Retrograde adaptive resonance theory based on the role of nitric oxide in long-term potentiation Abstract Adaptive resonance theory (ART) demonstrates how the brain learns to recognize and categorize vast amounts of information by using top-down expectations and attentional focusing. ART 3, one member of the ART family, embeds the computational properties of the chemical synapse in its search process, but it converges slowly and is lack of stability when being applied in pattern recognition and analysis. To overcome these problems, Nitric Oxide (NO), which serves as a newly discovered retrograde messenger in Long-Term Potentiation (LTP), is introduced in retrograde adaptive resonance theory (ReART) model presented in this paper. In the presented model a novel search hypothesis is proposed to incorporate angle and amplitude information of an external input vector to decide whether the input matches the long-term memory (LTM) weights of an active node or not, and the embedded NO retrograde mechanism makes the search procedure a closed loop, which improves the stability and convergence speed of the transmitter releasing mechanism in a synapse. To make the model more adaptive and practical, a forgetting mechanism is built to improve the weights updating process. Experimental results indicate that the proposed ReART model achieves low error rate, fast convergence and self-organizing weights regulation. In this section, the performance evaluation of ReART is given. Table 1 shows the parameters used for the simulations.

O B I I O O O O O B I O B I O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O B I O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


GUARDS: A Generic Upgradable Architecture for Real-Time Dependable Systems AbstractÐThe development and validation of fault-tolerant computers for critical real-time applications are currently both costly and time consuming. Often, the underlying technology is out-of-date by the time the computers are ready for deployment. Obsolescence can become a chronic problem when the systems in which they are embedded have lifetimes of several decades. This paper gives an overview of the work carried out in a project that is tackling the issues of cost and rapid obsolescence by defining a generic faulttolerant computer architecture based essentially on commercial off-the-shelf (COTS) components (both processor hardware boards and real-time operating systems). The architecture uses a limited number of specific, but generic, hardware and software components to implement an architecture that can be configured along three dimensions: redundant channels, redundant lanes, and integrity levels. The two dimensions of physical redundancy allow the definition of a wide variety of instances with different fault tolerance strategies. The integrity level dimension allows application components of different levels of criticality to coexist in the same instance. The paper describes the main concepts of the architecture, the supporting environments for development and validation, and the prototypes currently being implemented. The GUARDS project is an ambitious one. We have defined a generic fault-tolerant architecture based on COTS components and a small set of purpose-designed hardware and software building blocks. This architecture can be configured along three different dimensions (channels, lanes, integrity levels) to meet the dependability requirements of a wide variety of end-user applications.. The design of the architecture has shamelessly borrowed ideas from previous work (in particular, SIFT [47] , MAFT [37] , FTPP [30] , and Delta-4 [52] ). Like SIFT and Delta-4, the focus has been on software-implemented fault tolerance, with a minimum of special-purpose hardware. Like SIFT and MAFT, the architecture uses a fully connected broadcast bus network for interchannel communication. Furthermore, the architecture uses the ZA algorithm for interactive consistency [28] , which resulted from work done in the MAFT project. Like FTPP, the architecture allows parallel processing within each channel (the M dimension). As in Delta-4, the focus has been on the use of COTS operating systems. The architecture also includes several completely innovative aspects: support for multiple levels of integrity, a novel error-filtering technique (-count), and support for a wide range of scheduling models, including preemptive scheduling. At the time of writing, the first prototypes were nearing completion and it is hoped that performance measurements and fault injection results will soon be available.. A particularly constraining design requirement was that only COTS operating systems were to be used. This requirement appears to leave just two options to the faulttolerant system designer. The first option is to use a hardware-intensive approach so that the hardware, although fault-tolerant, presents a standard interface to an unmodified COTS operating system, e.g., as in [1] . This approach, which precludes the use of COTS hardware boards, might nevertheless be necessary in some performance-critical applications. The second option, which is the one followed in GUARDS, is to use high-granularity replication managed by software above the COTS operating systems of interconnected COTS processor boards. One consequence of this choice is that the operating systems themselves cannot be protected from errors. This means that even a transient fault might require a processor to be completely reinitialized. Furthermore, the fault tolerance management software cannot access data structures that are internal to the operating systems. This leads to a nontrivial channel reintegration procedure that relies on programmerdefined context objects. One interesting direction for future research on this aspect would be to explore how compiletime reflection could be used to render context definition transparent to the application programmer [58] . Dr. Arlat's research interests focus on the evaluation of hardware and software fault-tolerant systems, including both analytical modeling and experimental fault injection approaches, subjects on which he authored or coauthored more than 70 papers for international and national journals and conferences. Dr. Beus-Dukic's research interests include real-time operating systems, real-time communication, safety-critical systems, requirements engineering, reuse, and acquisition of COTS software components. She is currently a senior lecturer at the University of Northumbria at Newcastle.. Andrea Bondavalli (M'97) received his ªLaur-eaº degree in computer science from the University of Pisa in 1986. In the same year, he joined CNUCE-CNR, where he holds a position of ªricercatoreº working in the Dependable Computing System group. From April 1991 to February 1992, he was a guest member of the staff at the Computing Laboratory of the University of Newcastle-upon-Tyne (UK).. Since 1989, he has been working on several European projects, such as Esprit BRA PDCS, Esprit BRA PDCS2, Esprit 27439 HIDE, and various national projects on dependable computing He is currently managing the PDCC partnership in the Esprit 20716 GUARDS project. He also acted as a consultant for transportation companies and software houses.. Dr. Bondavalli has served as a program committee member for international conferences and symposia and as a reviewer for conferences and journals. His current research interests include the design of dependable real-time computing systems, software and system fault tolerance, the integration of fault tolerance in real-time systems, and the modeling and evaluation of dependability attributes like reliability, availability, and performability. He has managed several national and European development projects and research contracts, mainly concerning embedded software systems for space, defense, and industrial applications. Particular interests are design methods for hard-real-time systems, including techniques and tools for the specification and verification of timing requirements and constraints.. Dr. Coppola is member of the EUROSPACE Software Engineering panel and the program committee of the ªData Systems in Aerospaceº (DASIA) conference.. Alessandro Fantechi received is ªLaureaº degree in computer science from the University of Pisa in 1978. He has been an associate professor on the Faculty of Engineering of the University of Florence since 1995, and an associate of the Istituto di Elaborazione dell'Informazione (IEI) del CNR, Pisa since 1992. Previously, he was an associate professor at the University of Pisa (from 1992) and a researcher at IEI-CNR (from 1983). He was involved in the Esprit LOTOSPHERE project before the current involvement in the GUARDS project described in this paper. He has taught foundations of computer science, software engineering, and dependable systems engineering at the Universities of Florence and Pisa, and presented several software engineering lectures at main Italian aerospace industries.. Prof. Fantechi's current research is focused on the industrial application of formal verification methods. In this field, he has recently worked for a pilot project with Ansaldo Trasporti on the verification of a railway signaling system. Other research interests have included formal description techniques, temporal logic, distributed systems programming and modeling, and applications of natural language understanding to requirements engineering. He has written more than 40 papers for international journals and conferences. Prof. Fantechi is a member of the ACM.. Eric Jenn received his Engineer Degree in computer science from the National Institute of Applied Sciences, Toulouse, France, in 1989 and a PhD in computer science from the Toulouse National Polytechnic Institute in 1994.. His main interests include hardware and software fault tolerance for real-time dependable systems, validation by modeling and fault injection, and object-oriented design.. He is currently working as a software engineer at Technicatome, the company which develops the nuclear reactors of the submarines and the nuclear aircraft carrier of the French navy.. Christophe Rabe Â jac received a degree from the French Ecole Polytechnique (Palaiseau) in 1991, a degree from ENSEEIHT (National School for Engineers in Computing Science, Toulouse) in 1993, and his PhD from the Toulouse National Polytechnic Institute in 1995. He has been at Matra Marconi Space France (MMS) since 1992.. He has been involved in the architecture of a distributed mission-planning software tool for ground segments, implemented above COTS CORBA technology. He is currently the MMS manager of the GUARDS Esprit Project and, in that context, is in charge of technological developments in fault-tolerant architectures for MMS.. Dr. Rabe Â jac's main fields of interest are avionics architectures for real-time critical embedded systems and all related software techniques. He has published several papers for international conferences such as FTCS and Safecomp.. Andy Wellings is a professor of real-time systems at the University of York, UK in the Computer Science Department. He is interested in most aspects of the design and implementation of real-time dependable computer systems. He has authored/coauthored more than 150 papers/reports. He is European editor-in-chief for the computer science journal SoftwarePractice and Experience.. Professor Wellings teaches courses in operating systems, real-time systems, and network and distributed systems. He is the author of several books, including ªHard Real-Time HOOD: A Structured Design Method for Hard Real-Time Ada Systems,º ªCon-currency in Ada,º and ªReal-Time Systems and Programming Languages.º

O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B I O O O B I O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B I O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O


GF(4) Based Synthesis of Quaternary Reversible/Quantum Logic Circuits Galois field sum of products (GFSOP) Multiple-valued quantum logic synthesis, specially, ternary logic synthesis has become popular in the recent years [1] [2] [3] [4] [5] [6] [7] . Among them [3, 5, 6 ] used cascades of ternary reversible gates like Feynman and Toffoli gates to realize ternary logic functions. The advantage of this approach is that ternary logic functions having many input variables can be easily expressed as ternary Galois field sum of products (TGFSOP) expression and can be realized using cascade of ternary Feynman and Toffoli gates [3, 5, 6] .. Though a considerable number of good works have been done on reversible/quantum ternary logic synthesis, it has the limitation that conventional binary logic functions cannot be very easily represented using the ternary base and the developed methods are applicable only for logic functions expressed in ternary base. A very promising alternative may be quaternary logic, using which, besides quaternary logic functions, binary logic functions can be expressed by grouping 2-bits together into quaternary values. This sort of encoded realization of binary logic functions will theoretically reduce the total volume of the physical devices needed to approximately 1/log 2 4 = 1/2 times the original volume of the devices needed for binary case. However, for this purpose, circuits for input encoding and output decoding will be needed and we show such encoder and decoder circuits in Section 11.. From the experience of ternary logic, it can be expected that quaternary logic functions having many input variables can also be easily expressed as quaternary Galois field sum of products (QGFSOP) expression and can be realized using cascade of quaternary Feynman and Toffoli gates. But the question arises whether quaternary Feynman and Toffoli gates are physically realizable or not. Muthukrishnan and Stroud [8] proposed a family of 2-qudit multiple-valued (d ≥ 2) quantum gates, which is theoretically realizable in liquid ion-trap technology. The macro-level quaternary Feynman and Toffoli gates can be realized on the top of Muthukrishnan-Stroud gates as discussed in Sections 8 and 9.. The advantages of quaternary logic and physical realizability of quaternary Feynman and Toffoli gates require that methods should be developed for synthesizing quaternary logic functions as a cascade of quaternary Feynman and Toffoli gates. However, as far as we know, no work has yet been done on expressing quaternary logic function as QGFSOP expression and realizing the QGFSOP expression as a cascade of quaternary Feynman and Toffoli gates. Realization of QGFSOP expression as a cascade of quaternary Feynman and Toffoli gates is discussed in Section 10. But the main difficulty arises with expressing quaternary logic function as QGFSOP expression. The standard technique used in binary and ternary cases is that a set of expansions is used to construct optimum decision diagram (DD) and the DD is flattened to determine the minimized GFSOP expression. In the QGF case the same technique will be useful. But, as far as we know, no such quaternary Galois field expansion (QGFE) and algorithm for constructing optimum quaternary Galois field decision diagram (QGFDD) have yet been reported in the literature.. In this paper, we have developed ten QGFEs using which we can construct optimum QGFDD. However, constructing optimum QGFDD requires efficient algorithm for selecting QGFE for each variable and algorithm for variable ordering. In this paper we concentrated only on developing QGFEs and showing their usefulness. Development of the above mentioned algorithms will be the focus of future research. By flattening the optimum QGFDD we can generate minimized QGFSOP expression. This QGFSOP expression can be realized as cascade of quaternary 1-qudit gates and multi-qudit Feynman and Toffoli gates. In this paper, we have developed ten quaternary Galois field expansions (QGFE). These expansions can be used for constructing quaternary Galois field decision diagrams (QGFDD) of any quaternary function. By flattening the QGFDD we can generate quaternary Galois field sum of products (QGFSOP) expression for the function. We have also shown example of implementation of QGFSOP expression as a cascade of quaternary 1-qudit gate, Feynman gate, and Toffoli gate.. For QGFSOP based quantum realization of functions with many input variables, we need to use quantum gates with many inputs. However, quantum gates with more than two inputs are very difficult to realize as a primitive gate, since interaction of more than two particles is nearly impossible to manage. In this paper, we have shown the quantum realization of macro-level quaternary 2-qudit Feynman and 3-qudit Toffoli gates on the top of theoretically liquid ion-trap realizable 1-qudit gates and 2-qudit MuthukrishnanStroud primitive gates [8] . We also show the realization of m-qudit (m > 3) Toffoli gates using 3-qudit Toffoli gates.. The quaternary base is very useful for encoded realization of conventional binary function by grouping two bits together into quaternary values. We show quantum circuit for binary-to-quaternary encoder and quaternary-to-binary decoder for this purpose.. The presented method is especially applicable to quantum oracles where only one function output is of importance and input qudits are copied to output. Such circuits are of particular importance in Grover algorithm or similar quantum algorithms. The developed method, in contrast to most methods from literature, performs a conversion of a non-reversible function to a reversible one as a byproduct of the synthesis process. Comparing to the methods from literature, our method can be used for large functions. As it is using Galois logic, the circuits are highly testable [9] .. Our future research includes (1) developing more QGFEs, if such expansions exist and (2) developing algorithms for (i) selecting expansion for each variable, (ii) variable ordering, and (iii) constructing QGFDD (Kronecker and pseudo-Kronecker types) for both single-output and multi-output functions so that the resulting QGFDD and the corresponding QGFSOP expression are minimized.

O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O B I I I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Segmentation

of

tongue

muscles

from

super-resolution

magnetic

resonance

images

Imaging

and

quantification

of

tongue

anatomy

is

helpful

in

surgical

planning,

post-operative

rehabilitation

of

tongue

cancer

patients,

and

studying

of

how

humans

adapt

and

learn

new

strategies

for

breathing,

swallowing

and

speaking

to

compensate

for

changes

in

function

caused

by

disease,

medical

interventions

or

aging.

In

vivo

acquisition

of

high-resolution

three-dimensional

magnetic

resonance

(MR)

images

with

clearly

visible

tongue

muscles

is

currently

not

feasible

because

of

breathing

and

involuntary

swallowing

motions

that

occur

over

lengthy

imaging

times.

However,

recent

advances

in

image

reconstruction

now

allow

the

generation

of

super-resolution

MR

images

from

sets

of

orthogonal

images,

acquired

at

a

high

in-plane

resolution

and

combined

using

super-resolution

techniques.

This

paper

presents,

to

the

best

of

our

knowledge,

the

first

attempt

towards

automatic

tongue

muscle

segmentation

from

MR

images.

We

devised

a

database

of

ten

super-resolution

MR

images,

in

which

the

genioglossus

and

inferior

longitudinalis

tongue

muscles

were

manually

segmented

and

annotated

with

landmarks.

We

demonstrate

the

feasibility

of

segmenting

the

muscles

of

interest

automatically

by

applying

the

landmark-based

game-theoretic

framework

(GTF),

where

a

landmark

detector

based

on

Haar-like

features

and

an

optimal

assignment-based

shape

representation

were

integrated.

The

obtained

segmentation

results

were

validated

against

an

independent

manual

segmentation

performed

by

a

second

observer,

as

well

as

against

B-splines

and

demons

atlasing

approaches.

The

segmentation

performance

resulted

in

mean

Dice

coefficients

of

and

for

the

second

observer,

GTF,

B-splines

atlasing

and

demons

atlasing,

respectively.

The

obtained

level

of

segmentation

accuracy

indicates

that

computerized

tongue

muscle

segmentation

may

be

used

in

surgical

planning

and

treatment

outcome

analysis

of

tongue

cancer

patients,

and

in

studies

of

normal

subjects

and

subjects

with

speech

and

swallowing

problems.

Oral

cancer

is

among

the

most

prevalent

cancers

in

the

world,

with

an

estimated

new

cases

in

(Parkin

et

al.,

and

in

(Jemal

et

al.,

Although

the

mortality

rate

of

oral

cancer

patients

is

not

considered

to

be

high,

the

disease

and

its

treatment

severely

affect

their

speech,

swallowing

and

mastication,

and

thus

their

quality

of

life.

Assessing

and

understanding

the

tongue

morphology

is

valuable

for

proper

surgical

planning,

which

may

considerably

reduce

post-operative

complications

and

lead

to

a

faster

rehabilitation

(Matsui

et

al.,

Besides,

quantification

of

tongue

anatomy

may

help

to

better

understand

how

humans

adapt

and

learn

new

strategies

for

breathing,

swallowing

and

speaking

to

compensate

for

changes

in

function

caused

by

disease,

medical

interventions

or

aging.

The

main

imaging

modalities

that

serve

these

purposes

are

ultrasound

(US)

and

magnetic

resonance

(MR)

imaging..

During

the

last

couple

of

decades,

real-time

US

has

been

the

primary

imaging

modality

for

providing

information

on

the

morphology

and

motion

of

the

tongue,

and

thus

enabling

linguistic

and

Elsevier

B.V.

All

rights

reserved.

swallowing

studies.

To

perform

a

computerized

analysis

of

tongue

anatomy,

Unser

and

Stone

applied

deformable

contours,

i.e.

snakes,

to

determine

tongue

boundaries

from

two-dimensional

US

images,

which

required

user

interaction

to

specify

the

region

of

interest

or

correct

the

snakes

if

they

started

to

follow

wrong

boundaries.

On

the

other

hand,

Akgul

et

al.

proposed

a

fully

automatic

segmentation

approach,

where

snakes

were

applied

to

segment

US

images

acquired

during

speech.

The

same

authors

augmented

snakes

by

prior

knowledge

in

the

form

of

predefined

speech

patterns,

which

increased

the

accuracy

of

tongue

boundary

detection

(Akgul

et

al.,

Li

et

al.

combined

features

based

on

gradients,

regions

of

interest

and

orientation

of

boundaries

for

robust

semi-automatic

tongue

detection.

Roussos

et

al.

proposed

to

use

active

appearance

models,

which

allowed

tongue

segmentation

from

a

limited

field

of

view

and

extrapolation

of

tongue

boundaries

outside

the

target

US

image.

Fasel

and

Berry

first

filtered

US

images

by

applying

a

type

of

neural

networks

called

deep

belief

networks,

and

then

tracked

tongue

boundaries

as

paths

through

the

most

emphasized

image

pixels.

Tang

et

al.

modeled

tongue

movements

by

Markov

random

fields

and

demonstrated

the

superiority

of

their

segmentation

results

in

comparison

to

snake-based

approaches.

Although

standard

US

imaging

is

inexpensive

and

noninvasive,

the

obtained

images

have

a

limited

field

of

view

and

often

do

not

clearly

depict

important

anatomical

details,

which

limit

the

applicability

of

US

in

tongue

anatomy

studies.

By

providing

better

contrast

of

soft

tissues,

MR

imaging

may

overcome

the

drawbacks

of

US..

Similarly

to

US

images,

MR

images

with

short

acquisition

times

facilitate

the

investigation

of

tongue

motions,

including

segmentation

of

the

vocal

tract

(Bresch

et

al.,

Proctor

et

al.,

statistical

modeling

of

speech

patterns

(Stone

et

al.,

comparison

of

such

patterns

between

healthy

and

diseased

subjects

(Stone

et

al.,

and

segmentation

of

tongue

area

structures

including

lips,

hard

and

soft

palate,

pharyngeal

wall,

etc.

(Bresch

and

Narayanan,

Chong

et

al.

applied

seeded

region

growing

to

semi-automatically

segment

tongue

carcinoma,

and

validated

the

obtained

results

against

manual

segmentation.

Recently,

Lee

et

al.

addressed

the

problem

of

tongue

segmentation

from

dynamic

three-dimensional

MR

images.

In

this

work,

a

user

was

required

to

manually

determine

the

approximate

position

of

the

tongue

and

locate

a

small

number

of

seed

points

in

the

background,

which

were

then

propagated

to

consecutive

time

frames

by

non-rigid

B-spline

registration,

and

finally

used

to

initialize

the

random

walker

segmentation

algorithm.

In

contrast

to

MR

images

with

low

acquisition

time,

lengthy

high-resolution

MR

imaging

preserve

a

large

amount

of

anatomical

detail,

which

is

essential

for

studying

individual

tongue

muscles.

Tongue

muscle

segmentation

obtained

from

high-resolution

MR

images

with

high

muscle

contrast

combined

with

the

whole

tongue

segmentation

and

tongue

motion

estimation,

both

obtained

from

dynamic

MR

images,

brings

the

community

closer

to

automatic

computerized

analysis

of

the

behavior

of

individual

tongue

muscles

during

speech

and

mastication.

Modern

MR

protocols

allow

limited

field

of

view

imaging

with

a

resolution

of

around

mm

per

voxel,

which

was

demonstrated

to

be

sufficient

for

in

vivo

speech

studies

(Kim

et

al.,

However,

the

achieved

level

of

contrast

and

image

detail

are

still

not

adequate,

and

make

tongue

muscle

boundaries

ambiguously

defined

and

poorly

visible

for

computerized

or

manual

delineation.

In

vivo

acquisition

of

high-resolution

MR

images

with

visible

inter-muscle

boundaries

requires

subjects

to

stay

motionless

for

min,

which

is

almost

impossible

due

to

breathing

and

involuntary

swallowing.

Despite

the

existence

of

cine

and

multi-slice

MR

imaging,

up

until

now

this

obstacle

represented

a

limitation

for

visualization

and

analysis

of

individual

tongue

muscles

and

post-operative

monitoring.

However,

recent

achievements

in

image

reconstruction

allow

the

generation

of

super-resolution

MR

images

of

the

tongue

from

sets

of

orthogonal

images,

acquired

at

a

lower

resolution

and

combined

using

super-resolution

techniques

Fig.

(Woo

et

al.,

In

this

study,

we

propose,

to

the

best

of

our

knowledge,

the

first

attempt

to

segment

individual

tongue

muscles

from

MR

images.

Tongue

muscle

segmentation

is

a

challenging

task

because

the

tongue

is

a

muscular

hydrostat,

i.e.

a

composition

of

agonist/antagonist

muscles

without

any

rigid

structures

for

the

muscles

to

act

upon

(Levine

et

al.,

Because

of

this,

tongue

muscles

have

a

relatively

similar

physical

structure

and

appearance

when

observed

in

MR

images,

and

finding

the

boundaries

of

individual

muscles

in

muscular

hydrostats

is

therefore

challenging

even

for

an

experienced

observer.

Moreover,

non-trivial

speech

and

swallowing

motions,

and

lack

of

anchor

bones

are

reflected

in

a

complex

morphology

of

tongue

muscles.

To

address

these

challenges,

we

propose

to

apply

the

game-theoretic

framework

(GTF)

for

landmark-based

image

segmentation,

which

was

already

successfully

applied

to

segment

lung

fields

from

radiographs,

heart

ventricles

from

MR

cross-sections,

and

lumbar

vertebrae

and

femoral

heads

from

computed

tomography

(CT)

images

(Ibragimov

et

al.,

(Ibragimov

et

al.,

In

the

present

study,

GTF

is

adapted

to

segment

the

genioglossus

and

inferior

longitudinalis

tongue

muscles

from

super-resolution

MR

images.

However,

poor

visibility

of

tongue

muscle

boundaries

and

presence

of

reconstruction

artifacts,

such

as

intensity

mismatches,

blur,

blank

image

regions,

etc.,

call

for

improving

and

extending

the

original

GTF.

For

this

aim,

to

describe

landmarks

we

first

replace

individual

voxel

intensity-based

appearance

features

by

more

sophisticated

Haar-like

features,

and

the

consecutive

computational

costs

are

reduced

by

selecting

and

computing

the

optimal

set

of

most

descriptive

Haar-like

features

for

each

landmark.

Moreover,

the

landmarks

are

no

longer

positioned

on

the

surface

of

objects

of

interest,

as

such

surfaces

are

often

poorly

visible,

but

inside

and,

more

importantly,

outside

of

these

objects,

which

makes

GTF-based

segmentation

more

universal,

accurate

and

robust.

To

objectively

estimate

the

performance

of

GTF,

we

also

apply

and

evaluate

the

performance

of

B-splines

and

demons

atlasing

approaches.

The

obtained

results

are

compared

with

the

inter-observer

segmentation

variability,

which

facilitates

to

understand

the

complexity

of

the

segmentation

problem

and

its

potential

for

computerized

tongue

muscle

analysis..

The

paper

is

organized

as

follows.

Section

presents

the

details

of

GTF,

augmented

by

Haar-like

appearance

features

for

landmark

detection.

Section

focuses

on

the

tongue

image

database

with

the

corresponding

tongue

muscle

reference

segmentation

and

landmark

annotation,

and

comparison

of

the

obtained

results

to

alternative

segmentation

approaches.

Section

discusses

the

obtained

results

from

the

perspective

of

segmentation

performance,

computation

time

and

applied

methodology.

We

conclude

in

Section

with

directions

for

future

research.

Computerized

segmentation

of

tongue

muscles

is

valuable

not

only

as

a

diagnostic

tool

but

also

as

a

support

to

manual

segmentation.

This

study

is

the

first

attempt

to

automatically

segment

tongue

muscles

from

MR

images.

The

muscles

of

interest

represented

by

the

genioglossus

and

inferior

longitudinalis

were

automatically

segmented

by

applying

GTF

as

well

as

B-splines

and

demons

atlasing.

The

obtained

results

were

validated

against

two

manual

segmentations,

one

of

which

was

used

as

a

reference

standard,

whereas

the

other

one

served

as

the

inter-observer

variability

estimation.

Although

only

two

tongue

muscles

were

considered

as

objects

of

interest,

the

analyzed

segmentation

approaches

can

segment

the

whole

tongue

area

without

computation

performance

deterioration

or

training

dataset

modification.

In

the

case

of

GTF,

this

universality

is

ensured

by

the

fact

that

landmarks

evenly

cover

not

only

the

muscles

of

interest,

but

the

whole

tongue

and

some

distinguishable

anatomical

structures

around

it.

In

the

future,

we

therefore

plan

to

segment

other

tongue

muscles,

such

as

the

superior

longitudinalis,

hyoglossus,

styloglossus,

etc.,

without

or

with

minor

training

dataset

modifications.

When

a

sufficient

level

of

segmentation

accuracy

is

reached,

we

can

focus

on

analyzing

pathological

and

postoperative

cases.

Segmentation

of

tongue

muscles

from

high-resolution

MR

images

combined

with

whole

tongue

segmentation

from

dynamic

low-resolution

MR

images

is

namely

of

great

importance

in

oral

cancer

surgery

planning.

We

presented

the

first

attempt

to

automatically

segment

tongue

muscles

from

MR

images.

Being

a

muscular

hydrostat,

the

tongue

does

not

contain

any

bony

structures,

which

are,

in

general,

easier

to

identify

and

segment

because

they

have

clearly

visible

boundaries

and

rigid

shape.

Moreover,

without

bony

structures

to

act

upon,

tongue

muscles

form

a

complex

system,

where

each

muscle

lengthens

by

acting

upon

other

tongue

muscles.

Such

tongue

morphology

therefore

does

not

only

limit

the

applicability

of

computerized

segmentation

methods

based

on

intensity

classification

and

surface

evolution,

but

makes

also

manual

segmentation

challenging.

In

this

study,

we

addressed

this

problem

by

adapting

an

existing

computerized

landmark-based

segmentation

framework

to

tackle

the

morphological

properties

of

the

tongue

and

its

muscles,

and

validated

the

obtained

segmentation

results

against

manual

and

alternative

computerized

segmentation

approaches..

All

of

the

applied

segmentation

approaches

suffer

from

artifacts

in

tongue

images

that

are

reconstructed

from

stacks

of

orthogonal

images.

As

each

image

has

to

be

acquired

in

a

short

time

frame,

the

orthogonal

images

do

not

completely

cover

the

imaged

volume

but

overlap

only

with

the

tongue

region

(Fig.

This

introduces

abruptions

followed

by

blank

regions,

i.e.

regions

without

assigned

intensities,

in

the

reconstructed

image.

These

blank

regions

are

located

in

the

eight

corners

of

the

image

and

considerably

affect

the

computation

of

appearance

likelihood

maps

for

voxels

close

to

the

tongue

surface

or

on

the

chin

and

mandible.

Moreover,

eventual

rotations

of

the

observed

anatomy

together

with

the

natural

variability

of

the

size

of

the

jaw

do

not

allow

an

observer

to

estimate

the

anatomical

regions,

which

will

be

covered

by

blank

regions.

The

described

limitation

is

less

pronounced

in

the

case

of

B-splines

and

demons

atlasing,

as

the

images

were

cropped

to

the

volume

of

interest

containing

the

tongue.

Another

disadvantage

of

reconstructed

images

is

related

to

intensity

mismatches

that

appear

due

to

slight

misalignments

of

orthogonal

images

or

when

intensities

of

orthogonal

images

do

not

perfectly

correspond.

These

mismatches

introduce

false

boundaries

and

affect

the

performance

of

both

appearance

likelihood

maps

used

in

GTF

and

similarity

measures

used

for

registration

in

B-splines

and

demons

atlasing..

The

previously

described

disadvantages

of

reconstructed

images

and

poor

visibility

of

inter-muscle

boundaries

may

lead

to

distorted

segmentation

results.

The

number

and

strength

of

distortions

can

be

reduced

by

having

a

sufficiently

large

training

database.

Adding

new

training

images

is

especially

effective

for

Bsplines

and

demons

atlasing

approaches,

where

distorted

results

for

a

single

registration

can

be

compensated

by

the

remaining

correct

registrations

that

form

the

atlasing

procedure.

This

issue

can

be

additionally

addressed

by

limiting

the

elasticity

of

registration

transformations,

so

that

the

shapes

of

the

depicted

objects

can

be

preserved

during

registration.

However,

if

a

false

boundary

is

close

to

a

true

one

or

if

the

boundary

is

extremely

poorly

visible,

which

often

occurs

in

the

case

of

tongue

muscles,

distortions

may

not

be

avoided.

GTF

is

theoretically

more

sensitive

to

distortions,

as

a

single

registration

is

performed

after

landmarks

are

detected.

If

most

landmarks

located

on

the

periphery

of

the

landmark

set

are

considerably

shifted

from

their

actual

positions,

all

training

images

will

be

the

incorrectly

registered

to

the

target

image.

Similarly

to

B-splines

and

demons

atlasing,

the

distortions

can

be

reduced

by

limiting

the

elasticity

of

transformations

for

landmark-based

registration.

This

implies

that

the

detected

landmarks,

which

are

considerably

shifted

from

the

landmark

set,

will

not

be

aligned

with

corresponding

landmarks

from

the

training

set

if

the

alignment

requires

an

extremely

elastic

registration.

Although

such

sensitivity

to

incorrectly

detected

landmarks

can

potentially

reduce

the

segmentation

robustness,

GTF

resulted

in

a

higher

mean

value

and

lower

SD

of

the

Dice

coefficient

in

comparison

to

B-splines

and

demons

atlasing.

Better

results

were

obtained

due

to

the

manual

annotation

of

images

in

the

training

set

with

landmarks

that

have

distinctive

appearance

and

spatial

position,

which

reduces

the

number

of

incorrect

detections..

Object

landmarking

has

received

considerable

attention

in

the

literature

during

the

last

couple

of

decades.

Landmarks

are

always

defined

according

to

the

appearance

conditions

and/or

geometrical

conditions,

i.e.

as

points

that

are

clearly

visible

in

the

image

and/or

as

points

representing

curvature

extrema,

terminal

and

centerline

intersection

points

(Rohr,

Well-defined

landmarks

simultaneously

satisfy

several

of

the

above

mentioned

conditions

and

mark

anatomically

meaningful

points

(Lu

et

al.,

Proctor

et

al.,

Liu

et

al.,

Donner

et

al.,

object

corners

and

centers

(Ibragimov

et

al.,

and

evenly

cover

object

boundaries

(Stegmann

et

al.,

van

Ginneken

et

al.,

In

the

present

work,

all

types

of

landmarks

were

used,

namely

anatomically

meaningful

points

(e.g.

landmarks

marking

teeth),

object

corners

and

centers

(e.g.

tongue

tip

and

landmarks

on

genioglossus

mid-sagittal

plane),

and

points

evenly

distributed

on

object

surfaces

(e.g.

landmarks

on

digastric

and

inferior

longitudinalis)..

Introducing

prior

knowledge

in

the

form

of

landmarks

gives

a

certain

advantage

to

GTF,

whereas

B-splines

and

demons

atlasing

are

not

supported

by

any

prior

knowledge.

However,

the

independence

to

prior

knowledge

allows

B-splines

and

demons

atlasing

approaches

to

easily

incorporate

automatically

segmented

images

into

the

atlas

if

the

obtained

segmentation

results

are

of

exceptional

accuracy.

Segmented

target

images

can

be

also

added

into

GTF

to

enrich

the

landmark

detection

part

of

the

framework,

which

is

however

less

straightforward.

If

the

results

of

B-splines

or

demons

atlasing

can

be

quickly

visually

inspected

or

automatically

validated,

it

is

very

time-consuming

to

ensure

the

correctness

of

landmark

detection.

An

automated

validation

procedure

should

therefore

estimate

the

detection

accuracy

relying

on

partial

payoffs

for

each

individual

landmark.

The

optimal

candidate

points

with

high

payoffs

correspond

to

high

appearance

and

shape

likelihood

values,

and

therefore

there

is

a

higher

probability

that

they

are

correctly

detected

in

comparison

to

the

optimal

candidate

points

with

low

payoffs.

This

confidence

estimation

can

be

transformed

into

weighting

coefficients

so

that

newly

detected

optimal

candidate

points

can

participate

in

defining

the

appearance

and

shape

likelihood

maps,

however,

with

smaller

weighting

coefficients

than

for

the

manually

positioned

landmarks..

The

segmentation

results

(Table

obtained

by

all

of

the

applied

approaches

are

promising,

with

GTF

performing

better

than

B-splines

or

demons

atlasing.

In

terms

of

the

symmetric

surface

distance,

segmentation

results

were

similar

for

both

the

genioglossus

and

inferior

longitudinalis

muscle.

In

the

case

of

GTF,

the

mean

values

were

around

d

mm

with

a

relatively

low

corresponding

SD,

which

can

be

considered

satisfactory

when

taking

into

account

image

voxel

size

of

Â

Â

mm.

In

terms

of

the

Dice

coefficient,

segmentation

results

were,

on

the

other

hand,

better

for

the

genioglossus

than

for

the

inferior

longitudinalis

muscle.

However,

the

genioglossus

is

a

larger

object

than

the

inferior

longitudinalis,

and

larger

objects

are

usually

associated

with

higher

Dice

coefficients

than

smaller

objects.

In

fact,

the

average

size

of

the

observed

genioglossus

muscles

was

around

mm

whereas

for

the

observed

inferior

longitudinalis

muscles

it

was

around

mm

Apart

from

the

difference

in

size,

when

observed

in

MR

images

the

genioglossus

has

more

clearly

pronounced

lateral

boundaries

in

the

region

where

it

is

connected

with

the

sublingual

gland

and

inferior

longitudinalis.

Moreover,

there

is

a

visually

distinctive

area

in

the

mid-superior

and

midposterior

part

of

the

muscle

(Fig.

On

the

other

hand,

the

inferior

longitudinalis

can

be

easily

mistaken

for

the

sublingual

gland..

All

computerized

segmentation

methods

show

inferior

results

in

terms

of

segmentation

accuracy

and

robustness

when

compared

to

the

performance

of

the

second

observer.

This

fact

indicates

that

there

is

still

room

for

improvement

before

computerized

tongue

muscle

segmentation

becomes

a

fully

reliable

diagnostic

tool.

On

the

other

hand,

the

relatively

low

level

of

agreement

between

manual

segmentations

confirms

that

the

problem

is

challenging

and

subject

to

ambiguities.

This

observation

correlates

with

the

general

rule

that

muscles,

lesions,

tumors

and

glands

have

in

MR

images

relatively

blurred

boundaries,

and

therefore

cannot

be

segmented

as

accurately

as

bones

in

CT

images.

Intensity

mismatches,

blur

and

presence

of

blank

regions

originating

from

image

reconstruction

represent

additional

obstacles

for

both

manual

and

computerized

segmentation.

However,

the

current

results

show

that

computerized

tongue

muscles

segmentation

has

potential,

and

that

the

obtained

results

can

be

already

used

for

assisting

clinicians

in

diagnosis

and

postoperative

monitoring..

The

applied

segmentation

approaches

are

not

limited

to

the

genioglossus

and

inferior

longitudinalis

muscles.

However,

to

segment

a

different

object

of

interest,

reference

segmentations

and,

in

the

case

of

GTF,

landmark

annotations

have

to

be

available.

Nevertheless,

the

inclusion

of

new

objects

of

interest

would

not

considerably

affect

the

computation

time.

In

the

case

of

GTF,

the

computation

time

depends

mostly

on

the

number

of

landmarks,

while

in

the

case

of

B-splines

and

demons

atlasing,

it

is

related

to

the

number

of

images

in

the

database.

According

to

the

applied

settings,

GTF

took

on

average

min

for

segmentation

(implementation

in

C++

with

code

parallelization,

execution

on

a

personal

computer

with

Intel

Core

processor

at

GHz

and

GB

of

memory),

which

proved

to

be

more

than

faster

in

comparison

to

alternative

approaches.

However,

it

must

be

emphasized

that

GTF

and

B-splines

atlasing

were

both

implemented

in

C++

using

code

parallelization,

whereas

demons

atlasing

was

implemented

in

Matlab

and

without

code

parallelization.

Although

direct

comparison

of

computation

times

is

not

fully

transparent

as

different

programming

languages

were

used,

the

computational

efficiency

of

GTF

is

supported

by

its

single

registration-based

architecture.

We

evaluated

the

segmentation

performance

in

terms

of

Dice

coefficient

j

and

symmetric

surface

distance

d

for

the

genioglossus

and

inferior

longitudinalis

muscles

(Table

For

both

muscles,

the

resulting

mean

SD)

values

were

j

and

d

mm

for

the

second

observer,

j

and

d

mm

for

GTF,

j

and

d

mm

for

B-splines

atlasing,

and

j

and

d

mm

for

demons

atlasing.

The

results

are

for

a

selected

image

shown

in

Fig.

We

additionally

evaluated

the

performance

of

landmark

detection

part

of

GTF.

The

resulting

mean

±SD

values

of

the

landmark

detection

error

(i.e.

the

distance

between

the

detected

and

reference

landmark

positions)

was

mm,

while

the

appearance

likelihood

value

was

for

the

detected

landmarks

and

for

the

reference

landmarks,

all

computed

for

the

whole

set

of

landmarks.

Relatively

large

values

for

the

landmark

detection

error

do

not

result

in

a

comparable

segmentation

error,

as

landmarks

located

on

object

surface

are

very

similar

to

the

neighboring

voxels,

and

can

therefore

slide

along

that

surface,

which

increases

the

landmark

detection

error

but

does

not

considerably

affect

the

segmentation

results.

The

high

appearance

likelihood

value

of

obtained

for

the

reference

landmarks

indicates

that

the

selected

Haar-like

appearance

features

can

correctly

model

landmarks

in

the

tongue

area.

Fig.

Atlasing

results

for

a

selected

super-resolution

MR

image

of

the

tongue,

shown

in

a

sagittal

cross-section

and

obtained

by

applying

(a)

the

game-theoretic

framework,

(b)

B-splines

atlasing

and

(c)

demons

atlasing.

In

the

first

row,

the

results

are

shown

as

semi-transparent

domains,

where

the

red

color

indicates

the

accumulated

propagations

of

reference

segmentations

from

images

in

the

training

set,

while

the

green

color

indicates

the

majority

voting

of

the

accumulated

propagations.

In

the

second

row,

the

results

are

shown

as

colored

volumes,

where

the

yellow

color

indicates

the

segmented

genioglossus

muscle,

while

the

blue

color

indicates

the

segmented

inferior

longitudinalis

muscle.

(For

interpretation

of

the

references

to

color

in

this

figure

legend,

the

reader

is

referred

to

the

web

version

of

this

article.)

Table

Segmentation

results

of

the

genioglossus

and

inferior

longitudinalis

tongue

muscles

in

terms

of

mean

(±standard

deviation)

Dice

coefficient

j

and

symmetric

surface

distance

d

for

the

second

observer,

game-theoretic

framework

(GTF),

B-splines

atlasing

and

demons

atlasing.

A

leave-one-out

cross-validation

experiment

was

performed

to

evaluate

the

performance

of

the

proposed

segmentation

framework,

which

means

that

GTF

was

iteratively

trained

on

nine

images

and

used

to

segment

the

remaining

target

image.

Each

of

the

jPj

¼

landmarks

was

searched

for

within

a

spatial

domain

that

encompassed

that

landmark

across

all

images

in

the

training

set.

For

each

landmark

p

P,

we

extracted

nine

types

of

Haar-like

features

(Fig.

at

large

scales,

computed

at

voxels

of

the

-voxels

large

neighborhood

of

the

voxel

representing

landmark

p

(Fig.

Among

the

resulting

features

types

Â

scales

Â

voxels),

jN

p

j

¼

features

with

the

highest

predictive

power

were

automatically

selected

and

used

to

define

the

appearance

likelihood

map

f

p

of

landmark

p

(Eq.

which

was

further

used

to

select

M

candidate

points

for

that

landmark

in

the

target

image.

For

each

pair

of

landmarks

p;

q

P,

a

shape

likelihood

map

g

p,q

(Eqs.

and

was

defined

by

using

r

D

mm

for

the

histogram

of

distances

D

p,q

and

r

U

-r

h

histograms

of

azimuth

angles

U

p,q

and

polar

angles

h

p,q

and

by

weighting

the

contribution

of

these

histograms

by

k

and

k

(Ibragimov

et

al.,

The

OAG-C

shape

representation

was

obtained

by

applying

the

k-means

algorithm

to

separate

jPj

¼

landmarks

into

k

clusters,

each

consisting

of

k

¼

landmarks

(as

k

Á

k

¼

jPj,

fifteen

dummy

landmarks

were

added

to

corresponding

clusters),

and

then

solving

the

previously

described

transportation

and

assignment

problems

to

obtain

the

set

of

indicator

functions

and

The

generated

appearance

and

shape

likelihood

maps

were

incorporated

into

matrices

of

partial

payoffs

W

p,q

(Eq.

by

using

s

(Ibragimov

et

al.,

and

then

combined

with

the

OAG-C

shape

representation

to

detect

landmarks

in

the

target

image

(Eq.

The

segmentation

of

the

object

of

interest

in

the

target

image

was

finally

found

by

atlasing

the

segmented

objects

of

interest

from

images

in

the

training

set

according

to

landmarks

detected

in

the

target

image

(Fig.

Note

that

most

of

framework

parameters,

including

the

number

of

candidate

points

M,

standard

deviations

r

D

r

U

and

r

h

for

distance

and

angle

likelihood

maps,

the

rule

for

defining

the

number

of

clusters

k

and

number

of

landmarks

per

cluster

k,

were

adopted

from

our

previous

work

(Ibragimov

et

al.,

To

validate

the

results

of

GTF

segmentation,

we

compared

the

obtained

results

to

an

independent

manual

segmentation

performed

by

a

second

observer,

and

to

the

results

obtained

by

two

alternative

segmentation

approaches,

namely

B-splines

and

demons

atlasing,

both

of

which

are

registration-based,

not

landmark-based.

For

computerized

segmentation,

images

from

the

database

(i.e.

the

GTF

training

set)

were

first

registered

to

the

target

image

using

ever

B-splines

or

demons

registration

and

the

obtained

transformation

fields

were

then

used

to

propagate

the

segmented

objects

of

interest

from

images

in

the

database

to

the

target

image.

Finally,

a

majority

voting

of

the

accumulated

propagations

was

applied

to

segment

the

object

of

interest

in

the

target

image

(Fig.

In

the

case

of

B-splines

atlasing,

a

publicly

available

toolbox

(Klein

et

al.,

was

used

for

image

registration,

which

consisted

of

an

initial

rigid

followed

by

a

B-spline

transformation

using

the

advanced

mean

square

and

normalized

correlation

metrics

as

similarity

measures,

i.e.

as

it

was

recommended

for

the

head

and

neck

segmentation

from

CT

images

(Fortunati

et

al.,

In

the

case

of

demons

atlasing,

a

publicly

available

implementation

(Kroon)

was

used

for

image

registration,

which

consisted

of

an

initial

rigid

followed

by

a

demons

transformation

using

a

voxel

velocity

field

with

the

Gaussian

kernel

(SD

of

voxels)

and

diffusion

regularization

(SD

of

voxel).

Moreover,

as

in

the

case

of

GTF

each

landmark

was

searched

for

within

a

spatial

domain

that

was

limited

to

the

region

encompassing

that

landmark

across

all

images

in

the

training

set,

the

images

were

in

the

The

image

database

is,

together

with

reference

segmentations

and

landmark

annotations,

planned

to

be

publicly

released.

case

of

B-splines

and

demons

atlasing

cropped

to

a

volume

of

interest

containing

the

tongue

in

order

to

ensure

a

proper

comparison

of

segmentation

approaches.

Restricting

the

volume

of

interest

is

a

valid

and

safe

step

for

the

tongue

muscle

segmentation

problem

considering

the

nature

of

analyzed

images.

The

original

images

with

high

in-plane

resolution

were

acquired

in

such

a

way

that

all

of

them

depict

the

tongue

region.

During

the

reconstruction

procedure,

the

images

are

combined

so

that

their

intersection,

i.e.

the

tongue

region,

is

located

in

the

center

of

the

resulting

volume.

Genioglossus

muscle

Inferior

longitudinalis

muscle

Both

muscles.

Second

observer

GTF

B-splines

atlasing

Demons

atlasing

B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O B O O B O O O O O O O O O O O O O O O O O O B O O B O O O O O B O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O B O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O


IMAGE DESCRIPTION WITH NONSEPARABLE TWO-DIMENSIONAL CHARLIER AND MEIXNER MOMENTS This paper presents two new sets of nonseparable discrete orthogonal Charlier and Meixner moments describing the images with noise and that are noise-free. The basis functions used by the proposed nonseparable moments are bivariate Charlier or Meixner polynomials introduced by Tratnik et al. This study discusses the computational aspects of discrete orthogonal Charlier and Meixner polynomials, including the recurrence relations with respect to variable x and order n. The purpose is to avoid large variation in the dynamic range of polynomial values for higher order moments. The implementation of nonseparable Charlier and Meixner moments does not involve any numerical approximation, since the basis function of the proposed moments is orthogonal in the image coordinate space. The performances of Charlier and Meixner moments in describing images were investigated in terms of the image reconstruction error, and the results of the experiments on the noise sensitivity are given. Moments have been extensively used in image processing, pattern recognition and computer vision. 1, 8, 13, 19, 24, 25, 28 Teague proposed continuous orthogonal polynomials as the basis functions to calculate continuous moments. 16 These orthogonal polynomials include Zernike polynomials, Legendre polynomials, and pseudo-Zernike polynomials. Practical implementations of continuous orthogonal moments in digital image analysis involve two main dilemmas 9 : (i) discrete approximation of the continuous integrals, and (ii) transformation of the image coordinate system into the domain of polynomials. Consequentially, the development of moments led to their discrete versions. Recently, Mukundan et al. and Yap et al. de¯ned discrete orthogonal moments based on the discrete Tchebichef and Krawtchouk orthogonal polynomials respectively. 10, 22 For the discrete orthogonal moments to be of use in image processing, it must be extensible to two dimensions. Two forms of twodimensional moments have been suggested: a separable form and a nonseparable form. A standard method computing two-dimensional separable form of moments is via the row-column decomposition, which takes advantage of the separability of basis functions of the moments. 10, 22, 23 That is, the two-dimensional moment is broken up into two one-dimensional moments computed in row-column or column-row wise format. The nonseparable form moments do not work the same way; however, it can be written using bivariate polynomials as the basis function of moments. This requires less computation than for the separable moments. To the best of our knowledge until now, no nonseparable form of two-dimensional moments has been de¯ned in pattern recognition community. This is mainly due to the fact that bivariate orthogonal polynomials are too di±cult to use. The purpose of this paper is to introduce bivariate discrete orthogonal polynomials as basis functions of the moments, and to expect that they have potential applications in image processing and pattern recognition.. Actually, bivariate orthogonal polynomials have been investigated by many authors. 2À5,14,15,20,21 Bivariate orthogonal polynomials have been studied as the generalization of one variable's orthogonal polynomials. 3 However, comparing to the theory of one variable, the structure of bivariate discrete orthogonal polynomial is much more complicated. In 1982, Kowalski introduced a matrix notation for polynomials applied in multiple variables, and showed the matrix notation with the properties similar to three-term recurrence relations. 4, 5 Xu also presented a secondorder di®erence equations and bivariate discrete orthogonal polynomials in Refs. 20 and 21. More recently, Rodal et al. made a systematic study of the orthogonal polynomials solutions of a second order partial di®erence equation with hypergeometric type on two variables in Refs. 14 and 15. Although bivariate orthogonal polynomials play an important role in applications such as numerical analysis, optics, and quantum mechanics, 11, 12, 18 much less attention has been paid to the application of bivariate orthogonal polynomials in image analysis.. In this study, we have introduced the bivariate Charlier and Meixner polynomials derived from the methods proposed by Tratnik. 17 Then, the nonseparable form bivariate moments, Charlier and Meixner, are constructed using their orthogonal polynomials, respectively. Due to the new sets of moments being orthogonal in the discrete domain of the image coordinate space, the proposed moments completely eliminate the two problems referred to above. The image can be reconstructed from a su±ciently large number of computed moments. In order to reduce the numerical errors caused in the computation of Charlier and Meixner moments, this study presents the three-term recurrence relations about variable x and polynomials order n. The simulated results demonstrate that the proposed two-dimensional nonseparable form moments Charlier and Meixner have better image description capabilities.. The organization of this paper is given as follows: in Sec. 2, we recall the de¯nition of the classical discrete orthogonal polynomials of one variable. Section 3 shows two recurrence relations about univariate Charlier and Meixner polynomials. It is followed by bivariate discrete orthogonal polynomials in Sec. 4. In Sec. 5, we de¯ne the nonseparable discrete orthogonal moments with bivariable orthogonal polynomials as basis functions. Some experimental results are presented and discussed in Sec. 6. Section 7 concludes the study. Although moment functions had been extensively utilized for a number of image processing tasks, no bivariate discrete orthogonal polynomials had been used as basis function sets to directly de¯ne the two-dimensional moments. In this paper, we introduced two nonseparate discrete orthogonal moments: Charlier and Meixner moments. The image representation capability of the proposed moments had been veri¯ed. We did the comparison of two most recent orthogonal moments: continuous orthogonal Legendre moments and discrete orthogonal Tchebichef moments. Experimental results showed that the proposed moments were comparable to Legendre moments and moderately poorer than Tchebichef moments.. The main contribution of this study is as follows: (1) This work has presented two formulae to obtain x and n based recurrence relations calculating the univariate Charlier and Meixner polynomials. (2) We de¯ned two-dimensional nonseparable discrete orthogonal moments based on bivariate discrete orthogonal polynomials in the image processing and pattern recognition¯eld. (3) The proposed method here could be easily extended to obtain other bivariate orthogonal polynomials and their corresponding moments. Due to the nonsepariability of bivariate orthogonal polynomials, Charlier and Meixner moments' values could not be computed in two steps by successive onedimensional operations on rows and columns of an image. Thus, pixel by pixel calculation was needed to obtain the moments' values, and this process was very expensive. Further on, our work will focus on the fast algorithm to calculate nonseparable Charlier or Meixner moments.

O O O O O B O B O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O B I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O B I I O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O B I I I O O O O O O O O O B I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O B I I I O O B I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O


A simulation-based method to evaluate the impact of product architecture on product evolvability Products evolve over time via the continual redesigns of interdependent components. Product architecture, which is embodied in the structure of interactions among components, influences the ability for the product to be subsequently evolved. Despite extensive studies of change propagation via inter-component connections, little is known about the specific influences of product architecture on product evolvability. Related metrics and methods to assess the evolvability of products with given architectures are also under-developed. This paper proposes a simulation-based method to assess the isolated effect of product architecture on product evolvability by analyzing a design structure matrix. We define product evolvability as the ability of the product's design to subsequently generate heritable performance-improving variations, and propose a quantitative measure for it. We demonstrate the proposed method by using it to investigate a wide spectrum of model-generated DSMs representing products with varied architectures, and show that modularity and inter-component influence cycles promote product evolvability. Our primary contribution is a repeatable method to assess and compare alternative product architectures for architecture selection or redesign for evolvability. A second contribution is the simulation-based evidence about the impacts of two particular product architectural patterns on product evolvability. Both contributions aim to aid in designing for evolvability. Products or engineering systems continually evolve over time via heritable design changes, which can be either initiated or emergent (Otto and Wood 1998; Eckert et al. 2004; Fricke and Schulz 2005; Rajan et al. 2005) . Product evolvability reduces long-term difficulties for design advancements over the product's life span. It is particularly desirable in industries where innovation dynamism is high and product redesign is a norm (Suh 1990; Silver and de Weck 2007; Beesemyer et al. 2011) , and for start-up companies for which markets are uncertain and frequent redesigns are foreseeable. Different product designs may inherit different degrees of evolvability. Knowledge about the determinants of product evolvability and the methods to assess it are needed to guide designing for evolvability.. The engineering design literature has suggested that product architecture, i.e., the pattern of interdependences following which components influence each other, can affect the ability of a product's design to be evolved in the future (Ulrich 1995; Whitney et al. 2004; Tilstra et al. 2012 ). In particular, many studies on product architecture and design changes have been based on the analysis of design structure matrix (DSM) in different forms Eppinger and Browning 2012; Tilstra et al. 2012) . However, quantitative methods to assess alternative product architectures in terms of product evolvability are still lacking. As a result, our knowledge of the impact of product architecture on product evolvability is limited.. In this paper, we focus on the evolvability of a product and investigate how it can be conditioned by product architecture. The concept of evolvability arose in biology. In a Darwinian evolutionary process, variations that have fitness improvements are most likely to be selected and heritable (Wagner and Altenberg 1996; Kirschner and Gerhart 1998) . Following an analogy between how the interactions of genes condition their variations in biological evolution and how the interdependences among components condition their design changes in product evolution, we define ''product evolvability'' 1 as the ability of a given product design to subsequently generate heritable performance-improving variations in design configuration, i.e., alternative combinations of design choices of all components.. Our aimed contribution is a simulation-based method that analyzes a design structure matrix to assess the isolated effects of product architecture on product evolvability. The core of the method was drawn from the ''NK model,'' which was originally created to study organism evolution via genome mutations (Kauffman and Weinberger 1989; Kauffman 1993) and later adopted into the field of organization sciences (Levinthal 1997) . We also propose a metric of product evolvability, based on the NK framework. The model and metric are based on simulating and analyzing the overall landscapes of performances (or fitness) mapped from the total design choice space of a given product. This method is then applied to assessing the evolvability of a wide spectrum of model-generated networks (or DSMs) that represent products with gradually varied architectures.. The simulation exercises lead to our second contribution-evidence about the impacts of two particular product architectural patterns, including component influence cycles and interaction density, on product evolvability. ''Cycle'' is the set of components which have an influence or dependency path to every other 2 (MacCormack et al. 2006; Sosa et al. 2013) . Prior research has shown that component cycles require iterative problem solving and give rise to product defects (Smith and Eppinger 1997a, b; Mihm et al. 2003; Sosa et al. 2013) . Instead, herein we are interested in the impact of component dependence cycles on product evolvability. Component interaction density denotes the number of dependences among a given set of components and has been used as a proxy of product modularity in the literature (Martin and Ishii 2002; MacCormack et al. 2006; Sosa et al. 2007 Sosa et al. , 2013 . If a component is influenced by or dependent on fewer other components (implying a lower interaction density), it is more modular.. The remainder of the paper is organized as follows. In Sect. 2, we review the relevant literature. Section 3 introduces the simulation-based method to assess a product's evolvability by DSM analysis. Section 4 applies the method to assessing a wide spectrum of simulated DSMs that represent products with gradually varied architectures, followed by a discussion of theoretical and practical implications in Sect. 5. Section 6 concludes with the contributions and limitations of the present paper, and future research directions. Product evolvability is particularly important for start-up companies which face high uncertainty in market demands, and the companies in highly dynamic industries. This study makes both methodological and theoretical contributions to the studies of product evolvability, as well as changeability. Our proposed method and theories are useful for the assessment, comparison and selection of alternative or competing product architectures, in addition to the redesign of product architecture purposefully for either improving or reducing evolvability, depending on the interests of the engineers or system architects.. Methodologically, we have presented a repeatable method and a quantitative metric of product evolvability to assess the isolated impact of product architecture on the product's evolvability. The method and metric incorporate the emphases of the evolvability concept on inheriting the architecture and selecting fitness-improving variations, beyond the general changeability concept, and measure evolvability as the potential of a product design, given its architecture, to have fitness-improving variations, instead of the extent to which the product has evolved. The assessment method can be potentially embedded into CAD/ CAE software and existing DSM software as an additional function of DSM analysis, to aid in designing for evolvability. Note that our simulation-based method is easy to implement because it only requires the most basic binary DSM data that capture the topological pattern of component interactions. With focusing on the impact of product architecture on evolvability, the impacts of other physical, social and probabilistic aspects of component interactions are all randomized in the simulations and thus neutralized when statistically associating product architecture with evolvability. Such randomization reduces the barriers for the application of the proposed method in practices.. Theoretically, this paper also provides evidence on the specific impacts of two product architectural patterns on product evolvability. Specifically, product evolvability is promoted by component influence cycles, but is limited by component interaction density. Such understandings allow engineers and system architects to infer and predict the evolvability of their products using only the most basic DSM data. The new understanding also provides guidance on redesigning product architectures purposefully to adjust fitness landscape ruggedness for the desired level of product evolvability or guidance on product redesign strategies (e.g., one or many component changes at a time) for fixed product architectures. In the other words, such knowledge provides architecture design guidelines for evolvability. In brief, both of our methodology and theoretical contributions aid in designing for evolvability.. Note that, this paper examines the evolvability of a product at a given point of time, as determined by its component DSM. The present analysis is static in nature. The real product evolution process and dynamics are not investigated, and the evolution of evolvability itself and product architectures over time are also not investigated. As the next step, we plan to develop a dynamic model of product evolution processes to investigate alternative evolutionary trajectories and long-run performances of product designs conditioned by different product architectures and redesign strategies.. This paper has only analyzed two exemplary architectural lenses, i.e., cycle and density, to demonstrate the influences of product architecture on evolvability, whereas product architectures vary and be characterized in many more ways. Future research may investigate the influences of additional product architecture patterns on evolvability and develop more design guidelines for evolvability. We also hope this study can stimulate the development of more and better product evolvability metrics and calculation methods. By then, test cases will be needed to assess and compare alternative metrics and methods. In addition, future research should validate the proposed method in real engineering design practices and investigate the effectiveness of adding evolvability assessment of product architectures into the prototype evaluation and selection activities of engineers and system architects, in the prototyping process.. (1) Network size (N): the total number of components in the product. (2) Interaction density (K): the average number of components that each component influences. For a product with N components and M influence links, K = M/N. In the context of product design, it is an indicator of product integrality or reverse indicator of product modularity. (3) Influence diversity (D): the scope of other components that an average component can influence in an ideal and hypothesized product hierarchy (Fig. 6a ) or a ''serial design chain,'' as Sosa et al. (2013) put it. Its reverse concept is ''influence specificity,'' which indicates the degree to which a component's influences concentrate on a subset of components that are proximate to each other in the product hierarchy. As influence diversity increases, interinfluence relationships among components will gradually deviate from the pure serial or upstreamdownstream manner.. Baseline Scenario (D 5 0). We begin by creating an ideal and hypothesized sequential (upstream-downstream) influence or dependence relationship between components in their interaction network, which will be rewired later to generate more general and cyclic networks. To do this, each of the N components is assigned to a uniformly distributed random position k i , along an axis ranging from 0 to 1 (Fig. 6a ). Consider a focal component i with position value k i , the entire downstream interval for component i has a length (1 -k i ). The component's ''influence niche'' range r i is the interval containing the components that it can influence, as defined by. where X is a random variable between 0 and 1, and the probability distribution of X is component independent (to be set up later).. The focal component's influence niche range can be located anywhere downstream. The position parameter b i fixes the location of component i's niche range by defining its left most point. b i is assumed to be uniformly distributed between k i and (1r i ). Networks generated this way are strictly acyclic; there is no influence cycle among any components. Thus, they can be used as the basis for later rewiring to introduce cycles.. The niche range of a particular component r i , as defined in Eq. (4), is a random variable whose statistical properties are affected by the number of components (N) and interaction density (K) of the product. Now we explain this association further. First, the density of components on the entire segment is N. Because the distribution of these components is uniform, the expected number of components in the niche for component i is as follows:. For the entire system, excluding the rightmost component, the sum of the expected number of component that each component can influence is as follows:. Eðr i Þ ð 6Þ. In addition, the expected average number of components that each components influences is simply. Thus, the random variable X is not only constrained to be between 0 and 1, but its expected value is. E(K) is given as the input variable K to the network construction model. Note that, although K i is componentspecific and randomly distributed, K is the average and an empirically measurable property of a given product's component network. To generate a network, we need to choose an appropriate functional form for the distribution of X and then impose the constraint of Eq. (8). For computational ease, a beta-distribution with parameters (1, b) is used for the random variable X. This allows E(X) to be in a computationally convenient form, 1/ (1 ? b). Given K and N as inputs, b will be determined by. Then, a random niche range constrained by (4) can be given to each of the aforementioned array of components randomly organized between 0 and 1 on the axis. The focal component is then linked to each component in its influence niche. First, the negative impact of component interaction density on product evolvability is intuitive. It supports the assertion that modular product architecture promotes product

O O O O O O O O B I O B I O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I O O O B I I O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O B I O O