13)

where yLeft & yRight are the shock positions at the left and right HE/PMMA inter-

face, respectively, at time t, and υ represents the shock velocity. The functions for

the 6.5 mm XTX 8004 charge diameter are represented in the following equations:

yLeft(t) = 7.4860t− 0.2000 where υ = 7.4860 mm/μs,

yRight(t) = 7.5509t− 0.3539 where υ = 7.5509 mm/μs.(14)

52

Table 2: Manually Selected Corner Results: 6.5 mm XTX 8004 Charge Diameter.yLeft & yRight represented as pixel locations.


1 0.19 0 02 0.38 0 03 0.57 155 1524 0.76 220 2205 0.95 283 2756 1.14 345 3377 1.33 404 3998 1.52 461 4599 1.71 518 51810 1.90 576 57511 2.09 633 63312 2.28 687 69013 2.47 745 74814 2.66 803 80415 2.85 860 86016 3.04 917 916

The published value for the detonation velocity of 1.5 g/cm3 XTX 8004 at a

charge diameter of 2.0 mm is given as 7.2 mm/μs in [1]. For the same explosive

with a charge diameter greater than 4.5 mm, the published value is 7.45 mm/μs.

Further detonation velocities for various charge diameters can be seen in Table 3.

The velocity values obtained from the SWIFT data by Murphy are close to

those of the published values, with a deviation between 0.35—1.35 % normalized

with respect to the published values. Such deviation is considered acceptable by

the authors of [5].

53

Table 3: Detonation Velocity: XTX 8004 Charge Diameter from [1].

Effects of Charge RadiusDiameter (mm) Detonation Velocity (mm/μs)

∞ 7.454.5 7.353.3 7.302.0 7.221.75 7.151.6 Detonation Failure

7.2 Algorithm Results

The application of ACWE and robust corner detection to SWIFT datasets is a

means of automatically analyzing data and producing consistent results for the

same manual analysis summarized in Section 7.1. In Chapters 5 and 6, interme-

diate results were displayed to provide a detailed understanding of the processes

taking place. In Figures 16 & 17, we display a single image for the 2.0 mm and

6.5 mm SWIFT datasets showing the evolution of the shock wave with respect

to time. Evolution images for the intermediate charge diameters are displayed in

Appendix D. These images color code the segmented boundary of the shock front

with respect to time as well as mark the corner points representing the HE/PMMA

interface.

The positions of the corner points representing the HE/PMMA interface are

also displayed in Tables 4 & 5 for the extremes of 2 mm and 6.5 mm. As before, for

the experiment consisting of 6.5 mm XTX 8004 Charge Diameter, the positions

of the corners for the first two time series images are represented as zero and

are ignored due to the lack of defined corners between the shock wave and the

HE/PMMA interface at early stages of the shock wave’s propagation from the

54

Figure 16: Evolution of the shock wave resulting from the detonation of a 2.0 mmHE column of XTX 8004.

initiation of the HE detonator.

The data produced from the application of the algorithms, and displayed in

the Tables 4 & 5, are fit using a linear least-squares approach to generate represen-

tative position time functions. Furthermore, the slope of the function represents

the velocity of the shock waves propagations. Recall that the data is converted

from pixels to millimeters using the transformation 1 pixel = 24.50 μm. The

least-squares linear functions for the 2.0 mm XTX 8004 charge diameter are given

by:


yRight(t) = 7.2229t+ 0.9463 where υ = 7.2229 mm/μs.(15)

55

Figure 17: Evolution of the shock wave resulting from the detonation of a 6.5 mmHE column of XTX 8004.

The least-squares linear functions for the 6.5 mm XTX 8004 charge diameter are

given by:



Calculated errors characterizing how well the fitted equations represent the data

for both Murphy’s and our automated results are displayed in Tables 6 & 7.

The deviation of these velocities with the published velocities in [1] are between

0.32—1.50 %, normalized with respect to the published values. The deviation

56

Table 4: Automated Corner Results: 2.0 mm XTX 8004 Charge Diameter. yLeft& yRight are represented as pixel locations.


1 0.19 96 972 0.38 148 1513 0.57 205 2074 0.76 260 2615 0.95 321 3206 1.14 377 3737 1.33 432 4308 1.52 486 4879 1.71 542 54210 1.90 599 59611 2.09 658 65612 2.28 713 71113 2.47 772 76614 2.66 823 82115 2.85 879 88316 3.04 933 935

of these velocities with those produced by Murphy are between 0.05—0.51 %,

normalized with respect to Murphy’s values.

7.2.1 Contour Extraction Comparison

As stated in Chapter 6, the use of a Canny edge detector was recommended by

the authors of [3]. However, we have elected to also conduct corner detection

without the use of the Canny edge detector and a smoothing kernel for result

comparisons. In this case, the raw contours located by the application of ACWE

are used directly in place of the Canny edge detector and processed using the

remaining steps in the corner detection algorithm. The resulting positions of the

57

Table 5: Automated Corner Results: 6.5 mm XTX 8004 Charge Diameter. yLeft& yRight are represented as pixel locations.


1 0.19 0 02 0.38 0 03 0.57 157 1564 0.76 223 2235 0.95 286 2776 1.14 348 3417 1.33 405 4018 1.52 461 4599 1.71 520 52010 1.90 578 57611 2.09 635 63612 2.28 690 69413 2.47 747 75314 2.66 805 80815 2.85 863 86516 3.04 920 918

Table 6: Fit Error: 2.0 mm XTX 8004 Charge Diameter. % are normalized withrespect to their fitted velocities (υ).

2.0 mm XTX 8004 Charge Diameter

Fit ErrorMurphy Algorithm

Left Right Left Rightmm/μs % mm/μs % mm/μs % mm/μs %

Average 0.037 0.513 0.032 0.446 0.045 0.628 0.032 0.437Maximum 0.070 0.971 0.080 1.112 0.102 1.406 0.102 1.409Minimum 0.002 0.024 0.000 0.003 0.011 0.152 0.003 0.047

corner points can be observed in Tables 8 & 9 for the extremes of 2 mm and

6.5 mm. As before, for the experiment consisting of 6.5 mm XTX 8004 Charge

Diameter, the positions of the corners for the first two time series images are

represented as zero and ignored due to the lack of defined corners between the

58

Table 7: Fit Error: 6.5 mm XTX 8004 Charge Diameter. % are normalized withrespect to their fitted velocities (υ).

6.5 mm XTX 8004 Charge Diameter

Fit ErrorMurphy Algorithm

Left Right Left Rightmm/μs % mm/μs % mm/μs % mm/μs %

Average 0.091 1.219 0.085 1.129 0.084 1.113 0.079 1.040Maximum 0.270 3.600 0.226 2.994 0.270 3.608 0.195 2.583Minimum 0.022 0.291 0.002 0.031 0.019 0.255 0.017 0.221

Table 8: Automated Corner Results without Canny Edge Detector: 2.0 mm XTX8004 Charge Diameter. yLeft & yRight are represented as pixel locations.


1 0.19 96 972 0.38 147 1533 0.57 205 2074 0.76 260 2625 0.95 323 3216 1.14 377 3747 1.33 432 4318 1.52 487 4889 1.71 543 54310 1.90 599 59711 2.09 658 65712 2.28 713 71213 2.47 769 76614 2.66 824 82115 2.85 879 87916 3.04 934 936

shock wave and the HE/PMMA interface at such early stages of the shock waves

propagation from the initiation of the HE detonator.


the Tables 8 & 9, are fit using a linear least-squares approach to generate repre-

59

Table 9: Automated Corner Results w/o Canny Edge Detector: 6.5 mm XTX8004 Charge Diameter. yLeft & yRight are represented as pixel locations.


1 0.19 0 02 0.38 0 03 0.57 157 1554 0.76 225 2245 0.95 288 2786 1.14 348 3427 1.33 405 4038 1.52 463 4609 1.71 522 52110 1.90 578 57711 2.09 635 63612 2.28 690 69513 2.47 748 75314 2.66 805 80815 2.85 863 86616 3.04 920 917

sentative position versus time functions. Furthermore, the slope of the function

represents the velocity of the shock waves propagations. Recall that the data

is converted from pixels to millimeters using the transformation 1 pixel = 24.50

μ/mm The functions for the 2.0 mm XTX 8004 charge diameter are represented

in the following equations:


yRight(t) = 7.2093t+ 0.9806 where υ = 7.2093 mm/μs.(17)

The functions for the 6.5 mm XTX 8004 charge diameter are represented in the

60

following equations:



The deviation of these velocities with the published velocities in [1] are be-

tween 0.13—1.41 %, normalized with respect to the published values. The devia-

tion of these velocities with those produced by Murphy are between 0.06—0.32 %,

normalized with respect to Murphy’s values. Most notably, the deviation of these

velocities in comparison to those produced by the algorithm using the Canny edge

detector is between 0.006—0.188 %, normalized with respect to the values pro-

duced with the Canny edge detector. Such a small deviation provides clarification

that both methods produce nearly identical results.

7.3 Intermediate Dataset Results

In this section, we summarize the results of the intermediate datasets spanning

between 2.0 mm and 6.5 mm diameter and displayed in Appendix A. These re-

sults are validated using published values from [1]. Appendix B and C display

the results of applying the ACWE and CPDA algorithms to each of the interme-

diate datasets. Furthermore, Appendix D displays evolution of the shock wave

with respect to time for each intermediate dataset. The positions of the corner

points representing the HE/PMMA interface are also displayed in Tables within

Appendix E.


Appendix E, are fit using a linear least-squares approach to generate representa-

tive position time functions where the slope of the functions represents the velocity

61

of the shock waves propagations. Recall that the data is converted from pixels

to millimeters using the transformation 1 pixel = 24.50 mm. The resulting veloc-

ities for each intermediate dataset are displayed in Table 10 where the left and

right interface velocities were averaged together and compared to the published

values in [1] with the closest diameter. From these results, we can conclude that

the deviation of these velocities with the published velocities in [1] are between

0.064—1.184 %, normalized with respect to the published values. Such a small

deviation provides validation of accurate detection and tracking of shock waves

for the intermediate datasets.

Table 10: Averaged (left and right interface) detonation velocities for intermediatedataset’s: XTX 8004 charge diameters compared to nearest published values in[1]. Percent Errors normalized with respect to the nearest published values. Forpublished detonation velocities, refer to Table 3.

Intermediate Detonation VelocitiesDiameter Detonation Velocity Nearest Published Value from [1] Error

(mm) (mm/μs) (mm) | (mm/μs) (%)2.5 7.2693 2.0 | 7.22 0.6833.0 7.2804 3.3 | 7.30 0.2693.5 7.3512 3.3 | 7.30 0.7014.0 7.3235 4.5 | 7.35 0.3614.5 7.3453 4.5 | 7.35 0.0645.0 7.3778 4.5 | 7.35 0.3785.5 7.4290 ∞ | 7.45 0.2826.0 7.5382 ∞ | 7.45 1.184

7.4 Summary

From the above sections, it can be summarized that the detection and tracking of

shock waves is validated with several quantitative metrics, and the results prove

62

that SWIFT datasets can be accurately and efficiently analyzed with automated

methods. An important property of SWIFT datasets is the nature in which the

data is displayed. The explosive time series images contain a strong gray level

intensity difference along the shock front, which is advantageous for ACWE to

segment the precise shock wave boundary. This boundary can then be tracked

using two curvature corners as reference to compute a position versus time velocity

calculation. These reference points are detected using a robust corner detection

technique. The accuracy of such results is validated using manually predetermined

results carefully produced by scientist Michael Murphy, the SWIFT experiment

developer, and velocity measurements characteristic to the explosives used to drive

the shock waves. A single dataset can be processed within minutes versus hours

with manual analysis techniques.

63

8 CONCLUSION

In this work, we proposed an algorithm to detect and track shock waves in an

automated manner. The main goal of this thesis was to improve SWIFT analysis

methods compared to the existing manual techniques. For this study, datasets

produced by SWIFT were collected for ten experimental tests with varying cylin-

drical XTX 8004 diameters and results are verified against manually defined shock

front points and against expected detonation velocities for XTX 8004.

The segmentation algorithm first identifies shock wave boundaries using the

ACWE algorithm. After obtaining the segmented shock wave boundaries, points

of reference are detected using a robust corner detection algorithm and position

measurements are observed for each time series image. Additionally, the position

versus time measurements are used to determine the shock wave’s propagation

velocities. Results are validated with known parameters characteristic to the high

explosives used in the experiment, and by comparing to pre-determined results

carefully produced by existing manual techniques. For the range of 2.0 mm to

6.5 mm cylindrical charge diameter, we found errors between 0.064—1.50 % when

comparing the algorithm’s results to published results.

The developed algorithm is efficient, robust, and most importantly, automated.

As opposed to previous methods, where results were produced using manual se-

lection techniques, here, the method uses advanced image processing techniques

to detect and track shock wave’s. Due to the efficient and automated approach of

this method, it allows analysis of large SWIFT datasets and can be used to study

the evolution of a shock wave’s propagation. Although automated, the proposed

64

approach is by no means complete and we conclude that an extensive study of

further SWIFT data should be conducted.

65

9 Future Work

There are several considerations that might lead to a better and more signifi-

cant automation in future studies. Firstly, the ACWE algorithm and the robust

corner detection algorithm can be put through a study to determine optimal pa-

rameter selection. Secondly, although, the ACWE algorithm is not dependent on

the defined initial curve, it is initialized using basic thresholding whose threshold

value was hard-coded and chosen based on the visualization of histograms from

the data. This threshold can be selected using more quantitative techniques rather

than just visualizing the histograms. This would allow the ACWE algorithm to

evolve to the optimal boundary with fewer iterations. However; further analysis

needs to be carried out to justify the threshold.

Another consideration is to automate the determination of the two subimages

used as the input to the CPDA algorithm as discussed in Section 6.1. A possible

solution is to consider the expected velocity of the HE and times of each image

to determine each subimage selection. A study of all possible methods should be

conducted.

Lastly, it would be beneficial to carry out a long-term study and apply this

algorithm to other SWIFT experiments, analyzing other tests such as spherical

charges or even charges consisting of other high explosive materials. After all, the

primary goal of SWIFT is aimed at understanding high explosive materials and

characterizing their performance. Therefore, the application is endless as research

is consistently poured into the development of current and new HE materials.

66

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