Rawan Ghnemat

Cyrille Bertelle

Gérard H E Duchamp

Swarm Intelligence for Urban Dynamics Modelling

Keywords: swarm intelligence, complex systems, self-organization, ant systems, spatial organization PACS: 02.70, 07.50, 89.70, 89.75

In this paper, we propose swarm intelligence algorithms to deal with dynamical and spatial organization emergence. The goal is to model and simulate the developement of spatial centers using multi-criteria. We combine a decentralized approach based on emergent clustering mixed with spatial constraints or attractions. We propose an extension of the ant nest building algorithm with multi-center and adaptive process. Typically, this model is suitable to analyse and simulate urban dynamics like gentrification or the dynamics of the cultural equipment in urban area.

INTRODUCTION

Many natural and artificial systems have emergent properties based on spatial development. This spatial development is both the result of some mecanisms from the system behavior and the actor of the system formation by morphogenetic feedbacks. Natural ecosystems or social organizations in urban dynamics are typically such emergent spatial organizations. The goal of this paper is to study some computable mecanisms and algorithms able to model such spatial self-organization processes, taking into account the complexity of the phenomena.

In section "Modelling spatial complexity", complex systems concepts are defined and their applications to urban dynamics understanding are described. Section "Swarm intelligence and spatial environment" presents swarm intelligence algorithms as methodologies to implement the complex systems concepts, using distributed computations. Section "Emergent Spatial organizations over complex behavioral clustering" proposes some specific swarm intelligence methods based on ant systems in order to model the spatial organizations emergence. Ant clustering is presented as the basis of the selforganization process. An algorithm based on the usage of pheromon template is proposed as an extension of this self-organization process, allowing to control some spatial constraints during the self-organization phenomenon. Using multi-template, we propose a general methodology to model multi-criteria spatial self-organization. Experiments are given, using repast agent platform mixed with a geographical information system.

MODELLING SPATIAL COMPLEXITY

Complex System Concepts

From Entities to Systems

Complex system theory [START_REF] Le Moigne | La modélisation des systèmes complexes[END_REF] is based on the fact that for many applicative domains, we can find similar processes linking emergent global behavior and interaction network of constituents. The global behavior is generally not accessible using classical analytical methods.

In classical analytical methods, the global behavior of the system is the description of the equations. Simulations from these formulations, consist in obtaining the trajectories of the behavior predefined in the equation formulation.

In complex systems modelling, we have to model the constituents of the system and the interaction network or system which links these constiuents, using a decentralized approach. So the global behavior of the system cannot be understood by the description of each constituent. In complex systems modelling, the global behavior is an emergent property from the interaction network or systems between its constituents and leads to the creation of an dynamical organization of these constituents This dynamical and emergent organization retro-acts on its own components. Two kinds of feedback allow to describe these phenomenon. The positive feedback means that the emergence increases the organization constitution. the negative feedback means that the emergence has regulator properties which finally stop the increasing organization constitution and allow the system stabilization.

Spatial emergence from system and environment interaction

Another major aspect of complex systems is that they can be considered as open systems. This means that they are crossed by energetical fluxes that make them evolve in a continuous way. From these energetical fluxes, complex systems can evolve through critical states, using bifurcation schema and attractors behaviors. One of the major vector or support of these energetical fluxes is the environment itself where the complex systems and their entities evolve. In many natural and artificial systems, the environement has some spatial effects which interact on the whole complexity of the phenomenon. This spatial environment can be modified by the system but he can also be the catalyst of its own evolution. Understanding and modelling the deep structural effect of the interaction between the systems and its spatial environment is the goal of the study presented in the sequel.

Application to urban dynamics

Social and human developments are typical complex systems. Urban development and dynamics are the perfect illustration of systems where spatial emergence, selforganization and structural interaction between the system and its components occur. In figure 1, we concentrate on the emergence of organizational systems from geographical systems. The continuous dynamic development of the organization feed-back on the geographical system which contains the organization components and their environment. The lower part of this figure explains our analysis methodology. It consists to describe many applicatives problems by dynamical graphs or environments in order to detect organizations over these dynamical environment. For the organization detection, we use swarm intelligence processes. We model the feed-back process of this emergent organization on the system constituents and its environment. To analyse or simulate urban dynamics, nowadays, we can use the great amount of geographical databases directly available for computational treatment within Geographical Information Systems. On the organizational level description, the new development of multiagent systems (MAS) allows nowadays to develop suitable models and efficient simulations.

The applications we focus on in the models that we will propose in the following concerns specifically the multi-center (or multi-organizational) phenomona inside urban development. As an artificial ecosystem, the city development has to deal with many challenges, specifically for sustainable development, mixing economical, social and environmental aspects. The decentralized methodology proposed in the following allows to deal with multi-criteria problems, leading to propose a decision making assistance, based on simulation analysis.

Gentrification phenomena can be modelled using such methodology. It is typically a multi-criteria self-organization process where appears emergent coming of new population inside urban or territorial areas. This new population firstly attracted by some criteria, brings some other charateristics which are able to modify and feedback over the environment.

Cultural dynamics processes in urban areas are also such complex systems where multi-criteria must be taken into account. A modelling of these dynamics is presented latter in this paper.

SWARM INTELLIGENCE AND SPATIAL ENVIRONMENT

Decentralized algorithms have been implemented for many years for various purposes. In this algorithm category, multi-agent systems can be considered as generic methods [START_REF]Multiagent Systems[END_REF]. Agent-based programming deals with two main categories of agent concepts: cognitive agents and reactive agents. The first category concerns sophisticated entities able to integrate, for example, knowledge basis or communications systems. Generally, efficient computations, based on these cognitive architectures, implement few agents. The second category of agents, based on reactive architecture, is expected to be used inside numerous entity-based systems. The aim of programs using such architectures, is to deal with emergent organizations using specific algorithms called emergent computing algorithms. Swarm Intelligence is the terminology used to point out such reactive agent-based methods where each entity is built with the same basis of behavior, but reacts in an autonoumous way. Swarm Optimization methods concern the problems of optimization where the computation of a function extremum is based on the concept of swarm intelligence.

Ant Colony Optimization (ACO) methods [START_REF] Bonabeau | Swam Intelligence, from natural to artificial systems[END_REF] is a bio-inpired method family where the basic entities are virtual ants which cooperate to find the solution of graph-based problems, like network routing problems, for example. Using indirect communications, based on pheromon deposites over the environment (here a graph), the virtual ants react in elementary way by a probabilistic choice of path weighted with two coefficients, one comes from the problem heuristic and the other represent the pheromon rate deposit by all the ants until now. The feed-back process of the whole system over the entities is modelled by the pheromon action on the ants themselves.

Particule Swarm Optimization (PSO) is a metaheuristic method initially proposed by J. Kennedy and R. Ebenhart [START_REF] Kennedy | Particle Swarm Optimization In Proceedings of IEEE International Conference on Neural Networks[END_REF].This method is initialized with a virtual particle set which can move over the space of solutions corresponding to a specific optimization problem. The method can be considered as an extension of a bird flocking model, like the BOIDS simulation from C.W. Reynolds [START_REF] Reynolds | Flocks, Herds and Schools: a distributed behavioral model In Computer Graphics[END_REF]. In PSO algorithm, each virtual particle moves according to its current velocity, its best previous position and the best position obtained from the particles of its neighborhood. The feed-back process of the whole system over the entities is modelled by the storage of this two best positions as the result of communications between the system entities.

Other swarm optimization methods have been developped like Artificial Immune Systems [START_REF] De Castro | Artificial immune system: a new computational approach[END_REF] which is based on the metaphor of an immune system as a collective intelligence process. F. Schweitzer proposes also a generic method based on distributed agents, using approaches of statistical many-particle physics [START_REF] Schweitzer | Brownian Agents and Active Particles[END_REF].

The method proposed in this paper is based on Ant Clustering and Ant Nest Building, allowing to deal with self-organization processes emerging from spatial constraints and attractive areas.

EMERGENT SPATIAL ORGANIZATIONS OVER COMPLEX BEHAVIORAL CLUSTERING

We will describe in this section, the general algorithm which is proposed to model emergent spatial organizations. This algorithm is based on the ant clustering. We introduce pheromon template to spatially control the clustering from local attraction. This method is a decentralized approach which allows to combinate multi-center and multi-criteria problems and we will show how we can apply it to model cultural dynamics in urban areas. We conclude this section with the description of an adaptive process which lead to model the feedback of the emergent system on its own mecanisms.

Ant clustering

Ant clustering algorithms are inspired by the corposes or larvea classification and aggregation that the ants colony are able to do in the real life. The ants are moving inside a closed area and are able to move some material which are randomly put on this area. After a while, and without any kind of centralized coordonation, the ants success to create some material clusters. The algorithm is based on the following and very simple behavioral rules that each ant implements :

• When an ant is moving without carrying yet material and finds some material, the ant will take the material respecting the probability number :

P p = k 1 k 1 + f 2 (1)
where f is the material density that the ant perceives locally around itself and k 1 is the treshold. It is easy to check that if f << k 1 then P p is near the value 1 and if f >> k 1 then P p is near the value 0. • When an ant is moving when carrying some material, the probability to deposit it is computed by :

P d = f k 2 + f 2 (2)
where f is still the material density that the ant perceives locally around itself and k 2 is another treshold. It is easy to check that if f << k 2 then P d is near the value 0 and if f >> k 2 then P d is near the value 1.

In figure 2, we show an implementation of this algorithm using the multi-agent platform called Repast [12]. The java version of this platform includes some packages allowing to interface with geographical databases and geographical information systems (GIS). In figure 2, the graphical output windows is made under OpenMap which is a GIS developped in Java. In figure, the materials moved by the ants are the small grey circles, the ants moving without material are the light circles and the ants carrying material are the dark circles.

Spatial constraints using template

The ant clustering shows some spatial self-organizations but has the specificity to generate clusters at random places. According to the first random moves that the ants start to do in the beginning of the algorithm, some material will initiate aggregation and the clustering processus will complete this aggregation from these initial random first aggregations. To simulate some urban dynamics, we need to introduce specific location with respect to city center for example or cultural equipments. The clustering here will represent the people usage of these centers or equipments and we need to introduce an attractive effect by using a pheromon template. This method follows the algorithm known as Ant Nest Building [START_REF] Bonabeau | Swam Intelligence, from natural to artificial systems[END_REF]. In ant colonies, the center corresponds to the position of the queen which needs to build the nest and the ant colony moves around it to protect the nest by various material taken on the ground. The queen emits a pheromon which allows to attract the ants during their building. The ant has to deposit the material carried only if the pheromon quantity perceived belongs to a specific range. We use an attractive fonction called P t , corresponding to a pheromon template and represented by the left top part of the figure 3.

Using this template function, we remplace in the clustering algorithm, the two provious probabilities defined in equation ( 1) and equation ( 2) by

P ′ p = P p (1 -P t ) (3)
P ′ d = P d P t ( 4

Multi-template modelling

The previous subsection describes one local attractive process characterized by the queen and its pheromon template emission. The advantage of this method is to be able to combine the solutions of multi-center and multi-criteria problems, using interactive processes, each one is represented by a queen and its pheromon template.

On figure 3, we can see on the left part, a single queen simulation and in the right part, a simulation with two queens and two pheromon templates. It is possible also for each queen to emit many different kinds of pheromons : we called them colored pheromons. Each colored pheromon will attract only the ants associated to its color.

Application to cultural equipment dynamics

The multi-template modelling can be used to model cultural equipment dynamics as described in figure 4. On this figure, we associate to each cultural center (cinema, theatre, ...) a queen. Each queen will emit many pheromon templates, each template is associated to a specific criterium (according to age, sex, ...). Initially, we put the material in the residential place. Each material has some characteristics, corresponding to the people living in this residential area. The simulation shows the self-organization processus as the result of the set of the attractive effect of all the center and all the templates.

Adaptive Spatial Organization Feedback Implementation

As explained previously, complex systems deal not only with emergent organization processus from the interaction of its own entities, but also with the feedback processus of the organization over its own components. In the proposed model, we can take into account such feedback process and we present in figure 5, an adaptive processus which makes the queen (which describes the organization itself) modify the environment and the clustering processus itself. Following the template function, the queen locally defines around it two zones. The first zone is near itself and it is expected not to find material there. The second zone corresponds to the template maximum and it is expected to find a great concentration of material there. In the simulation, we count in a dynamical way the number of materials in these two zones and when these numbers reach some tresholds, we make evolve the queen by increasing its own size and so increasing the 2 associated zones. After this evolution, the ants have to move some material following the new template function attraction. The low part of the figure shows the evolution of the queen which has evolved 6 times since the simulation beginning. On this figure, we can see the red curves counting the zones density. Each gap in these density curves correspond to an evolution of the queen.

CONCLUSION AND PERSPECTIVES

The paper develops some specific swarm intelligence algorithms based on ant colonies processes. Using such decentralized methods, we can model complex multi-center and multi-criteria self-organizations. Urban dynamics are one of the most relevant problems where these approaches can be efficient. These studies are supported by a french regional project (Haute-Normandie) dealing with the study of cultural dynamics over urban area.

FIGURE 1 .

 1 FIGURE 1. Spatial organizations Complexity Description and the Conceptual Generic Model Based on Swarm Intelligence

FIGURE 2 .

 2 FIGURE 2. Ant Clustering Simulation using Repast on OpenMap

FIGURE 3 .

 3 FIGURE 3. Templates and associated Ant Nest Building Simulation. On the left, with one queen. On the right with two queen

FIGURE 4 .

 4 FIGURE 4. Cultural Equipment Dynamics Modelling

  ) (a) after few step (b) after queen adaptive development

FIGURE 5 .

 5 FIGURE 5. Adaptive queen behavior modelling: according to its surround material spatial perception, the queen evolves


domain: sdv spi

text:
Philip Whybra

Alex Zwanenburg
email: alexander.zwanenburg@nct-dresden.de

Vincent Andrearczyk

Roger Schaer

Aditya P Apte

Alexandre Ayotte

Bhakti Baheti

Spyridon Bakas

Andrea Bettinelli

Ronald Boellaard

Luca Boldrini

Irène Buvat

Gary J R Cook

Florian Dietsche

Nicola Dinapoli

Hubert S Gabryś

Vicky Goh

Matthias Guckenberger

Mahdi Mathieu Hatt

Aditi Iyer

Mahdi Jacopo Lenkowicz

A L Loutfi

Steffen Löck

Francesca Marturano

Olivier Morin

Christophe Nioche

Fanny Orlhac

Sarthak Pati

Arman Rahmim

Seyed Masoud Rezaeijo

Christopher G Rookyard

Mohammad R Salmanpour

Andreas Schindele

Isaac Shiri

Emiliano Spezi

Stephanie Tanadini-Lang

Florent Tixier

Taman Upadhaya

Joost Vincenzo Valentini

J M Van Griethuysen

Fereshteh Yousefirizi

Habib Zaidi

Henning Müller

Martin Vallières

Adrien Depeursinge

A Z Contributed Equally

M Ho

The Image Biomarker Standardization Initiative: Standardized convolutional filters for quantitative radiomics

Background: Filters applied to medical imaging can highlight various structures and patterns. Despite their widespread use in radiomics analyses, lack of standardization of convolutional filters negatively affects reproducibility.

Purpose: To standardize convolutional filters for radiomics analyses.

Materials and Methods: This study consisted of three phases. In the first phase, we aimed to establish 36 reference response maps for convolutional filters based on digital phantoms: mean, Laplacian-of-Gaussian, Laws kernels, Gabor kernels, separable and nonseparable wavelets (including decomposed forms) and Riesz transformations of convolutional filters. In the second phase, we aimed to find reference values for 396 intensity-based features computed from response maps of 22 filter and image processing configurations, based on computed tomography (CT) imaging. Afterwards, reproducibility of standardized convolutional filters and feature values was assessed during a validation phase, using a public dataset of multi-modal imaging (CT, FDG-PET, T1w-MR) from 51 patients with soft-tissue sarcoma.

Results: In phase 1, 15 teams from 7 countries were able to find reference response maps for 33 of 36 filter configurations. In phase 2, 11 teams were able to find reference feature values for 323 of 396 features. Consensus on reference feature values for Riesz transformations was not established. During the validation phase, 458 of 486 features were found to be reproducible among 9 teams. Coefficient of variation and quartile coefficient of dispersion features were found to be poorly reproducible for band-and high-pass filters.

Conclusion: Eight types of convolutional filters for radiomics were standardized and reference responses and reference feature values for verification and calibration of radiomics software packages were obtained. A web-based tool is available for checking compliance of radiomics software with the reference.

Main body

Introduction

Radiomics is the high-throughput processing of medical images to support clinical decision making [START_REF] Gillies | Radiomics: Images Are More than Pictures, They Are Data[END_REF]. The intermediate steps in this process, and variability therein, are known to affect the reproducibility of the resulting decision support tools. The Image Biomarker Standardization Initiative (IBSI) previously established standards for digital image processing and computation of hand-crafted, quantitative radiomic features [START_REF] Zwanenburg | The Image Biomarker Standardization Initiative: Standardized Quantitative Radiomics for High-Throughput Image-based Phenotyping[END_REF]. This has improved interchangeability between IBSI-compliant radiomics software packages, provided that the same image processing and feature parameters are used [START_REF] Fornacon-Wood | Reliability and prognostic value of radiomic features are highly dependent on choice of feature extraction platform[END_REF][START_REF] Bettinelli | A Novel Benchmarking Approach to Assess the Agreement among Radiomic Tools[END_REF].

Filters are frequently used in radiomics studies as they allow characteristics to be emphasized such as edges (e.g., sharp tumor boundaries), vessels, blobs, or holes in medical imaging. However, the use of Laplacian-of-Gaussian, wavelets and other filters has not been standardized, and their use has been found to be poorly reproducible [START_REF] Bogowicz | Post-radiochemotherapy PET radiomics in head and neck cancer -The influence of radiomics implementation on the reproducibility of local control tumor models[END_REF]. Many of these filters are convolutional filters, hence the focus of this work. With convolution, filters are systematically slid across the entire image, yielding a response map that spatially locates the image characteristics mentioned earlier. Radiomic features, such as mean intensity, can then be computed from the region of interest (ROI) within the response map.

Here, the IBSI aimed to improve reproducibility of convolutional filters for radiomics by: (a) establishing definitions for convolutional filters, including commonly used ones such as wavelets; (b) integrating the convolutional filters into the previously established general radiomics image processing scheme (2); (c) providing datasets, associated reference response maps and reference feature values, as well as tools for verification and calibration of radiomics software packages; and (d) updating the IBSI guidelines for methodological reporting to include details concerning convolutional filters.

Materials and Methods

Figure 1: Study overview. The study is divided into three phases. In the first phase, convolutional filters were applied to digital phantoms to identify reference response maps. In the second phase, reference values were identified for intensity-based features computed from response maps of a chest CT image. In the third phase, the results of the first two phases were validated using a multi-modal dataset. Unlike the first two phases, the validation phase is not iterative.

Study design

This standardization effort was divided into three phases (Fig. 1). During the first two phases the implementation and use of convolutional filters were standardized. Phase 1 concerned the creation of reference response maps, i.e., the expected result of applying a convolutional filter with specific parameters to an image. In phase 2, convolutional filters were integrated into a radiomics workflow for the purpose of finding reference values for radiomic features computed from response maps. In phase 3, we assessed whether standardization of convolutional filters resulted in reproducible feature values.

Convolutional filters

Convolutional filters transform an image to a response map by convolution. These filters consist of numerical weights that are pre-defined or parameterized in the spatial domain or in the frequency (Fourier) domain. Several convolutional filters were assessed, i.e., mean filter, Laplacian-of-Gaussian filter, Laws kernels, Gabor kernels, separable and non-separable wavelets, and Riesz transformations of convolutional filters, see Fig. 2. Further details are supplied in supplementary note 1 and in the reference manual. . This workflow starts with an image that is obtained from a repository or archiving system in a digital format, such as DICOM. Then the image is optionally converted (e.g., from PET activity to standardized uptake values) and post-processed (e.g., MR biasfield correction). Segmentation masks are either loaded in a digital format, or automatically created. Both image and segmentation masks are then optionally resampled. Response maps are created by optionally filtering the image. Both response map and segmentation mask are then used to compute hand-crafted radiomic features. This study attempts to standardize several types of convolution filters (bottom panel). The original CT image is shown for reference. Decomposition of separable and non-separable wavelets is not shown. The image processing scheme and convolutional filters are described in more detail in the reference manual.

Participating teams

Teams of radiomics researchers were invited to participate in the IBSI. Participation was voluntary and open for the duration of the study. Teams were eligible to participate if they (a) developed their own radiomics software, and (b) their software is IBSI compliant. A team was not required to participate in all phases of the study.

Phase 1: Establishing reference response maps

In phase 1, several digital phantoms were used, and thirty-six convolutional filter configurations were defined to establish reference response maps (supplementary note 2). Teams computed response maps for each filter configuration and uploaded these to a central website (https://ibsi.radiomics.hevs.ch/; supplementary note 7).

The level of consensus for each response map was assessed using the same metrics as previously ( 2): (a) by the number of teams that matched the tentative reference response map (supplementary note 4); and (b) the previous number divided by the number of teams that contributed a response map. Level of consensus was then: none, if the tentative reference response map was not produced by over 50% of contributing teams; weak, match between fewer than three teams; moderate, three to five; strong, six to nine; very strong, ten or more.

Phase 2: Defining feature reference values

Convolutional filtering was integrated into the general radiomics image processing scheme (Fig. 2). Image processing and convolutional filter configurations were then defined for each filter. Both 2D and 3D filter configurations were created, yielding twenty-two configurations in total (supplementary note 3). Teams computed a response map for each configuration from a publicly available CT image of a patient with lung cancer [START_REF] Lambin | Data from: Radiomics Digital Phantom[END_REF]. Eighteen intensity-based features were then computed from the gross tumor volume ROI in each response map (supplementary note 5). After computing feature values, teams uploaded their results to the website. The level of consensus for feature values was assessed using the same metrics as in phase 1 by using contributed values for each feature as input and comparing matches within a tolerance margin (supplementary note 5).

Phase 3: Validation

After completing phases 1 and 2, teams were asked to compute intensity-based features from the gross tumor volume segmentation in response maps of a multimodality imaging cohort (co-registered CT, 18 F-FDG-PET, and T1-weighted MRI). This cohort consisted of 51 patients with soft-tissue sarcoma obtained from The Cancer Imaging Archive [START_REF] Clark | The Cancer Imaging Archive (TCIA): maintaining and operating a public information repository[END_REF][START_REF] Vallières | A radiomics model from joint FDG-PET and MRI texture features for the prediction of lung metastases in soft-tissue sarcomas of the extremities[END_REF][START_REF] Vallières | Data from: A radiomics model from joint FDG-PET and MRI texture features for the prediction of lung metastases in softtissue sarcomas of the extremities[END_REF]. PET and MRI were pre-processed to ensure that conversion of PET activity concentration to standardized uptake value and MR bias field correction and normalization could not affect validation results (supplementary note 3). Nine image processing and convolutional filter configurations were specified for each modality. Teams were blinded to the results submitted by other teams. After submitting results, obvious configuration errors were reported back to the submitting team.

Reproducibility was assessed using the two-way, random-effects, single rater absolute agreement intraclass correlation coefficient (ICC) [START_REF] Shrout | Intraclass correlations: uses in assessing rater reliability[END_REF]. Based on Koo and Li [START_REF] Koo | A guideline of selecting and reporting intraclass correlation coefficients for reliability research[END_REF], reproducibility of each feature was assigned to one of the following categories, based on the lower bound of the 95% confidence interval of the ICC (12): poor, lower bound less than 0.50; moderate, between 0.50 and 0.75; good, between 0.75 and 0.90; and excellent, greater than 0.90.

Results

Fifteen teams from seven countries participated in the first phase, eleven teams in the second phase, and nine teams in the validation phase. Eleven teams had developed publicly available software: CaPTk, CERR, FAST, LIFEx, MIRAS, MIRP, moddicom, S-IBEX, SPAARC, and the McGill and Université de Sherbrooke teams (see supplementary note 6).

Of the thirty-six response maps that were assessed in the first phase, moderate or better consensus was found for seventeen (47%) at the initial timepoint (Fig. 3). At the final timepoint, moderate or better consensus was achieved for thirty-three (92%) configurations, of which twenty-four (67%) were very strong. Full consensus was reached for configurations corresponding to mean filters, Laplacian-of-Gaussian filters, Laws kernels, Gabor kernels, as well as separable and non-separable wavelets (including decomposed forms). No or only weak consensus was achieved for three (8%) configurations, corresponding to configurations involving Riesz transformations (Fig. E1).

At the initial time point of the second phase, moderate or better consensus was achieved for 198 (50%) of 396 features, aggregated over twenty-two different filter configurations. At the final time-point 323 (82%) features had at least moderate consensus. Again, full consensus was reached for features computed from response maps of mean filters, Laplacian-of-Gaussian filters, Laws kernels, Gabor kernels, as well as separable and non-separable wavelets (including decomposed forms), except for the quantile coefficient of dispersion feature for three-dimensional non-separable wavelets. No consensus was established for features based on (steered) Riesz transformations (Fig. E2) because too few teams submitted values for these features.

In summary, eight types of convolutional filters were standardized in the first two phases. The reproducibility of features from response maps created by these filters was assessed in the third phase. Here, good to excellent reproducibility of features was found for 458 (92%) of 486 features. Overall, nineteen (4%) features were poorly reproducible, and were found for Laplacian-of-Gaussian, separable and non-separable wavelet filters. Most of these features were either coefficient of variation or quartile coefficient of dispersion features that represented eight and nine of nineteen features, respectively. A list of poorly reproducible features is provided in Table E1. No dependence on imaging modality could be observed. In phase 1, participating teams computed thirty-six response maps of convolutional filters according to predefined configurations. These response maps were compared, and consensus was measured. Teams updated their implementations iteratively, which led to an improvement of consensus over time (arbitrary unit, the entire process took twenty-four months). Consensus strength was based on matching the voxelwise difference between response maps and the tentative reference response map within a tolerance: weak, match between fewer than three teams; moderate, three to five; strong, six to nine; very strong, ten or more; none, 50% of the teams or more did not match. The number of participating teams at each timepoint is shown. In phase 2, participating teams computed 396 features from response maps of convolutional filters according to predefined filter and image processing configurations. As in phase 1, teams updated their implementations iteratively. However, unlike phase 1, improvement in consensus was mostly due to more teams enrolling over time (arbitrary unit, the entire process took eight months). Consensus strength was based on the number of teams matching the tentative reference feature value within a tolerance and was assigned according to the same categories as in phase 1. In phase 3, reproducibility of features computed from response maps was validated. Teams computed 486 features from a public dataset of fifty-one patients with softtissue sarcoma that were scanned using CT, FDG-PET, and T1w-MR imaging. Reproducibility was assessed using the lower bound of the 95% confidence interval of an intraclass correlation coefficient: poor, lower bound less than 0.50; moderate, between 0.50 and 0.75; good, between 0.75 and 0.90; excellent, greater than 0.90; and unknown, computed by fewer than two teams.

Discussion

Convolutional filters are commonly used in radiomics studies. However, due to lack of proper consensus-based reference implementations, features computed from response maps provided by these filters are difficult to reproduce [START_REF] Bogowicz | Post-radiochemotherapy PET radiomics in head and neck cancer -The influence of radiomics implementation on the reproducibility of local control tumor models[END_REF]. In this study, fifteen teams from seven countries collaborated to remedy this situation by providing reference response maps, reference feature values and reference documentation. We were able to standardize and validate eight different filter types: mean, Laplacian-of-Gaussian, Laws kernels, Gabor filters, and separable and non-separable wavelet filters in both undecomposed and decomposed forms.

The presented results complement the previous results of the Image Biomarker Standardization Initiative [START_REF] Zwanenburg | The Image Biomarker Standardization Initiative: Standardized Quantitative Radiomics for High-Throughput Image-based Phenotyping[END_REF]. That work focused on standardizing both the image processing scheme for radiomics and a large set of radiomic features. It aimed to improve reproducibility of radiomics studies by mitigating the effect of using different radiomics software packages, and by providing a common framework for describing methodological details. This work adds to the previous by standardizing the use of convolutional filters that are frequently used in radiomics.

This work has several implications: first, we found that most types of convolutional filters are not trivial to implement reproducibly across implementations, as evidenced by the initial lack of consensus on response maps in phase 1. Thus, we must assume that current clinical or research radiomics software in advanced image analysis workstations that offer convolutional filters yield feature values that are not reproducible in external settings, thereby hampering external validation and further clinical studies.

The second implication is that "IBSI-compliant" software is now expected to reproduce the reference response maps and reference feature values found in this study, insofar as convolutional filters are available in the software, in addition to the reference feature values that were previously found (2). Compliance may be checked using web-based tools (https://ibsi.radiomics.hevs.ch/), or manually using the provided reference response maps and feature values. Compliant software is expected to produce response maps where every voxel deviates from the reference response map by at most 1% of the range of intensity values of the reference response map. A feature value should be reproduced within the tolerance margin around the reference feature value.

Third, even though we contextualized our efforts within radiological imaging, our work is relevant for quantitative image analysis in general, including digital pathology. Finally, the IBSI reporting checklist for methodological details is now replaced by an updated version that includes reporting items for convolutional filters.

We standardized mean filters, Laplacian-of-Gaussian filters, Laws kernels, Gabor filters, and separable and non-separable wavelets. We also assessed Riesz transformations of convolutional filters in phases 1 and 2. Despite their attractive characteristics from a signal processing point-of-view, implementing Riesz transformations was not trivial and too few teams did so. Therefore, we could not provide reference response maps and reference values for Riesz transformations, and we did not assess these during the validation phase.

As Riesz transformations are only very rarely used in radiomics studies, the impact should be minimal.

Most features computed from response maps were reproducible after validation. However, several features could not be computed in a reproducible manner, notably the coefficient of variation and quartile coefficient features in conjunction with high-and band-pass convolutional filters. Such filters are characterized by a response map with a mean intensity of zero. Coefficient of variation relies on a division by the mean intensity the ROI that is close to zero. The quartile coefficient of dispersion relies on division by the sum values of the first and third quartiles of intensities in the ROI, which can be very similar except for their sign, as the distribution is again centered around zero. In the presence of high-and bandpass convolutional filters, the division operation present in both features led to otherwise negligible numeric differences between teams becoming relevant. This led to poor reproducibility. Therefore, these features should not be used in combination with high-and band-pass filters.

In this work, we standardized intensity-based statistical features computed from response maps, but not other types of features. Particularly, morphological features are mostly redundant as these are based on segmentation masks that are explicitly not altered by convolutional filtering. Most texture features, in our estimation, would be too abstract to allow for interpretation. We recommend computing only intensity-based features from response maps, as otherwise hundreds to thousands of features might be added to a radiomics analysis. This makes the process of creating a generalizable and interpretable radiomics model more difficult in the typical setting where at most a few hundred images are available for analysis [START_REF] Demircioğlu | The effect of preprocessing filters on predictive performance in radiomics[END_REF].

A limitation of this work is its necessarily restricted scope. Compliance with IBSI reference values helps to improve reproducibility of radiomic features [START_REF] Fornacon-Wood | Reliability and prognostic value of radiomic features are highly dependent on choice of feature extraction platform[END_REF][START_REF] Bettinelli | A Novel Benchmarking Approach to Assess the Agreement among Radiomic Tools[END_REF]. However, a radiomics study also comprises image acquisition, reconstruction, segmentation, and data analysis steps [START_REF] Zwanenburg | Radiomics in nuclear medicine: robustness, reproducibility, standardization, and how to avoid data analysis traps and replication crisis[END_REF][START_REF] Van Timmeren | Radiomics in medical imaging-"how-to" guide and critical reflection[END_REF], which we did not address here or in our previous work. Differences in, for example, image acquisition protocols are known to affect the appearance of an image, and therefore also reproducibility of radiomic features [START_REF] Berenguer | Radiomics of CT Features May Be Nonreproducible and Redundant: Influence of CT Acquisition Parameters[END_REF]. Such effects can be reduced by harmonization and cross-calibration of scanners and protocols [START_REF] Sullivan | Metrology Standards for Quantitative Imaging Biomarkers[END_REF] and post-hoc techniques such as perturbation [START_REF] Zwanenburg | Assessing robustness of radiomic features by image perturbation[END_REF][START_REF] Teng | Building reliable radiomic models using image perturbation[END_REF], batch normalization [START_REF] Orlhac | Validation of A Method to Compensate Multicenter Effects Affecting CT Radiomics[END_REF], and other methods [START_REF] Mali | Making Radiomics More Reproducible across Scanner and Imaging Protocol Variations: A Review of Harmonization Methods[END_REF].

Another limitation is that participation in the IBSI does not guarantee that a particular software package is compliant with the IBSI reference. Changes introduced in software (3), or design choices may limit compliance [START_REF] Wright | Reproducibility in medical image radiomic studies: contribution of dynamic histogram binning[END_REF]. It is therefore important that developers integrate comparison with the reference standard into their testing framework, and where absent, for users to assess whether the software is compliant.

The IBSI has so far focused on radiomics using hand-crafted features, and with this work offers a comprehensive reference standard for their computation. We recognize that there are more features and other filters than the ones we have standardized so far. These are not implemented often and will be hard to standardize for that reason. In the future, the IBSI will focus on deep learning applications of radiomics, with an aim to provide a reference standard for image pre-processing.

In conclusion, we standardized the use of eight types of convolutional filters for radiomics, and produced reference response maps, reference feature values and tools for verification and calibration of radiomics software packages.

Figure 2 :

 2 Figure 2: Convolutional filtering is positioned after resampling in the overall radiomics workflow (top panel). This workflow starts with an image that is obtained from a repository or archiving system in a digital format, such as DICOM. Then the image is optionally converted (e.g., from PET activity to standardized uptake values) and post-processed (e.g., MR biasfield correction). Segmentation masks are either loaded in a digital format, or automatically created. Both image and segmentation masks are then optionally resampled. Response

Figure 3 :

 3 Figure 3: Results overview.In phase 1, participating teams computed thirty-six response maps of convolutional filters according to predefined configurations. These response maps were compared, and consensus was measured. Teams updated their implementations iteratively, which led to an improvement of consensus over time (arbitrary unit, the entire process took twenty-four months). Consensus strength was based on matching the voxelwise difference between response maps and the tentative reference response map within a tolerance: weak, match between fewer than three teams; moderate, three to five; strong, six to nine; very strong, ten or more; none, 50% of the teams or more did not match. The number of participating teams at each timepoint is shown. In phase 2, participating teams computed 396 features from response maps of convolutional filters according to predefined filter and image processing configurations. As in phase 1, teams updated their implementations iteratively. However, unlike phase 1, improvement in consensus was mostly due to more teams enrolling over time (arbitrary unit, the entire process took eight months). Consensus strength was based on the number of teams matching the tentative reference feature value within a tolerance and was assigned according to the same categories as in phase 1. In phase 3, reproducibility of features computed from response maps was validated. Teams computed 486 features from a public dataset of fifty-one patients with softtissue sarcoma that were scanned using CT, FDG-PET, and T1w-MR imaging. Reproducibility was assessed using the lower bound of the 95% confidence interval of an intraclass correlation coefficient: poor, lower bound less than 0.50; moderate, between 0.50 and 0.75; good, between 0.75 and 0.90; excellent, greater than 0.90; and unknown, computed by fewer than two teams.

Funding information

The authors were supported by the National Cancer Institute grants P30CA008748 (A.P.A.), U01CA242871 (B.B., S.B.) and U24CA189523 (B.B., S.B.); UK Research & Innovation London Medical Imaging and Artificial Intelligence Centre (G.J.R.C.); UK Wellcome / Engineering and Physical Sciences Research Council Centre for Medical Engineering at King's College London (WT 203148/Z/16/Z) (G.J.R.C.); Cancer Research UK National Cancer Imaging Translational Accelerator awards C1519/A28682 (G.J.R.C., C.G.R.) and C4278/A27066 (V.G.); Swiss National Science Foundation grants 310030_170159 (H.S.G.), CRSII5_183478 (S.T.), 320030_176052 (H.Z.), 205320_179069 (A.D.), and 325230_197477 (A.D.); Natural Sciences and Engineering Research Council of Canada Discovery Grant (RGPIN-2019-06467) (A.R.); UK Engineering and Physical Sciences Research Council (EP/N509449/1) (E.S.); Canada CIFAR AI Chairs Program (M.V.); Swiss Personalized Health Network IMAGINE and QA4IQI projects (A.D.); and RCSO IsNET HECKTOR project (A.D.).

Manuscript Type

Original research

Word Count for Text 2323

Data sharing statement

Data generated by the authors or analyzed during the study are available at: https://github.com/theibsi/data_sets (imaging data) and https://github.com/theibsi/ibsi_2_reference_data (reference response maps and reference feature values). Code used to analyze the data and obtain the results can be found here: https://github.com/theibsi/ibsi_2_data_analysis (commit 778f813).

Abbreviated title page

Title

The Image Biomarker Standardization Initiative: Standardized convolutional filters for quantitative radiomics

Article type

Original research

Summary Statement

Eight types of convolutional filters were standardized for radiomics analyses.

Key Results

• Mean filters, Laplacian-of-Gaussian filters, Laws kernels, Gabor kernels, as well as separable and non-separable wavelets (including decomposed forms) are now welldefined and standardized for radiomic analyses. • Applying a filter to an image creates a response map. Thirty-three reference response maps and 323 reference feature values computed from response maps were identified.