Enumerated type semantics for the calculus of looping sequences Abstract. The calculus of looping sequences is a formalism for describing the evolution of biological systems by means of term rewriting rules. In this paper we enrich this calculus with a type discipline which preserves some biological properties depending on the minimum and the maximum number of elements of some type requested by the present elements. The type system enforces these properties and typed reductions guarantee that evolution preserves them. As an example, we model the hemoglobin structure and the equilibrium between cell death and division: typed reductions prevent undesirable behaviors. In the last few years, formalisms for the description and analysis of biological systems have been introduced and investigated, see [14] . These formalisms allow the study of biological systems by using methods, such as static analysis, model checking or quantitative computer simulations, which are practically unknown to biologists. Among the many formalisms that have either been applied to or inspired from biological systems, the most notable are: automata-based models [1, 10] , rewrite systems [8, 12] , and process calculi [7, [13] [14] [15] . Automata-based models permit the direct use of many verification tools such as model checkers; rewrite systems describe biological systems with a notation that can be easily understood by biologists; by means of process calculi the behavior of systems can be studied componentwise.. In [4, 5, 11] , Milazzo et al. introduced a formalism, called Calculus of Looping Sequences (CLS for short), for describing biological systems and their evolution. CLS combines rewrite systems, being based on term rewriting, and process calculi, using features such as a commutative parallel composition operator, and semantic notions such as bisimulations.. Homeostasis is the property of a system that regulates its internal environment and tends to maintain stable conditions that are optimal for survival: when this equilibrium is disturbed, built-in regulatory devices respond to establish again the balance. Different living organisms have some homeostatic mechanism to maintain some conditions in specific ranges: the human body, like in all the warm-blooded animals, maintain a near-constant body temperature using mechanisms such as vasodilation and vasoconstriction, and microorganisms maintain the iron presence above a minimum level to maintain life but up to a maximum level to avoid iron toxicity. In biology a huge number of elements are made up of a certain number of different subcomponents: proteins are composed by different domains, some proteins are multimers, rybosomes are a mixture of RNA and proteins, etc. Monomers are molecules that may become chemically bounded to other monomers to form a polymer: for example, antibodies can be monomers, dimers or pentamers, the Triose phosphate isomerase, an enzyme essential for efficient energy production, is a dimer of identical subunits, and the Glutamate dehydrogenase 1, a mitochondrial matrix enzyme with a key role in the nitrogen and glutamate metabolism, is a hexamer.. In [2, 3, 6, 9] different type disciplines for CLS are presented. The type discipline in [6, 9] preserves some biological properties deriving from the fact that certain elements may require the presence and the absence of others. With the type system introduced in [6, 9] , it is not possible to model constraints involved in homeostasis and polymers, because not only elements require the presence or absence of others, but they require that the numbers of these elements are in given intervals. In the type system introduced in this paper, we assume that for each element we fix the minimum and the maximum number of other elements that the element requires. We enrich CLS with a type discipline and typed reductions that guarantee the soundness of reduction rules with respect to the properties of biological systems deriving from the minimum and the maximum requested numbers of elements. This type discipline is a generalization of the one in [6, 9] .. The remainder of the paper is organized as follows. In Section 2 we introduce the calculus of looping sequences. In Section 3 we develop the type discipline for the minimum and the maximum requested elements and we embed it into the semantics of the calculus. In Section 4 we use the machinery of principal typing to infer the type constraints of rewrite rules, and check their applicability. In Section 5 we use our typing discipline to describe the hemoglobin structure and to regulate the equilibrium between cell death and division. Finally, in Section 6 we draw some conclusions. In this paper we introduced a type discipline for the Calculus of the Looping Sequences which allows to describe and to limit the structure of systems and subsystems: this behavior cannot be easily reproduced only by means of reduction rules. In this way we may transfer the complexity of some biological properties from reduction rules to types, describing the behavior of biological systems using only general rules. In [6, 9] some rules are classified as ∆-safe rules, i.e. rules having the same type for the left-side and the right-side patterns: these rules do not change the type of terms to which they are applied. In the present type discipline, for typing we count the number of elements of a term. Since rules usually change something in the term, adding or removing elements, in a rule the number of elements in the right-hand-side is different from the number of elements in the left-hand-side, and therefore their types are also different. According to this idea, we decided to not include ∆-safe rules in the present semantics, because using the present type discipline very few reduction rules are ∆-safe. In nature, the minimum and maximum levels presented in this paper can be sometimes exceeded, even if this would lead the system to disease: even if undesiderable, the balance between cell death and division can be broken, leading to death or tumors. On the contrary, our typed semantics completely exclude these kinds of situations. According to this idea, we could modify our typed semantics, allowing transitions which lead to untypable terms, but signaling that some undesired state has been reached. To this aim we should add to our typed semantics the rule ℜ = P 1 → P 2 ∈ R is a ∆-(P, L, M)-safe rule. to advise the modeller that some unwanted behavior is happening in the system. In this way, the modeller can check if, starting from the initial term and using the given rules, we can reach a non-typable term, i.e. a term that breaks some biological property. In biology, we do not always know the precise numbers of elements in the system, but we know their concentration, as percentage of the single elements in the whole system: for example, the corpuscles in blood are usually given as a percentage or as an absolute number per litre. Our type discipline cannot manage these cases, because it checks the exact numbers of elements in every compartment. As a possible future development, we plan to modify our type discipline to work on these cases, checking, in every compartment, not the exact numbers, but the ratio of elements with respect to the other elements.

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The concept and impact analysis of a flexible mobility on demand system Fujitsu Laboratories funding under the OSP account 6925717 ::: Fujitsu Laboratories funding under the OSP account 6927900 ::: Fujitsu Laboratories funding under the OSP account 6929605

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Agents in a Nutshell - A Very Brief Introduction Abstract-Agent-based approaches are becoming increasingly important because of their generality, flexibility, modularity, and ability to take advantage of distributed resources. Agents are used in information retrieval, entertainment, coordinating multiple robots, and modeling economic systems. Agents can recommend music, tell stories, and interact with people. They are useful for reducing humans' work and information load in tasks such as medical monitoring and battlefield reasoning. Agents are already changing the way in which we gather information, manage investments, and conduct business. This article provides an introduction to agent issues, outlines motivations for using agent-based paradigms, and describes some of their current uses. GENTS have been around for many years, but recently agent paradigms have become increasingly popular. Some of the reasons for the popularity of agents paradigms is their flexibility, modularity and general applicability to a very wide range of problems. Their recent increase in popularity is partially due to technological developments in distributed computing and robotics, and the emergence of object-oriented programming paradigms. Advances in distributed computing and robotic technologies has given rise to a greater need for paradigms such as agents that can model distributed problem solving. Object-oriented programming had introduced concepts into the main stream that are condusive structuring agent-based approaches. The goal of this paper is to provide a very brief and high level introduction to what agent systems are, including their unique properties, challenges in designing agent systems, and examples of applications. Agent-based approaches are becoming increasingly important because of their generality, flexibility, modularity, and ability to take advantage of distributed resources. Agents are used for information retrieval, entertainment, coordinating systems of multiple robots, and modeling economic systems. They are useful for reducing humans' work and information overload, in complex tasks such as medical monitoring and battlefield reasoning. They can serve as knowledge resources for designers and engineers. Agents can recommend music, tell stories, and interact with people. Continuing research issues include agent architectures, communication and coordination protocols, control, negotiation, and reuse. Deployed agents are already changing the way in which we gather information, conduct business, and manage our lives. In short, agents are here to stay [31] .

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The dialectical potential of Cultural Historical Activity Theory for researching sustainable CSCL practices This article explores conceptual and methodological challenges in researching sustainable computer-supported collaborative learning (CSCL) within authentic educational settings. It argues that to investigate the sustainability of CSCL in such settings, we need to understand how new innovations become enculturated as part of educational communities and the shared repertoires and practices of learners and teachers. The potential for Cultural Historical Activity Theory (CHAT) as a relational, dialectical framework for researching collaborative learning is examined. The article argues that, although CHAT is increasingly being used for researching educational settings, it is often employed only descriptively or as a set of guiding principles and the dialectical method, which focuses on emergent contradictions and tensions, is not always fully explored. An integrated conceptual and methodological CHAT framework is proposed for understanding the complex interrelations between discourse, actions and community and as a result how new technological innovations and knowledge creation practices can be appropriated and sustained. This is illustrated through the analytical processes undertaken in a recent empirical study of undergraduates working on an online collaborative research project. The article concludes by arguing that the dialectical method at the heart of CHAT is both unifying and problematizing and could allow us to develop a richer, more integrated and explanatory picture of sustainable CSCL activities. The field of technology-enhanced learning is highly interdisciplinary with significant communities working in and across other fields, for example psychology, sociology, sociolinguistics, cultural theory, anthropology, education, computer science, communication studies and others (Sutherland et al, 2012) . This results in wide variations in discourses and purposes; in particular, divides between sociological and psychological perspectives (Selwyn, 2011) and between macro and micro sociology (Lemke, 1990) . Related to this, computer supported collaborative learning or CSCL has always been an interdisciplinary research field whose focus of attention is on language, culture and social context (Koschmann, 1996) . Chan argues that CSCL research includes a rich array of theoretical and methodological approaches and that the field is growing as new technological affordances for interaction and engagement emerge, alongside an increasing understanding of how students engage in collaborative problem solving and coconstruction (Chan, 2011) . Stahl & Hesse (2010) also emphasize the need to push understandings and conceptualizations further; to continue to problematize and develop how we understand and conduct research in CSCL (Stahl & Hesse, 2010) . This indicates that CSCL is both a maturing and an evolving research field.. Stahl, Koschmann and Suthers (2006, p.424) suggest that there are no welldefined, consistent and comprehensive definitions of CSCL theory or methodology, which can lead to fragmentation in approaches and a lack of shared understanding. Nevertheless, most CSCL researchers share an understanding of the concept of collaboration, namely, the negotiation, construction and maintenance of shared meaning, goals and tasks Dillenbourg, 1999 , Roschelle & Teasley, 1995 . This suggests that discourse, encompassing communication and joint meaning making, are very important, though not exclusive, aspects of collaboration. Knowledge building or knowledge creation practices can also be regarded as a key aspect of collaborative learning in which new knowledge objects or social practices are created through collaboration (Lipponen, Hakkarainen & Paavola, 2004) . I argue that when investigating how knowledge creation and collaboration develop within authentic educational settings, discourse should be a key focus of analytic attention. However, I also argue, in line with Chan (2011) that a broader, multi-level analysis is required to account for the social, cultural and historical dynamics that influence and constrain this. Furthermore, we often understand very little about how these practices can endure or become mainstream or why, in so many cases, this fails to happen. Researching the sustainability 1 of practices in authentic educational settings is very important because all sectors of education suffer from an overload of innovative ideas and new pedagogical methods that are not sustained in the longer term.. This paper proposes a theoretical and methodological approach to understanding the sustainability of CSCL practices in formal and informal educational settings. I argue that to understand how CSCL designs can be sustained over time in educational settings, we need to interrogate the interconnections between meaning making and knowledge creation practices constituted in interactions between learners and the wider dynamics of educational communities. Cultural Historical 3 Activity Theory (CHAT) is proposed as an integrated conceptual and methodological framework for understanding the complex interrelations between discourse, actions and community and, as a result, how new technological innovations and knowledge creation practices can be appropriated and sustained.. Sustainability and how organizations and groups adapt and change over time are central concerns for CHAT. CHAT developed from the cultural-historical school (Cole & Engeström, 1993; Daniels, 2001; Y. Engeström, 1987) and specifically from the work of Vygotsky on the relationship between mind, activity and meditational means in human development (Vygotsky, 1978 (Vygotsky, , 1986 . There has been a dramatic growth in the popularity of CHAT (Roth, 2004; Roth & Lee, 2007) and in its use for studying educational phenomena in particular (Nussbaumer, 2011; Williams, Davis, & Black, 2007; Roth & Lee, 2007) . In part this can be attributed to the ability it affords to focus attention on the troubling divides between individual and collective, material and mental, biography and history, and praxis and theory (e.g., Cole, 1996; Roth & Lee, 2007) . Fenwick (2010) argues that CHAT forms part of an emerging grouping of socio-material approaches for understanding how the 'material' mediates everyday life. Under 'material,' she includes tools, technologies, bodies, actions, and objects, texts and discourses. She sees all these as meditational means, acting together in concert with social and political analysis of human activity. "CHAT affords a rich approach to analyzing precisely these political dynamics that are so important to workplace organizations while insisting that these dynamics intermingle the material with the social" (Fenwick 2010, p112) .. The paper first explores some of the methodological issues arising from CSCL research in authentic educational settings. This is followed by an examination of the potential of CHAT to address these challenges by paying attention to its relational and dialectical approach to analysis and by expanding CHAT to include the concepts of dialogicality and communicative action. Drawing on a recent empirical study, a multi-dimensional framework and analytical process are outlined, illustrated with related findings from the study. This paper has emphasized the importance and value of investigations into the sustainable practice of computer supported collaborative learning within educational settings. It has highlighted some of the challenges of CSCL studies that seek to pay attention to evolving and dynamic contexts and the need for a more relational perspective. Ritella and Hakkarainen (2012) highlight the gap in CSCL between one off experiments and static studies of generalized understandings, arguing that what are needed are more development studies, investigating how innovative knowledge-creation practices emerge over time. Cultural Historical Activity Theory (CHAT) has been explored for its potential to address these challenges, including a proposed multi-level relational approach to analysis. This has been illustrated by showing the analytical processes in a recent empirical study of undergraduates engaged in an online collaborative project.. In employing CHAT analytically, I have argued that we need to move beyond description and overreliance on the expanded triangle models to embrace the dialectical approach at the heart of CHAT. This involves identifying contradictions and tensions that emerge from the relations within and across the different levels and elements within an activity system and sometimes between systems (Engeström, 1987 , Rasmussen & Ludvigsen, 2009 . Developing the multidimensional aspects of the analysis helps in understanding how the object influences discourse and action at all levels within the activity system and over time. Integrating CHAT with Bakhtin's dialogic interpretation of discourse and theories of affect and relational agency (Crook, 2000 , Rommetveit, 2003 Edwards, 2005) through an expanded unit of interaction (R. Engeström, 1995) , places greater emphasis on the multivoicedness imbued in utterances, interactions and human relations within the activity system.. Understanding how collaborative and knowledge creation practices can be sustained in educational communities requires researchers to both acknowledge and address the 'cauldron' of activity, relationships and creative disturbances (Williams et al, 2007 ) that dynamic educational communities embody. Education across all sectors is subject to continual multi-dimensional transformations, which may conflict or jeopardize the integration and sustainability of new innovations and collaborative knowledge creation practices and yet some practices and innovations endure. Conceptual and methodological approaches that can help to explain the 'how' and 'why' are therefore critical for the development of teaching and learning at all stages of education. CHAT's insistence on understanding the purpose of activity (the object) and how this is interpreted by different actors in the system and instantiated within activity, discourse and practice can show how shared understandings and joint actions emerge (Lipponen et al, 2004) . Equally, the central pillar of mediation (Vygotsky, 1978) within activity systems supports the investigation of new knowledge objects, discourse and practices, created and transformed through their relations with mediational means, including digital tools and artifacts within a cultural setting. Recent attention to activity systems as sites of affective relations and dialogic communications (Roth, 2007 , Hiruma et al, 2007 Engeström, 2009 ) also enriches the investigative possibilities and as shown in this article, throws a different light on how collaborative practices are sustained over time. CHAT's multi-dimensionality, as this article has sought to show, is much more than a multi-level approach, it is holistic, iterative and relational; the dialectical method deliberately problematizes, seeking to avoid simplification and reductionism.. There are risks in trying to expand the analytical focus and consider multiple dimensions where the analysis could become too diffuse. Indeed, one of the dangers of CHAT is the tendency to try to explore everything. Engeström (2001) cautions against this in favor of focusing attention on one or more specific aspects or subsystems of a larger system, as shown in the empirical study presented here. One of the powerful aspects of CHAT is how it opens up further avenues for research through the deconstruction -reconstruction process. Applying a CHAT framework for analysis produces further questions at all stages and levels of the activity which can be drawn together for final analysis and help to identify important areas for further research.. The importance of an historical analysis and the need to conduct studies over sufficient timescales in order to understand how practices become enculturated into the community are also critical to CHAT. In the special interest group study, a 12 week module appeared at the outset to be a long timescale. However, it became clear that focusing on one module was limiting, in part because it was not possible to investigate the effects of the work on the module on students' longer term practices or how this related to other work that the students were doing in other parts of their program of study. The study also illustrates how understanding the historical context and how a curriculum innovation has developed historically adds another valuable explanatory layer and raises questions for further research. Although there are many constraints on longitudinal research, to understand how practices can be sustained and embedded in institutions, longer-term studies are needed.. The articulation of the analytical process followed in the research cited here was undertaken because little can be found in the literature about how to 'do research' using Cultural Historical Activity Theory, in particular in educational settings. However, it would be a mistake to see the analytical framework and process outlined in this paper as a 'road map' or blueprint to be followed step by step and stage by stage in an uncritical manner. It is rather an illustration of how CHAT's philosophical principles and core activity concepts can be interpreted, augmented and operationalized without losing its theoretical and dialectical values. As Roth & Lee argue "CHAT cannot be viewed as a master theory or quick fix, for true to its origins, it is subject to inner contradictions, which compel researchers to update, transform, and renew constantly so that it becomes a reflection of its object" (2007; p.218).. Furthermore, I am not arguing that CHAT is the answer to all research challenges and it should also be acknowledged that taking a multidimensional approach to CHAT can be complex and time-consuming to conduct. However, in seeking to increase understanding of how and why the practices of collaborative knowledge creation take place and are sustained in naturalistic settings, the multidimensional and dialectical method at the heart of CHAT provides a powerful explanatory tool. The dialectical method is both unifying and problematizing, allowing us to interrogate the different goals and objects in collaborative activity and explain why disturbances occur (Roth & Lee, 2007) . This can help to develop a richer, more integrated and explanatory picture of CSCL activities and how they are sustained through the relations between people, their actions and interactions within activity systems. It enables us to understand how collaborative and knowledge creation practices can be enculturated and sustained in educational communities and the reasons why this is sometimes resisted or constrained.

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


A

decoding-based

fusion

rule

for

cooperative

spectrum

sensing

with

nonorthogonal

transmission

of

local

decisions

Cooperative

spectrum

sensing

in

cognitive

radio

(CR)

networks

is

studied

in

which

each

CR

performs

energy

detection

to

obtain

a

binary

decision

on

the

absence/presence

of

the

primary

user.

The

problem

of

interest

is

how

to

efficiently

report

and

combine

the

local

decisions

to/at

the

fusion

center

under

fading

channels.

In

order

to

reduce

the

required

transmission

bandwidth

in

the

reporting

phase,

the

paper

examines

nonorthogonal

transmission

of

local

decisions

by

means

of

on-off

keying.

Proposed

and

analyzed

is

a

novel

decoding-based

fusion

rule

that

essentially

performs

in

three

steps:

estimating

minimum

mean-square

error

of

the

transmitted

information

from

cognitive

radios,

making

hard

decisions

of

the

transmitted

bits

based

on

the

estimated

information,

and

combining

the

hard

decisions

in

a

linear

manner.

Simulation

results

support

the

theoretical

analysis

and

show

that

the

added

complexity

of

the

decoding-based

fusion

rule

leads

to

a

considerable

performance

gain

over

the

simpler

energy-based

fusion

rule

when

the

reporting

links

are

reasonably

strong.

Cognitive

radio

(CR)

is

an

attractive

technology

to

deal

with

the

spectrum

scarcity

issue

as

the

number

of

wireless

applications

and

systems

grows

quickly.

The

main

principle

behind

cognitive

radio

is

to

provide

wireless

access

to

potential

users

by

opportunistically

detecting

the

unused

licensed

bands,

originally

allocated

to

some

primary

users.

The

key

for

enabling

such

an

opportunistic

access

lies

in

a

reliable

spectrum

sensing

technique.

The

technique

of

distributed

spectrum

sensing,

in

which

the

observations

of

CR

nodes

are

collected

and

transmitted

to

a

fusion

center

(FC)

for

a

final

sensing

decision,

has

received

a

great

interest

in

recent

years.

The

fusion

center

aggregates

the

information

pieces

transmitted

from

the

CRs

and

combines

them

according

to

some

fusion

rule

in

order

to

make

a

final

decision

about

the

absence

(denoted

by

H

or

presence

(denoted

by

H

of

the

primary

user

in

the

band

of

the

interest..

Since

the

transmission

of

the

local

sensing

data

to

the

FC

can

be

costly

in

terms

of

bandwidth

requirement,

particularly

for

large-scale

distributed

CR

networks,

some

form

of

local

data

compression

is

preferred

in

which

each

CR

sends

to

the

FC

only

one

or

a

few

bits

of

data,

representing

its

local

sensing

result.

To

further

reduce

bandwidth

consumption

while

maintaining

simple

fusion

processing,

nonorthogonal

transmission

of

local

decisions

can

be

employed

by

means

of

on-off

keying

(OOK)

In

such

a

transmission

technique,

the

CRs

are

allocated

with

nonorthogonal

(correlated)

signature

vectors

(SVs).

If

the

length

of

the

signature

vectors

is

substantially

less

than

the

number

of

CRs,

the

bandwidth

efficiency

can

be

significantly

improved

Our

earlier

work

in

proposes

a

collaborative

weighted

energy-based

fusion

rule

with

noncoherent

transmission

of

decisions

and

when

the

sensing

results

are

reported

to

the

FC

over

orthogonal

channels.

The

main

focus

of

the

work

in

is

to

optimize

the

sensing

thresholds

at

the

local

CRs,

the

combining

gains

at

the

fusion

center,

and

the

sensing

time

to

maximize

the

secondary

throughput

of

a

CR

network.

However,

for

large-scale

CR

networks,

assigning

orthogonal

channels

to

all

CRs

might

lead

to

an

unaffordable

bandwidth

expenditure..

This

paper

adopts

the

same

nonorthogonal

transmission

framework

of

for

the

reporting

phase.

Different

from

our

main

contribution

is

to

develop

a

lowcomplexity

decoding-based

fusion

rule

as

an

alternative

to

the

energy-based

fusion

rule

in

order

to

efficiently

suppress

the

noise

in

the

received

signal

at

the

fusion

center

and

achieve

a

better

sensing

performance

when

the

reporting

channels

are

strong.

The

performance

of

the

proposed

fusion

rule

is

analyzed

and

compared

with

the

performance

of

the

energy-based

fusion

rule

under

different

scenarios..

The

remaining

of

the

paper

is

organized

as

follows.

Section

introduces

the

model

of

cooperative

spectrum

sensing

with

nonorthogonal

transmission

of

local

decisions.

Section

summarizes

the

energy-based

fusion

rule,

whereas

the

decoding-based

fusion

rule

is

developed

and

analyzed

in

Section

Simulation

results

are

presented

and

discussed

in

Section

Finally,

Section

draws

conclusions.

This

paper

has

proposed

a

low-complexity

decodingbased

fusion

rule

for

cognitive

radio

networks

with

nonorthogonal

transmission

of

local

decisions

in

the

presence

of

channel

impairments

and

noise.

The

proposed

fusion

rule

first

performs

the

MMSE

estimation

of

the

transmitted

information,

makes

decisions

on

the

individual

bits

sent

by

the

cognitive

radios,

and

then

combines

these

hard-decision

bits

in

a

linearly

weighted

manner.

Performance

comparison

with

the

energy-based

fusion

rule

shows

the

superiority

of

the

proposed

fusion

rule

when

the

reporting

channels

are

reasonably

strong.

The

excellent

match

between

simulation

and

analytical

results

verify

the

accuracy

of

the

performance

analysis

of

the

proposed

fusion

rule.

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


Efficient root-finding algorithm with application to list decoding of Algebraic-Geometric codes A list decoding for an error-correcting code is a decoding algorithm that generates a list of codewords within a Hamming distance t from the received vector, where t can be greater than the error-correction bound. In [18] , a list-decoding procedure for Reed-Solomon codes [19] was generalized to algebraic-geometric codes. A recent work [8] gives improved list decodings for Reed-Solomon codes and algebraic-geometric codes that work for all rates and have many applications. However, these list-decoding algorithms are rather complicated. In [17], Roth and Ruckenstein proposed an efficient implementation of the list decoding of Reed-Solomon codes. In this correspondence, extending Roth and Ruckenstein's fast algorithm for finding roots of univariate polynomials over polynomial rings, i.e., the Reconstruct Algorithm, we will present an efficient algorithm for finding the roots of univariate polynomials over function fields. Based on the extended algorithm, we give an efficient list-decoding algorithm for algebraicgeometric codes. Suppose C is a [n, k, d] code over the finite field F q , t < n is a positive integer. For any received vector y = (y 1 , · · · , y n ) ∈ F n q , we refer to any codeword c in C satisfying d(c, y) ≤ t as a t-consistent codeword. A decoding problem is in fact the problem of finding an effective (or efficient) algorithm which can find t-consistent codewords, and we call such an algorithm a decoding algorithm that can correct t errors. The classical decodings (sometimes called unique decodings) of error-correcting codes consider the algorithms which can correct τ = d− 1 2 or fewer errors ( [5] , [11] ). It is clear that in any Hamming sphere in F n q of radius ≤ τ , there exists at most one codeword of a [n, k, d] code. We call τ the error-correction bound of the code. On the other hand, if the number of errors t > τ then there may exist several distinct t-consistent codewords. A list decoding is a decoding algorithm which tries to construct a list of t-consistent codewords. Thus, a list-decoding algorithm makes it possible to recover the information from errors beyond the traditional error-correction bound.. List decoding was introduced by Elias [4] and Wozencraft [20] . In [19] , Sudan proposed a list-decoding algorithm for Reed-Solomon codes. Shokrollahi and Wasserman generalized Sudan's algorithm and derived a list-decoding scheme for algebraic-geometric codes [18] . These algorithms are effective only for codes of relatively low rates. In a recent paper [8] , Guruswami and Sudan proposed improved algorithms for Reed-Solomon and algebraicgeometric codes. The algorithms have better error-correction capabilities than previous algorithms for any code rate. However, the implementations of the list-decoding algorithms are rather complicated, especially for algebraic-geometric codes. As we will discuss in the next section, the list-decoding procedures consist of two main steps. The first step is in fact reduced to the problem of solving a system of homogeneous linear equations, which can be implemented with low complexity using Gaussian elimination. The second step is a problem of finding roots in some spaces of univariate polynomials H(T ) over polynomial rings for Reed-Solomon codes and over function fields for algebraic-geometric codes, respectively. Shokrollahi and Wasserman [18] and Guruswami and Sudan [8] proposed factorization (or root-finding) algorithms to find the roots of H(T ), but the implementation of these algorithms is rather arduous. Gao and Shokrollahi [6] designed an algorithm for computing roots of polynomials over the fields of rational functions on plane curves. Their work also includes an algorithm for finding roots of H(T ) over polynomial rings. In [9] , Høholdt and Nielsen studied fast list decoding for Hermitian codes. They transformed the factorization of H(T ) over the Hermitian function field into a problem of factoring a univariate polynomial over a large finite field. Their algorithm remains to be extended to general algebraic-geometric codes. In [1] , Augot and Pecquet proposed root-finding algorithms. Augot and Pecquet's algorithms do not work for the improved list decodings for Reed-Solomon and algebraicgeometric codes in [8] . Recently, Roth and Ruckenstein [17] presented a fast list-decoding scheme for Reed-Solomon codes. They sped up the first step of the list-decoding algorithm for Reed-Solomon codes in [19] , making use of special properties of the system of homogeneous linear equations that arises. More importantly, based upon a different approach, they proposed an efficient algorithm for finding roots of univariate polynomials over polynomial rings to accelerate the second step of the list decoding for Reed-Solomon codes.. In this correspondence, extending Roth and Ruckenstein's algorithm, we derive an efficient root-finding algorithm for finding roots of polynomials over function fields. As an application of the root-finding algorithm we then present an efficient list-decoding procedure for algebraic-geometric codes.. In the next section, we will give the basic definitions and properties of algebraic-geometric codes and a statement of the root-finding problem. In Section 3, we will present an efficient root-finding algorithm for finding roots of polynomials over function fields and prove the correctness of the algorithm. The efficient list-decoding algorithm for algebraic-geometric codes will be given in Section 4. In Section 5, we present our conclusions. We will give an example and the complexity analysis for the root-finding algorithm in Appendix A and Appendix B, respectively. In this paper, we have presented an efficient root-finding algorithm for polynomials over function fields, extending Roth and Ruckenstein's Reconstruct Algorithm [17] for finding roots of univariate polynomials over polynomial rings. Again by Algorithm 3.1, we can take φ 1 = x 10 y 5 . So, G 1 (X; T ) = G 1 (X; T )/(x 10 y 5 ), and. 2 )T ). We then get. Solving G 2 (Q; T ) = 0, we get f 4 = 0.. From f 4 = 0, we have G 3 (X; T) = G 2 (X; T) and G 3 (X; T) = G 3 (X; (ϕ 3 /ϕ 4 )T ) = G 3 (X; (x/y)T ). We then get. Solving G 3 (Q; T ) = 0, we get f 3 = 0.. From. Solving G 4 (Q; T ) = 0, we get f 2 = 1 or f 2 = 0.. From f 2 = 0, we have G 5 (X; T) = G 4 (X; T) and G 5 (X; T) = G 5 (X; (ϕ 1 /ϕ 2 )T ) = G 5 (X; (1/y)T ). We then get G 3 (Q; T ) = T . Solving G 5 (Q; T) = 0, we get f 1 = 0.. So, we obtain two rational functions f with form f = f 1 ϕ 1 + f 2 ϕ 2 + f 3 ϕ 3 + f 4 ϕ 4 + f 5 ϕ 5 . They are ζ 6 + ϕ 2 + ζ 3 ϕ 5 and ζ 3 ϕ 5 .

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


Inference of segmented color and texture description by tensor voting Abstract-A robust synthesis method is proposed to automatically infer missing color and texture information from a damaged 2D image by ND tensor voting (N > 3). The same approach is generalized to range and 3D data in the presence of occlusion, missing data and noise. Our method translates texture information into an adaptive ND tensor, followed by a voting process that infers noniteratively the optimal color values in the ND texture space. A two-step method is proposed. First, we perform segmentation based on insufficient geometry, color, and texture information in the input, and extrapolate partitioning boundaries by either 2D or 3D tensor voting to generate a complete segmentation for the input. Missing colors are synthesized using ND tensor voting in each segment. Different feature scales in the input are automatically adapted by our tensor scale analysis. Results on a variety of difficult inputs demonstrate the effectiveness of our tensor voting approach. T HE human visual system enables us to make robust inference from insufficient data. We can perform an amazing job of extrapolating shape and texture information despite severe occlusion and noise. In this paper, we present a computational framework to fill in missing geometry, color, and texture information in large image holes, present encouraging results in 2D and 3D, and propose useful applications:. . 2D data-from only a single image with large holes, our method synthesizes missing color and texture information seamlessly. . Range or 3D data-from a single depth map, stereo data, or noisy 3D data, we recover missing data and correct erroneous geometry, and repair colors and textures on surfaces. No a priori complex scene or texture model is assumed in our tensor voting approach, which adopts an adaptive continuity constraint in 2D, 3D, and ND. Because of this, our method has certain limitations which are absent from our powerful visualsystem whereprior knowledgeareemployed. They will be discussed in the conclusion section. In this paper, we first approach the more difficult problem in 2D and then generalize our synthesis method to range and 3D data, when some insufficient depth or geometry information exists. By adopting recent texture segmentation algorithms, we describe how tensor voting provides a robust and effective methodology to perform image segmentation and to synthesize missing geometry as well as color and texture information. In this section, we have extended our methodology to repair a 3D mesh. Here, we qualify our proposed method, where the four results depicted in Figs. 23, 24 , and 25 also show the limitation of our extension, and they can be improved in the future. Our 3D extension works in the presence of discontinuities (C 0 continuous but C 1 discontinuous), large amount of noise and missing data, as long as the local geometric scales remain approximately constant. When the hole to be repaired covers geometric features of multiple scales, the complete segmentation must be performed also in multiple scales, which is under investigation [39] . For example, because of self-occlusion, the hole may cover both the nose (small scale geometric feature) and cheek (large scale geometric feature) of a defective face mesh at the same time, when only a sparse set of scans is available. The output of the complete segmentation in multiscales is a segmented multiresolution mesh where different scale features are coherently integrated along scale transition (curves), in addition to discontinuity curves described above for restricting the color/texture synthesis, so that only relevant information in each segmented patch is used in the synthesis process. Let us first motivate our work by studying the 2D image repairing problem [21] . Today, powerful photo-editing softwares and large varieties of retouching, painting, and drawing tools are available to assist users to refine or redefine images manually. For instance, we can easily outline and remove a large foreground object by intelligent scissors [30] or JetStream [32] , leaving behind a large background hole. However, filling the background hole seamlessly from existing neighborhood information of damaged images is still a difficult problem. A skilled art designer repairs them mostly through his experience and knowledge. Alternatively, some stereo algorithms [22] , [37] use a dense set of images to infer the color of occluded pixels.. Given as few as one image and no additional knowledge, is it possible to automatically repair it? The main issues to be addressed are as follows:. . How much color and shape information in the existing part is needed to seamlessly fill the hole? . How good can we achieve in order to reduce possible visual artifacts when the information available is not sufficient? Inpainting [8] , [2] is an automatic method to fill small holes by exploiting color and gradient information in the neighborhood of the holes. It successfully restores images with little visual artifact. However, when the method does not take texture information into account, blurring in a textured region will be introduced.. In this paper, we propose a unified approach to gather and analyze statistical information so as to synthesize proper pixel values in image holes. This is achieved by computing a tensor to encode the underlying point and texture distribution (smooth or discontinuous), in the geometry and texture space respectively. Our method generalizes well to range and 3D data under certain conditions to be discussed. Instead of simply extending neighboring color information, we use the robust, noniterative ND tensor voting [29] to globally infer the most suitable pixel value in the neighborhood under the Markov Random Field (MRF) constraint. A texture-based segmentation [13] is adopted to partition images into different region segments. Depending on the data dimensionality, 2D or 3D curve connections are voted for, in order to complete the segmentation in image holes. Missing colors are synthesized by ND tensor voting, which adapts to different feature and texture scales.. The rest of this paper is organized as follows: We discuss and compare related work in Section 3. In Section 4, we review the tensor voting algorithm. In Section 5, we describe our 2D method in detail, where the adaptive ND tensor voting for color and texture synthesis is introduced. In Section 6, 3D/ range data repairing on geometry, color, and texture is described, which is a generalization of 2D repairing. Detailed time complexity analysis is given in Section 7. Our 2D and 3D results are presented and explained in Section 8. Finally, we discuss the limitation of our approach, propose future work and conclude our paper in Section 9.. The conference version of this paper first appeared in [21] , which mainly focuses on 2D image repairing. In this coverage, we provide full details, expand our approach to range and 3D data, and present many new results. One contribution of our work is the robust synthesis of missing image or texture information in large holes. To extrapolate details, the Markov Random Fields (MRF) have been widely used to describe textures [5] , [15] , [43] , including this work. Texture synthesis techniques can be roughly categorized into three classes. The first class uses a parametric model to describe statistical textures. Portilla and Simoncelli [35] used joint wavelet coefficients to parameterize and synthesize textures. Heeger and Bergen [18] made use of Laplacians, steerable pyramids, and histogram analysis of a texture sample to synthesize textures. While impressive results are obtained for highly stochastic textures, these methods are not well-suited to represent highly structured textures such as that of a brick wall.. The second class consists of nonparametric sampling and synthesis techniques. Efros and Leung [15] synthesized textures by copying pixels that are matched with the neighborhood of a pixel being synthesized. It works very well to reproduce structured textures as well as stochastic textures.. The third class is to synthesize textures by procedural means. Solid textures, proposed independently by Perlin [33] and Peachey [31] , involve a function that returns a color value at any given 3D point. Reaction-diffusion techniques [44] build up spot and stripe patterns which can be used to synthesize textures.. To accelerate the synthesis process and avoid the problems inherent in pixel-wise generation, Xu et al. [45] proposed a block-wise synthesis algorithm to seamlessly copy sample patches in an overlapping manner to create a new image. Image quilting [16] extends this algorithm by a minimum error boundary cut so that synthesized patches naturally connect to each other. Wei et al. [43] described another hierarchical texture synthesis algorithm to speed up the perpixel generation process by matching the neighborhood of lower resolution image pixels with the synthesized ones, and applying tree-structured vector quantization to accelerate the process.. Masnou and Morel [28] presented a variational formulation to fill in, or inpaint regions to be disoccluded by joining points of the isophotes. Inpainting [8] , [2] is an algorithm to restore damaged 2D images. Instead of performing matching and copying, the basic idea of image inpainting is to smoothly propagate information from the surrounding areas in the isophotes direction. This algorithm generates satisfactory results when holes are small and the gradient information in holes does not change abruptly. In more recent development, textures as well as structures are taken into consideration [3] . However, in a situation where large holes and complex scene components (e.g., single image input as shown in Fig. 19 ) exist, we argue that segmentation information (such as discontinuity curves to partition distinct geometry and textures) should be considered. Moreover, in the texture synthesis process in [3] , it requires either manual parameter adjustment for different texture patterns, or simple constant texture/color assumption. Although there are some preset parameters in our method, our adaptive high dimensional tensor can automatically measure different feature scales in the input image. Our goal is similar to image completion [14] , which also recovers a large portion of disoccluded missing background. One major difference is that explicit segmentation is considered and robustly inferred in this work, in order not to blur important edges. In [46] , images are restored by combining texture synthesis and image inpainting in multiresolution. Critical edge regions are still blurred. Criminisi et al. [10] combined texture synthesis and image inpainting. Levin et al. [24] inpaint images by taking global image statistics into consideration. A training image is used.. The secondary contribution is the robust inference of geometric features, such as curves inside image holes and missing data in range and 3D images, to assist texture and color synthesis. In [29] , a survey and comparison of tensor voting with representative computer vision approaches in surface inference from a 3D cloud of points, e.g., deformable models [23] and computational geometry [19] , are given.. For range and 3D data, unorganized sampled data are common input. To infer missing geometry or depth information, many algorithms have been proposed to regularize and reorganize the points [38] , [20] , [6] , [17] . Turk and O'Brien [40] used variational implicit surfaces. Hoppe et al. [20] adopted a combinational energy function which takes connectivity and distance factors into consideration to refine the original meshes. Curless and Levoy [11] set some additional unseen and empty states, and fill holes by a space carving step. Therefore, after isosurface extraction, aliasing artifacts in the holes are observed. In order to smooth these areas, postfiltering is performed to blur the hole-filled surface for generating a smooth connection. In their examples, holes are relatively small so that they can be filled by simple smooth surface elements. In the postrendering 3D warping algorithm [27] , to fill an uncovered portion in image without obvious artifact, splat and mesh reconstructions are implemented. For each gap area with high-connectedness, a set of quadrilateral meshes are stretched to cover the hole, and the vertex colors of the reconstructed triangles are linearly interpolated. For lowconnectedness, a heuristic is used to flat-shade the triangle using vertex color, if it is far away from the reference frame viewpoint. Chang et al. [9] extended the layered depth image (LDI) tree algorithm to fill the gaps by two-pass pixel filtering. Instead of meshing the foreground and background, their algorithm fills the gap by splatting the filtered samples from surrounding surface patches in the output. Therefore, a better result can be obtained. However this splatting may not respect surface orientation discontinuities (e.g., corners).. In [1] , a variational approach for filling in missing data in 2D and 3D digital images is proposed, which is based on a joint interpolation of the image gre-levels and gradient/ isophotes direction. In [41] , inpainting surface holes is achieved by extending the image inpainting algorithm. Hole filling algorithm in [42] deals with locally smooth structures, while our hole filling can deal with discontinuities. A locally smooth surface is also a requirement in [7] , which uses radial basis function for interpolating missing information from depth maps resulting from medical data. Pfeifle and Seidel [34] used B-splines for hole filling.

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A bibliometric analysis on tobacco regulation investigators Background: To facilitate the implementation of the Family Smoking Prevention and Tobacco Control Act of 2009, the Federal Drug Agency (FDA) Center for Tobacco Products (CTP) has identified research priorities under the umbrella of tobacco regulatory science (TRS). As a newly integrated field, the current boundaries and landscape of TRS research are in need of definition. In this work, we conducted a bibliometric study of TRS research by applying author topic modeling (ATM) on MEDLINE citations published by currently-funded TRS principle investigators (PIs). Results: We compared topics generated with ATM on dataset collected with TRS PIs and topics generated with ATM on dataset collected with a TRS keyword list. It is found that all those topics show a good alignment with FDA's funding protocols. More interestingly, we can see clear interactive relationships among PIs and between PIs and topics. Based on those interactions, we can discover how diverse each PI is, how productive they are, which topics are more popular and what main components each topic involves. Temporal trend analysis of key words shows the significant evaluation in four prime TRS areas.The results show that ATM can efficiently group articles into discriminative categories without any supervision. This indicates that we may incorporate ATM into author identification systems to infer the identity of an author of articles using topics generated by the model. It can also be useful to grantees and funding administrators in suggesting potential collaborators or identifying those that share common research interests for data harmonization or other purposes. The incorporation of temporal analysis can be employed to assess the change over time in TRS as new projects are funded and the extent to which new research reflects the funding priorities of the FDA.To facilitate the implementation of the Family Smoking Prevention and Tobacco Control Act (FSPTCA) of 2009, the Federal Drug Agency (FDA) Center for Tobacco Products (CTP) was formed to oversee tobacco regulatory activities. Its responsibilities include setting performance standards, reviewing premarket applications for new and modified risk tobacco products, requiring new warning labels, and establishing and enforcing advertising and promotion restrictions. In order to meet these responsibilities, the CTP has identified research priories for tobacco regulatory science (TRS) in order to inform and guide the CTP's regulatory decision-making. While tobacco researchers BioData Mining In this work, we employed author topic modeling to conduct a bibliometric analysis on the publications of principle investigators on tobacco. We only reported topic interpretations and observations for the TRSAwardeeSet, as our primary interests were the TRS investigators. In fact, the KWset were diverse in both author and topics, and thus a more in-depth exploration is needed to understand this dataset. Nonetheless, we did temporal trend analysis based on the results of ATM for KWset. It showed us how the significance of key words in different topics evolved over time.. Author topic modeling has been shown to be an effective approach in modeling corpus of computer sciences as well as more general ones, like publicly available emails, collections of diverse research articles. No research is done in modeling a constraint domain like tobacco regulations yet. The results show that this approach can efficiently cluster collections of articles into discriminative categories without any supervision. More interestingly, it can associate topics to authors in a high accuracy. This indicates that we may incorporate author topic modeling into author identification systems to infer the identity of an author of articles using topics generated by the model.. The relevance of this analysis to TRS is multiple folds. First, this analysis is a 'proof of concept' that it can be beneficial to assess the change over time in TRS as new projects are funded and collaborative science in this area changes. This is particularly important because the FDA must use the data from funded research to inform their regulatory decision-making, so if there are 'holes' in the types of research being conducted or published, a bibliometric analysis with ATM could be helpful for the FDA to make decisions. The results can be used to assess the extent to which new research reflects the funding priorities of the FDA.. Second, ATM outcomes can be used by investigators to assess who is conducting research in a particular research domain in order to foster collaborative science [25, 26] . Again, this is very important for the FDA to know given their need to make regulatory decisions. For example, if the FDA is contemplating a regulation that would lead to reductions in nicotine within cigarettes, assessing who is conducting research that can inform that regulatory process is important. Similarly, if the FDA needs to conduct rapid research to address an emerging issue, they can use this type of data to identify likely research teams to carry out that research. Since many issues in tobacco regulatory science require trans-disciplinary science, which cannot be addressed through the research of a single discipline, the ability to assess who is doing relevant research can lead to the development of unique teams that have the best potential to address those complex problems rapidly.. Third, these analyses begin to demonstrate the evolving research productivity of investigators, which we anticipate will occur to a greater extent as publications increase due to FDA funding. For example, we found that 'cessation' and 'treatment' clustered even though that topic is not really included in tobacco regulatory science. This clustering seems to reflect that some leading scientists who conducted research on tobacco treatment have successfully either shifted or expanded their research focus on tobacco regulatory science. Future analyses can further delineate how scientists transition into tobacco regulatory science research, particularly as a result of new funding, to better understand both the scientific expertise relevant to the TRS field, and also to understand the impact in other fields of scientists following the increased funding in TRS.. By fostering collaborative science in TRS, it becomes possible to speed advances in that science by fostering communication between scientists that can avoiding unneeded duplication and impact decision-making on new science that can benefit regulatory decision-making. Articles' yearly distributions Figure 1 shows that from the year 2000 onward, there were about 10,000 newly published articles related to tobacco regulatory science each year. Among them, TRS awardees contributed about 10%. TCORS awardee publications made up half of TRS awardee contributions.. The total number of articles have seen a slight increase from year-toyear over the past 10 years, with the exception of 2007 to 2009, where there was a large jump in numbers. Yet, after 2009, the number becomes stable. This may be related to the short-term grants funded during economic stimulus efforts (ARRA grants) [16] , which had some different publication and research dissemination stipulations than more traditional grants.. We also investigated the distribution based on Mesh headings [17] , which is a comprehensive controlled vocabulary for the purpose of indexing journal articles and books in the life sciences (illustrated in Figure 2 ). The general trend looks quite similar to that in Figure 1 , in that there were slight increases from year-to-year. However, a few differences can be observed as well. Among the literature retrieved using the keyword search queries, based on CTP research interest areas, a more diverse range of research topics can be observed over time. Due to this large array of diversity, only 10-14% are from TRS-funded researchers, with TCORS awardee publications again constituting half of TRS researcher contributions.

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


Feasibility and impact of a computerised clinical decision support system on investigation and initial management of new onset chest pain: a mixed methods study Background: Clinical decision support systems (CDSS) can modify clinician behaviour, yet the factors influencing their effect remain poorly understood. This study assesses the feasibility and acceptability of a CDSS supporting diagnostic and treatment decisions for patients with suspected stable angina. The OMA CDSS, and its underpinning NICE guidance, required contextualised and nuanced clinical information Fig. 9 Problems with entry of patient information into the CDSS to be categorised in a way that did not fit with clinicians' ways of working. This, in combination with a belief on the part of participating clinicians that clinical decision making should not be driven by technology, meant that the CDSS did not substantially inform individual patient management. Qualitative methods, proved essential in deepening our understanding of the factors affecting CDSS use. Use of the CDSS may have been improved by the provision of guidance for both practitioners and patients [5] and a more intensive training and monitoring programme [22] . CDSSs for the assessment and management of new onset chest pain may be more successful if they reflect more closely the ways in which clinicians assess chest pain. Our study has articulated barriers to CDSS use that need to be addressed in the design of future interventions. Our study contributes new findings to the understanding of how a CDSS is used in the initial management of a common symptom. Despite use of the OMA CDSS in 86 % of consultations for which it was available, there was little evidence of impact on medication prescribing or on investigation choice. Through qualitative data analysis we gained an in-depth understanding of the reasons for this discrepancy. We identified problems in entering patient data into the CDSS. These included difficulties in classification of symptoms and risk factors, and in the incorporation of all available clinical information emerging during the consultation. In the majority of observed cases, the CDSS was used after the patient had left the room. Structural and practical barriers to the use of the CDSS included the availability of investigations and the prescribing competencies of the clinicians. Analysis of observational data revealed how clinicians privileged their clinical expertise over CDSS advice, responding to CDSS recommendations as 'decision feedback' rather than 'decision support'. There was most disagreement with CDSS recommendations for patients whose pain was categorised as atypical, the group for which mapping patient symptoms to the CDSS had proved most challenging. Chest pain clinicians were rarely observed prescribing medication from the clinic. Taken together these data indicate little chance of the OMA CDSS influencing clinical outcomes, and as such we will not proceed to a cluster randomized controlled trial of the OMA CDSS.. Observing consultations in a chest pain clinic, Somerville and colleagues [12] found that doctors were engaged in practical interpretive work, actively restructuring patient narratives to meet an accepted diagnostic classification. Pain narratives were sometimes unstable and changing, and symptoms outside the canon were investigated less frequently. We have observed clinicians engaged in this interpretive work, but also struggling to use a classification that was sometimes at odds with their usual way of working, despite our efforts during CDSS development to understand clincians' working practices. Our clinicians worked creatively with the constraints of the tool, in line with Berg's description of how protocols for care can be circumvented, tinkered with and interpreted in many different ways [13] . We observed clinicians developing 'workarounds' to enable the system to be used, introducing the potential for unintended consequences of CDSS use [14] . Previous qualitative studies have identified CDSSs having little impact on decisions either through non-use of the CDSS [15] , or use after the consultation has been completed [16] . A study of nurses using CDSS identified how they were primarily used to confirm decisions that had already been made [17] .. The OMA CDSS delivered a national clinical guideline through patient specific recommendations. The constraining effects of guidelines have been previously articulated, including ignoring data that cannot easily be measured, and failing to allow the tailoring of advice to individual patients [18, 19] . A major limitation of guidelines is their poor fit to complex clinical problems, particularly in the presence of Fig. 6 Classification of chest pain. Source: NICE CG95 [9] multi-morbidity, being more suited to relatively straightforward clinical decisions, [20] . From our findings, this limitation extends to CDSSs.. A strength of our study lies in its mixed methods approach. Although the quantitative data suggested that the CDSS was used, the qualitative data were essential in developing a more complete understanding of how it was used. A limitation of the quantitative study was its relatively small sample size, precluding statistical analysis. It is possible that some appropriate investigations may have happened after six months, at which point our follow-up date was censored, so this was a conservative assessment of adherence to investigation recommendations. We have measured medication prescription in general practice six Fig. 7 Problems with entry of patient information into the CDSS months after the chest pain clinic visit, as a proxy for successful commencement or recommendation of long term secondary prevention medication at the time of the clinic. There are many other factors affecting whether medication is continued at six months, such as emergent indications for medication. Although CDSS use in both trusts was high, it appeared to be significantly different between Trust A and B. A limitation of the qualitative study is that were unable to observe Trust B after the introduction of the CDSS.. The OMA CDSS was introduced at a time of transition for chest pain services, the NICE guidance on which it was Fig. 8 Problems with entry of patient information into the CDSS based having been published four months earlier. At this time, the ETT test played a central role in chest pain clinic routines, and our main qualitative study site did not routinely use computerised tomography or computer tomography coronary angiography for the diagnosis of angina. The NICE guidance advised against the use of the ETT, and recommended increased numbers of non-invasive tests including computerised tomography investigations. We found that the failure of the guidance to incorporate a test that was an entrenched part of chest pain clinic practice [21] added to the difficulties of the clinicians in using the CDSS. It is possible that the CDSS would have been more able to impact upon clinic processes when chest pain clinics were more able to follow the guidance. We have reported how often clinicians' choice to investigate agreed with the CDSS recommendations (concordance). Although it might be assumed that concordance with NICE guidance reflects appropriate management, we acknowledge the limitations of concordance in the assessment of CDSS. Concordance may be affected by many and diverse things, for example the structural and practical barriers identified in this study, or the perceived appropriateness of the underpinning guidance for a specific clinical scenario. Before and after study 294 patients were recruited to the quantitative study between November 2009 and May 2011; 285 were included in the analysis at six months (Fig. 3) : 106 patients seen in a clinic that had not received the OMA programme (Before OMA) and 179 patients seen in a clinic that had received the OMA programme (After OMA). Characteristics at baseline (chest pain clinic consultation) including cardiovascular risk factors and current medications are shown in Table 2 . Clinicians seeing patients in the Before OMA group were cardiologists (3), specialist cardiology nurses (2) and a cardiac physiologist (1), and in the After OMA group were cardiologists (4), specialist cardiology nurses (3) and a cardiac physiologist (1). The CDSS was used for 86 % (154/179 95 CI 81-91 %) of patients in the After OMA group. CDSS was used for 81 out of 100 patients (81 %) in Trust A, and 73 out of 79 patients (92 %) in Trust B (difference 11, 95 CI 2-21 %).. The CDSS recommended investigation in 34 % (95 CI 25-43 %) of patients Before OMA and 41 % (95 CI 34-48 %) of patients After OMA. Table 3 shows the number of patients having any investigation done within six months, by CDSS recommendation. The proportion of patients for whom the CDSS recommendation was followed was 74 % (95 CI 65-82 %) in the Before OMA group and 75 % (95 CI 69-81 %) in the After OMA group. The proportion of patients for which the CDSS recommended no investigation that did not have one was the same before and after the OMA intervention. Where the CDSS recommended an investigation, the proportion receiving an investigation was 50 % [CI 34-66 %] in the Before OMA group and 59 % [95 CI 48-70 %] in the After OMA group. The CDSS recommended an increase in the number of medication classes for 25 patients (24, 95 CI 16-32 %) Before OMA. Of these, eight (32, 95 CI 14-50 %) patients received at least one additional medication class, two (8 95 CI −3-19 %) received fewer medication classes and 15 (60, 95 CI 41-79 %) had no change. In the After OMA group, the CDSS recommended an increase in the number of medication classes for 34 (19, 95 CI 13-25 %) participants. Of these, 17 (50, 95 CI 33-67 %) were prescribed at least 1 additional medication class, 7 (21, 95 CI 7-35 %) were prescribed at least 1 fewer medication classes and 10 (29, 95 CI 14-44 %) were unchanged. Clinicians need to use the best available evidence to inform patient management decisions. Clinical decision support systems (CDSSs) generate patient-specific assessments or recommendations to aid clinical decision making. CDSSs can improve practitioner performance and health care processes in a range of clinical scenarios including disease management, drug-dosing, prescribing and preventive care [1] [2] [3] . The effect of CDSSs on clinical outcomes is less frequently studied. In a systematic review of 148 randomised controlled trials of CDSSs implemented in clinical settings only 29 assessed clinical outcomes [1] . There was moderate evidence in support of an effect of CDSSs on morbidity from 16 studies; evidence for other clinical outcomes was of low quality.. Few studies have sought rigorous evidence to determine what factors contribute to the effectiveness of decision support systems [4] . A recent meta-regression of computerised CDSSs found sufficient quality evidence for the assessment of only six factors. Of these, success of CDSSs was positively associated with systems developed by the investigators of the primary studies, systems providing advice to patients and practitioners, and systems requiring a reason for overriding advice [5] . It has been argued that research based on randomised controlled trials is not sufficient to allow rigorous assessment of the factors that make CDSSs successful, and that qualitative contextual evaluation and observation are needed [4] .. In the United Kingdom (UK), initial specialist assessment of suspected angina is undertaken in chest pain clinics. Chest pain clinics may incorrectly diagnose some patients, and may not initiate secondary prevention in those with angina. In a cohort of 8762 patients followed for three years after attending a chest pain clinic, 33 % of all cardiovascular events occurred in patients with a diagnosis of non-cardiac chest pain [6] . This study reported under-prescription of effective secondary prevention: of those diagnosed with angina only 28 % were taking a statin [7] .. Our Optimising the Management of Angina (OMA) programme includes a web-based computerised CDSS to support investigation and medication decisions for patients with new onset stable chest pain. We hypothesised that appropriate investigation, leading to accurate diagnosis and effective secondary prevention, would lead to a reduction in cardiovascular events. Here we present a mixed methods study that aimed to understand the factors influencing the feasibility of the OMA CDSS in clinical practice, and the impact of the CDSS on investigation and prescribing behaviour, to inform potential progression to a cluster randomised trial of the intervention. The OMA programme is a complex intervention delivered at the level of the clinic. The programme has 3 stages: preparation, training and clinic tools (Fig. 1) . The preparation and training stages facilitate use of the OMA CDSS. The components of the intervention were developed using behavioural change domains identified by Michie and colleagues [8] .

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


A Novel Image Enhancement Algorithm for a Small Target Detection of Panoramic Infrared Imagery SUMMARY A novel image enhancement algorithm that can efficiently detect a small target of panoramic infrared (IR) imagery is proposed. Image enhancement is the first step for detecting and recognizing a small target in the IR imagery. The essence of the proposed algorithm is to utilize the independent histogram equalization (HE) separately over two sub-images obtained by decomposing the given image through the statistical hypothesis testing (SHT). Experimental results show that the proposed algorithm has better discrimination and lower false alarm rate than the conventional algorithms. The autonomous detection of a small moving target using an electro-optical sensor (IR sensor) imagery is required for the several defense applications. Such as IR Warning System (IRWS), IR Search and Tracking system (IRST), and etc are necessary for those military applications to warn the incoming small targets, such as aircrafts and helicopters of enemy, from a distance [1]- [3] . Recently, the IRWS and the IRST have been widely for the panoramic IR imagery which uses the 1-dimensional multi-array infrared sensor by rotating two or three times per second. Figure 1 shows two examples of the panoramic images acquired the IRWS. Since those IR images generally have a low signal to noise ratio and a narrow dynamic range, it is difficult to detect and recognize the small targets without the enhancing of IR signals. Thus, lots of researches have been centered on the contrast enhancement of the IR images to detect the small targets. Histogram stretching (HS) is a simple image enhancement algorithm that attempts to increase the dynamic range from the narrow dynamic range in an image by using linear transformation [4] . The linear transformation has a steep gradient in the region of many pixels of the image and a slow gradient in the rest region. In other words, the contrast enhancement in the background region has a better than † The authors are with the School of Electrical Engineering and Computer Science, Kyungpook National University, E-mail: alteir@ee.knu.ac.kr, heeyaa@ee.knu.ac.kr, dgkim@ee.knu.ac.kr † † The author is with the Agency for Defense Development E-mail:sonofkim@hanmail.net * This paper was presented at ITC-CSCC2004 Poster session2 (7F3P26) Fig. 1 The examples of the panoramic IR imagery.. that of the target region. When the contrast in the background region is increased, the background noises (or clutters) are also increased simultaneously by the characteristic of the linear transformation. Histogram equalization (HE) is the one of the well-known algorithm for enhancing the contrast of the given images in accordance with the sample distribution of an image [4], [5] . In spite of its high performance in enhancing the contrasts of a given image, it is rarely employed in the IR image viewing system since histogram equalization changes the original brightness of an input image, deteriorates visual quality, and produces some serious artifacts. In order to overcome such drawbacks of the histogram equalization, the plateau equalization was proposed by V. E. Vickers [6] . The plateau equalization is a general class of histogram-based mapping from the raw signal levels to output display value, and a class that includes the histogram projection and the histogram equalization as extreme cases. The effect of this method is to limit the influence of many pixels hav-

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