Nadège Popoff
email: nadege.popoff@inrae.fr

Renaud Jaunatre

Caroline Le Bouteiller

Yoan Paillet

Gilles Favier

Morgane Buisson

Camille Meyer

Eric Dedonder

André Evette

Optimization of restoration techniques: In-situ transplantation experiment of an endangered clonal plant species (Typha minima Hoppe)

Keywords:

In the current context of biodiversity erosion, ecological restoration is sometimes the only way to reinforce plant population and preserve them from the deterioration of their natural habitat. Dwarf bulrush (Typha minima Hoppe) is an endangered pioneer clonal plant, which grows in frequently disturbed habitats along Eurasian temperate piedmont rivers. In the Alps, its population has decreased by 85% over the last century and numerous pressures (e.g. river works) continue to threaten its remnants. The main objective of this study is to identify an adapted ecological engineering protocol for field transplantation of T. minima in order to maximize restoration success. Several transplantation experiments were implemented between 2013 and 2016 along a French alpine river, the Isère. Five distinct transplantation protocols were tested by individually varying the following parameters: bank type (redesigned bank and embankment protection), transplantation height above water level (5 levels between +0.45 m and + 1.55 m above the average water level), initial biomass transplanted (high, medium and low), initial plot shape (linear strip or square plots) and species association (without or with Salicaceae or Poaceae). During the first two or three years, several clonal traits relative to the spatial monopolization and colonization abilities of T. minima were monitored and analyzed. Our analysis showed that T. minima's ability to colonize was optimal on natural banks, at medium transplantation heights and in linear strip plots. In addition, spatial monopolization and colonization speed, through both sexual and vegetative reproduction, were maximized with a higher initial biomass. Lastly, species association did not affect the colonization ability of T. minima. Our study provides valuable information for future conservation plans and restoration projects for T. minima.

Introduction

Restoration through ecological engineering is often a necessary conservation tool for endangered plant populations [START_REF] Dobson | Hopes for the future: restoration ecology and conservation biology[END_REF]. This is particularly the case in urban and peri-urban areas, where plant extinction has drastically increased over the last two centuries due to artificialization and the subsequent loss of natural habitats [START_REF] Mcdonald | Research gaps in knowledge of the impact of urban growth on biodiversity[END_REF].

However, the success of a population restoration is not guaranteed; indeed, several studies have highlighted numerous failures which are often underestimated [START_REF] Godefroid | How successful are plant species reintroductions?[END_REF][START_REF] Silcock | Threatened plant translocation in Australia: a review[END_REF].

To limit restoration failures, enhanced knowledge of the target species' ecology is necessary [START_REF] Menges | Adaptive introductions: how multiple experiments and comparisons to wild populations provide insights into requirements for long-term introduction success of an endangered shrub[END_REF]. Field experiments based on plant ecology theories and scientific knowledge can help optimize ecological engineering success by testing hypotheses in-situ [START_REF] Falk | Restoring diversity: strategies for reintroduction of endangered plants[END_REF][START_REF] Gellie | Networked and embedded scientific experiments will improve restoration outcomes[END_REF].

A crucial preliminary step in restoration project is the identification of suitable sites for collecting the initial plant material and for subsequent transplanting. The selected sites must be environmentally similar to the historical species habitat and close to remnant populations of the target species to enable sufficient gene flow [START_REF] Proft | Making the connection: expanding the role of restoration genetics in restoring and evaluating connectivity: Incorporating connectivity into restoration genetics[END_REF]. In riparian areas, widespread human activities such as diking, bank artifi cialization and damming, often make it difficult to identify historical habitats (IUCN, 2016).

Once donor and transplanting sites have been found, a second step is the collection of initial plant material. Collection and growth can be challenging for endangered plant species and transplanted biomass should be optimized. For instance, clonal plant species can produce genetically identical ramets using vegetative propagation, making it easier to restore and conserve local populations [START_REF] Baldwin | Propagation Methods for Rivercane [Arundinaria gigantea L. (Walter) Muhl[END_REF]). Providing a higher amount of biomass could favor transplanting success: clonal plant stem and root production (regeneration) increases with the quantity of initial rhizome biomass transplanted [START_REF] Cordazzo | Vegetative regeneration of panicum racemosum from rhizome fragments on southern brazilian coastal dunes[END_REF][START_REF] Luo | Burial depth and diameter of the rhizome fragments affect the regenerative capacity of a clonal shrub[END_REF][START_REF] Wang | The invasive stoloniferous clonal plant Alternanthera philoxeroides outperforms its co-occurring non-invasive functional counterparts in heterogeneous soil environmentsinvasion implications[END_REF]. Indeed, greater carbohydrate reserves and more meristems are contained in a larger rhizome biomass, and this can positively affect clonal plant regeneration in the early stages [START_REF] Klimešová | Belowground plant functional ecology: Towards an integrated perspective[END_REF][START_REF] Ott | The ecology and significance of below-ground bud banks in plants[END_REF].

After transplantation, some factors likely to affect restoration success in these early stages are specific to riparian habitats. For example, vegetation is subjected to disturbance regimes such as flooding or erosion and important feedback loops occur between vegetation and water and sediment flows [START_REF] Vervuren | Extreme flooding events on the Rhine and the survival and distribution of riparian plant species[END_REF][START_REF] Corenblit | Control of sediment dynamics by vegetation as a key function driving biogeomorphic succession within fluvial corridors[END_REF]. Riparian clonal-plant restoration projects should therefore take into account the hydrogeomorphological processes at work. Riparian species are distributed along a gradient of distance to water table depth [START_REF] Allen-Diaz | Water Table and Plant Species Relationships in Sierra Nevada Meadows[END_REF][START_REF] Shafroth | Woody riparian vegetation response to different alluvial water table regimes[END_REF][START_REF] Chen | Response of riparian vegetation to water-table changes in the lower reaches of Tarim River, Xinjiang Uygur[END_REF]). Moreover, floods, erosion and burial by sediments induce a high turnover in riparian vegetation in the most exposed areas [START_REF] Arscott | Aquatic Habitat Dynamics along a Braided Alpine River Ecosystem (Tagliamento River, Northeast Italy)[END_REF][START_REF] Gurnell | Changing river channels: the roles of hydrological processes, plants and pioneer fluvial landforms in humid temperate, mixed load, gravel bed rivers[END_REF]. [START_REF] Junk | The flood pulse concept in River -Floodplain systems[END_REF] introduced the "flood pulse concept" to describe the close interactions between biological and hydrogeomorphological processes along the river corridor. On the one hand, hydrogeomorphological processes drive ecological dynamics through population destruction and propagule dispersion [START_REF] Boedeltje | Dispersal phenology of hydrochorous plants in relation to discharge, seed release time and buoyancy of seeds: the flood pulse concept supported[END_REF]). On the other hand, biological dynamics also affect hydrogeomorphological processes through bank stabilization and propagule trapping induced by engineer species [START_REF] Kuzovkina | The characterization of willow (Salix L.) varieties for use in ecological engineering applications: Co-ordination of structure, function and autecology[END_REF]. This could explain the positive effect of young Salicaceae and herbaceous species in the maintenance and survival of pioneer riparian communities that [START_REF] Corenblit | Control of sediment dynamics by vegetation as a key function driving biogeomorphic succession within fluvial corridors[END_REF] observed.

The Dwarf bulrush (Typha minima Hoppe) is a clonal pioneer plant species growing on gravel bars and riverbanks [START_REF] Csencsics | La petite massette. Habitant menacé d'un biotope rare[END_REF][START_REF] Prunier | Distribution and decline of Dwarf Bulrush (Typha minima) in the Alps[END_REF][START_REF] Jaunatre | Les populations iséroises de petite massette (Typha minima Hoppe) : suivis et perspectives de restauration[END_REF]. Over the last century, T. minima has suffered a drastic decline, estimated at 85% in the Alps, due to river containment and floodplain drainage [START_REF] Prunier | Distribution and decline of Dwarf Bulrush (Typha minima) in the Alps[END_REF].

In this study, we used a large-scale project with multiple transplanting sites of Dwarf bulrush (Typha minima Hoppe) to address the following question: How can we improve transplanting protocols for this clonal pioneer plant species of riparian habitats?

Our first specific question was: What kind of riverbank and transplanting height above water would optimize the clonal expansion and survival of T. minima? We hypothesized that: (1) T. minima would root and expand more easily on a managed riverbank that was physically and biologically close to a natural riverbank; (2) the optimal height above water for survival and expansion would provide a compromise between water availability and exposure to disturbance.

Our second question was: In view of the limited initial living material available, how could T. minima transplantation, spatial monopolization and colonization (asexual and sexual reproduction) be optimized through initial biomass and plot shape. We hypothesized that: (3) higher initial biomass, i.e. a higher initial amount of rhizomes transplanted, would speed up colonization due to greater clonal expansion; (4) a large-perimeter transplantation plot would maximize clonal expansion by offering a larger open space for clonal expansion.

Our third and final question was: How could association with a pioneer species improve T. minima clonal expansion though facilitation?

We hypothesized that: (5) association with other pioneer species could improve T. minima clonal expansion and survival through facilitation interactions.

Methods

Study site

The study site was located in France along the Isère River, a tributary of the Rhône River, between Pontcharra and Grenoble (Southeastern France) in the Alps (Fig. 1). During the nineteenth century, major embankment works were undertaken along the river to drain the floodplain and control flooding [START_REF] Girel | Biodiversity and land use history of the alpine riparian landscapes (the example of the Isère river valley, France)[END_REF][START_REF] Girel | Diking of the Isère river in Savoie: history and consequences on landscape patterns[END_REF]. Today, over the 60 km covered by the study area, the Isère River flows in a single embanked channel (contrary to the ancient braided river) with a slope of 0.1% on average [START_REF] Allain-Jegou | Relations végétation -écoulement -transport solide dans le lit des rivières. Etude de l'Isère dans le Grésivaudan. Etude de l'Isère dans le Grésivaudan[END_REF]. The space between the dikes (channel width: 70 m to 130 m) includes a few gravel bars and vegetated islands [START_REF] Vautier | Développement végétal dans le lit endigué de l 'Isère en amont de grenoble : du diagnostic à l'évaluation des pratiques de gestion[END_REF]. Dominant vegetation types comprise pioneer communities (Calamagrostis pseudophragmites (Haller f.) Koeler, Phalaris arundinacea L., Typha minima Hoppe, Salix spp., Populus spp. and Alnus spp.), hardwood communities (Fraxinus excelsior L., Robinia Pseudacacia L.) and intermediate stages i.e. post pioneer communities [START_REF] Vautier | Développement végétal dans le lit endigué de l 'Isère en amont de grenoble : du diagnostic à l'évaluation des pratiques de gestion[END_REF]. A snowmelt and rainfall regime characterizes the river hydrology (Vivian, 1969;Jourdain et al., 2015) and causes annual spring and fall floods (the average flow in Grenoble is 120 m 3 /s while annual flood flow is 420 m 3 /s) (EauFrance, 2020).

Typha minima Hoppe

The habitat of the Dwarf bulrush (Typha minima Hoppe) is characterized by sandy-silty moist substrates on gravel bars and riverbanks frequently disturbed by floods, which are crucial to maintaining its population dynamics [START_REF] Werner | Recent évolution of Typha minima in the Alps and recommendations for river restoration[END_REF][START_REF] Baur | Ecology and development of Typha minima illustrated by a re-introduced population at the Upper Drava River (Austria)[END_REF]. New habitat colonization is possible by clonal expansion, rhizome fragment dispersal (vegetative reproduction) and seed dissemination (sexual reproduction) through anemochory or hydrochory [START_REF] Csencsics | La petite massette. Habitant menacé d'un biotope rare[END_REF]). The species is fugacious in the sense that it has a high population turnover [START_REF] Trabaud | Diversity and stability in garrigue ecosystems after fire[END_REF] with continuous local extinctions and new colonization processes related to the high disturbance rate of its habitat [START_REF] Till-Bottraud | Spatial structure and clonal distribution of genotypes in the rare Typha minima Hoppe (Typhaceae) along a river system[END_REF]. According to the UICN species red-list (https://www.iucnredlist.org/), T. minima is considered extinct in Germany [START_REF] Greulich | Synthèse Typha minima Funck[END_REF], critically endangered (CR) in Austria and endangered (EN) in Switzerland. In France, the species is still classified as of Least Concern (LC, IUCN) but has been listed as endangered at the regional scale, making its populations a major conservation focus in the Alps.

Transplanting experiments

Between 2013 and 2016, clones of T. minima were transplanted along the Isere River in the context of compensatory measures associated with flood protection works (between 2004 and 2021) [START_REF] Jaunatre | Les populations iséroises de petite massette (Typha minima Hoppe) : suivis et perspectives de restauration[END_REF]. These transplantations were used as a basis for experiments and were carried out at six sites within the study area (Fig. 1,A). Initially, 7140 different ramets were collected at three locations within the study area and multiplied in a nursery. Then, the rhizomes were transplanted in situ during leaf-off season, following five distinct experimental protocols detailed below.

Bank type effect

The aim of this first experiment was to determine T. minima's capacity to take root and spread after transplanting according to the type of riverbank. Indeed, several riverbank types, arising from the flood protection works, are present in the study area and were tested for trans Fig. 1. A -Map and location of the study area with transplantation sites on the Isere River (southeastern France). Average river flows and altitude values are from the downstream and upstream hydrological stations (in white on the map). B -Schematic protocols implemented in the study area. First, bank type effect was tested on a redesigned bare bank (B3), mixed-technique banks (G1) and riprap (R1) with bucket transplants. Then 5 heights above the water level and 2 species associations were tested on a redesigned bare bank (B3) with container transplants. Third, initial biomass effect was tested on 2 redesigned bare banks (B1 and B2) with containers, buckets and bare root transplants. Finally, plot shape effect was tested on a redesigned bare bank (B4) with direct transplantation. plantation: 1) redesigned bare banks; 2) mixed-technique banks with riprap (civil engineering) and vegetation components (soil bioengineering); and 3) dikes protected by riprap. The riprap is composed of a coarse substrate (rocks and blocks) whose gaps are filled by a silty-sand substrate deposited by floods, whereas the bare banks are entirely composed of a fine substrate. In 2015, three sites with differing bank designs (redesigned bare banks (B3), mixed-technique banks (G1) and riprap (R1)) were transplanted with 100 plots each (300 plots). The transplants were of contained in medium biomass (mb) buckets (9 cm*9 cm) at each plot and the buckets were spaced four meters apart: (R1 -G1 and B3, Fig. 1,B).

Transplanting height above water

A second experiment, implemented in 2015, was designed to test the effect of height above the water line on T. minima clonal expansion and survival rate. Previous studies in the same area had shown that T. minima was naturally located between 0.45 m and 1.55 m above the average river level [START_REF] Jaunatre | Les populations iséroises de petite massette (Typha minima Hoppe) : suivis et perspectives de restauration[END_REF]. Following these results, 372 plots were randomly dispersed along five height lines relative to the average river water level (l1: +0.45 m x12, l2: +0.75 m x92, l3: +1 m x148, l4: +1.30 m x96, l5: +1.55 m x24). Along a given height line, the plots were separated from each other by at least 4 m; between two height lines, the plots were separated by at least 1 m (B3, Fig. 1,B).

Initial biomass effect

A third experiment consisted of transplantations with different initial biomass amounts to determine which one best optimized T. minima spatial monopolization and speed of colonization (sexual and vegetative). The experiment was implemented at two sites (B1 -B2, Fig. 1,B) on redesigned bare banks between 2013 and 2014. At site B2, ten blocks of three 2x8m plots each were selected and T. minima was randomly transplanted among the three plots at a high initial biomass ("hb": 44 containers of 30 L per plot), a medium biomass ("mb": 84 buckets of 9 × 9 cm per plot) and a low biomass ("lb": 82 bare roots per plot) (B2, Fig. 1,B). At site B1, five blocks were set up, each composed of one plot (2 × 8 m) at high biomass ("hb": 30 containers of 30 L per plot) and two plots (2 × 8 m) at low biomass ("lb" 130 bare roots per plot).

Plot shape effect

A fourth experiment was designed to determine the best plot shape to maximize T. minima colonization. Two simple easy-to-implement shapes were chosen: linear strips and squares. Rhizomes with their soil (without containers) were directly transplanted from nurseries in fall 2016 on redesigned flat bare banks in ten linear strip plots ("lp": 0.3 × 20 × 0.5 m, 1.26m 3 , perimeter = 42.6 m) and ten square plots ("sp": 2.5 m × 2.5 m × 0.5 m, 1.26m 3 , perimeter = 10 m) randomly dispatched along the banks (B4, Fig. 1,B). The square and linear strip plots were separated from each other by 5 (minimum) to 10 m (maximum). The same initial volume (1.26m 3 of rhizomes + soil) was transplanted to each plot; consequently, T. minima biomass was considered to be similar among plots.

Species association effect

A final experiment tested the species association effect on T. minima expansion and survival rate. In 2015, high biomass containers (30L) of T. minima were randomly transplanted on redesigned bare banks (B3, Fig. 1,A) according to three treatments: one with T. minima alone ('hb": 118 control) and two with species associations: T. minima + Poaceae species (randomly chosen between Calamagrostis pseudophragmites (Haller f.) Koeler and Phalaris arundinacea L.) (84 "hbh")); and T. minima + Salicaceae species (randomly chosen between Salix alba L. and Salix triandra L.) (76 "hbs")). The species-association plots had one central container of T. minima surrounded by four Salix spp. cuttings ("hbs") or four tussocks of Poaceae species ('hbp") (B3, Fig. 1, A andB).

U N C O R R E C T E D P R O O F N. Popoff et al. Ecological Engineering xxx (xxxx) xxx-xxx
2.4. Functional traits monitored [START_REF] Primack | The experimental ecology of reintroduction[END_REF] suggested that restoration success could be considered a success when plant populations had achieved the following: i) patchy expansion and new colonization and ii) seed production and dispersal related to self-persistence over time. To evaluate our experiments in terms of success, we monitored the functional traits representative of these capacities as follows: spatial monopolization (frequency) and colonization ability (patch expansion, vegetative and sexual reproduction).

We monitored T. minima traits related to competition and regeneration, to evaluate the effects of the different transplantation protocols in our experiment area. First, we used T. minima frequency to assess species abundance, as related to spatial monopolization and the plant's subsequent capacity to monopolize natural resources (Van Groenendael and de Kroon 1990; [START_REF] Klimes | Clonal Plant Architecture a Comparative Analysis of Form and Function[END_REF]. Second, we measured the internode length (length of the rhizomes between two connected ramets) and clonal expansion (from plot measurements taken both perpendicularly and parallel to the river) to assess the dispersal distance attained through vegetative multiplication [START_REF] Klimes | Clonal Plant Architecture a Comparative Analysis of Form and Function[END_REF][START_REF] Herben | Clonal growth and sexual reproduction: tradeoffs and environmental constraints[END_REF]. Lastly, we counted the number of inflorescences to assess the potential for short-and long-distance dispersal through sexual reproduction [START_REF] Pywell | Plant traits as predictors of performance in ecological restoration[END_REF][START_REF] Godefroid | How successful are plant species reintroductions?[END_REF].

Data acquisition and extrapolation

All the transplanted sites had been monitored annually from their implementation and until the plots had merged and covered all open space (between 2 and 3 years). T. minima frequency was estimated by the pinpoint contact method (at least 100 points) implemented along two transects through the initial plots B1, B2 and B4, perpendicular and parallel to the river through the plot center. The internode length between two ramets was measured on ten rhizomes on each of plots B1 and B2. We randomly selected 10 ramets on each treatment by threwing a stone into a T. minima patch, dug down and extracted the first rhizome available and measured it. Clonal expansion was assessed through direct measurement of "plot width" perpendicular to the river and "plot length" parallel to the river at all the transplanted sites. Finally, the total number of inflorescences per plot was counted at sites B1 and B2. Area and clonal expansion data were calculated from plot dimension measurements. Plot area was approximated by multiplying the plot width and length of the square plots (B1, B2, B4). For the strip transplantations (B3, R1 and G1), a proxy for plot area was obtained by calculating an ellipse to better match the plot shape. Lastly, inter-annual clonal expansion was calculated in terms of plot area, plot width and plot length for all the transplanted sites (Expansion X t = X t -X t-1 ). Supporting data are available in supplementary material (Table S1).

Statistical analyses

We used the R software (version 3.5.1) to process the statistical analyses. We applied mixed models with transplantation protocol (bank type, transplantation height, initial biomass, plot shape, species association) and monitoring year as fixed factors, and site as a random factor. Following [START_REF] Hervé | RVAideMemoire: testing and plotting procedures for biostatistics[END_REF], we used either LMM or GLMM with different error distribution families or link functions. For all continuous variables, we built LMMs (Table S2) with a Gaussian error distribution (default) for five explanatory variables: area expansion (at sites G1, R1 and B3), width and length expansion (at site B3, for the height and species association protocols), width and length expansion (site B4) (I only see five variables: area exp., width exp., length exp., height and species). We built GLMMs with a Gamma error distribution and a loga rithm link [lme4 package, [START_REF] Bates | Fitting linear mixed-effects models using lme4[END_REF]] for the continuous and strictly positive variables: internode length (B1-B2 site) and plot area (B3 site, elevation and association protocols; Table S2). We built two GLMMs with a Quasi-binomial error distribution and logit link for species frequency of occurrence (B1-B2 and B4 site; Table S2) [Matrix package, [START_REF] Bates | Matrix: Sparse and Dense Matrix classes and Methods[END_REF]]. Lastly, for over-dispersed count data, the number of inflorescences, we built a GLMM with a negative binomial error distribution (B1-B2 site; Table S2) [MASS package, [START_REF] Venables | Modern Applied Statistics with S[END_REF]]. Due to the limited number of replicates available for the lowest height above water line (l1: 0.45 m) at site B3 (Table S2), it was excluded from the analyses. We validated our models by assessing the independence between the model residuals and fitted values.

To assess the significance of each factor, we performed F-tests (for the linear models) or a Wald chi-square test (for the generalized models) [car package (Fox and Weisberg, 2019)]. If the fixed effect was significant (p value <0.05), the mixed models were then assessed with a post-hoc multi-comparison test [multcomp package [START_REF] Hothorn | Simultaneous Inference in General Parametric Models[END_REF]) and emmeans package [START_REF] Lenth | Emmeans: estimated marginal means, aka least-squares means[END_REF]] with 0.05 as the p-value threshold.

Results

Transplanting location

Bank-type effect

The riverbank type strongly affected the clonal expansion of T. minima (X 2 = 10.08, df = 2, p = 0.006). One year after completion, transplanting on redesigned bare banks (741 ± 274 cm 2 ) resulted in better vegetative colonization than on riprap (167 ± 54 cm 2 ) or on mixed-technique sites (78 ± 28 cm 2 ).

Effect of height above water line

Transplanting height did not affect the area occupied by T. minima for either monitoring year, whatever the elevation (from +0.45 m to +1.55 m above average water level). Only a year effect was found, with a larger area colonized the second year (X 2 = 361.52, df = 1, p < 0.001).

Nonetheless, expansion in width was affected by height above water line (X 2 = 8.96, df = 3, p = 0.03), monitoring year (X 2 = 193.29, Df = 1, p < 0.001) and their interaction (X 2 = 8.97, df = 3, p = 0.03) (Fig. 2). The greatest expansion in width was obtained for transplantations at plot l3: +1 m and the effect of height above water line was even more pronounced after two years (39 ± 3 cm, Fig. 2).

Similar trends were measured for expansion in length, which showed a significant effect of transplantation height (X 2 = 10.06, df = 3, p = 0.02) and monitoring year (X 2 = 193.45, df = 1, p < 0.001) at site B3. One year after implementation, greater length expansion was obtained for transplantations at plots l3: +1 m (86 ± 10 cm) and l4: +1.30 m (88 ± 10 cm). Two years after implementation, the pattern was the same but no longer significant. Height above average water level also affected transplants survival (X 2 = 17.72, df = 4, p = 0.001). Survival mostly increased with height (17% at plot l1, +0.45 m and 71% at l5: +1.55 m; Fig. 3). (See Fig. 4.)

Transplantation optimization

Initial-biomass effect

Initial biomass transplanted (X 2 = 47.19, df = 2, p < 0.001), monitoring year (X 2 = 23.05, df = 1, p < 0.001) and the interaction of the two (X 2 = 10.77, df = 2, p = 0.005) affected T. minima frequency at sites B1 and B2. Frequency increased with initial biomass during the two monitoring years though the increase was not significantly differ ent between medium and high initial-biomass transplantations in year two.

Initial biomass (X 2 = 39.47, df = 2, p < 0.001) and monitoring year (X 2 = 27.56, df = 1, p < 0.001) also affected the number of inflorescences: higher initial biomass produced a larger number of inflorescences than did medium biomass for both monitoring years. In addition, the number of inflorescences increased between the two monitoring years, for the high (t + 1 = 16.13 ± 5.55; t + 2 = 195.79 ± 53.66) and medium initial biomass treatments (t + 1 = 0.10 ± 0.10; t + 2 = 24.10 ± 12.28).

Finally, initial biomass (X 2 = 9.39, df = 2, p = 0.009) and monitoring year (X 2 = 4.23, df = 1, p = 0.03) had a significant effect on internode length: two years after transplantation, longer internode lengths were found for a high initial biomass (20 ± 4 cm) than for an initial low biomass (5 ± 1 cm). Moreover, internode length decreased with time for the low initial biomass (t + 1: 15.31 ± 1 cm, t + 2: 5.54 ± 0.5 cm).

Plot shape effect

Initial plot shape (X 2 = 5.90, df = 1, p = 0.01), monitoring year (X 2 = 49.22, df = 2, p < 0.001) and their interactions (X 2 = 24.30, df = 2, p < 0.001) affected expansion in width (perpendicular to the river) at site B4 (Fig. 5). The second year, linear strip width expansion was higher (127 ± 21 cm) compared to other monitoring years and to the square plot shape (Fig. 5). Nevertheless, plot width dropped the third monitoring year, both for linear strip plots (-36 ± 20 cm) and for square plots (-21.11 ± 20 cm), due to bank erosion.

Clonal expansion in length (parallel to the river) was only influenced by year (X 2 = 10.66, df = 2, p = 0.005). Finally, T. minima frequency was only affected by monitoring year (X 2 = 12.47, df = 2, p = 0.002) and the interaction between year and plot shape (X 2 = 10.85, df = 2, p = 0.004). However, due to the unbalanced data, the post hoc test did detect trends toward a higher T. minima frequency in square plots over time.

Species-association effect

Transplanting T. minima in association with other species did not affect plot area (X 2 = 0.88, df = 2, p = 0.64), plot width expansion (X 2 = 0.08, df = 2, p = 0.96) or plot length expansion (X 2 = 2.13, df = 2, p = 0.34). Only a year effect was detected for plot area (X 2 = 456.24, df = 1, p < 0.001), plot width expansion (X 2 = 204.35, df = 1, p < 0.001) and plot length expansion (X 2 = 127.14, df = 1, p < 0.001), with greater clonal expansion the second monitoring year. Moreover, no significant difference in survival rate was detected with species association (X 2 = 3.47, df = 2, p = 0.18).

Discussion

The restoration success of transplanting a given species by transplanting depends on the ability of the species to grow and reproduce effectively shortly after transplantation. Our results highlight that the spatial monopolization, colonization ability and the survival rate of Typha minima Hoppe could be optimized by adapting the transplanting protocol. Indeed, bank type, transplantation height above water, initial transplanted biomass and plot shape all significantly affected T. minima restoration, as reflected through certain clonal traits, during the early years after implementation. We found that T. minima colonization was higher on the most natural banks (redesigned flat bare banks) compared to mixed-technique banks and riprap, this validates our first hypothesis. Therefore, natural or redesigned bare banks should be preferred for transplanting. Our results are consistent with the findings of [START_REF] Guerrant | Reintroduction of rare and endangered plants: common factors, questions and approaches[END_REF], who showed that restoration site selection must be based on historical species habitat to maximize transplantation success. Among the three bank types we selected, the redesigned natural banks were the closest to historical T. minima habitat due to higher fine sediment cover available for vegetative colonization. However, we found that T. minima clonal expansion and maintenance were still possible on riverbank protection structures (mixed-technique banks and riprap), though with less success. Still, riverbank protection structures can serve as refuge zones for riparian plant species on urbanized rivers [START_REF] Cavaillé | Biodiversity assessment following a naturality gradient of riverbank protection structures in French prealps rivers[END_REF], as evidenced by the restored T. minima patches that grew on all three bank types and by spontaneous settlement observed on other riverbank protection structures where fine sediment deposition occurred.

Concerning the riparian elevation gradient, we showed that T. minima colonization by clonal expansion was optimal for medium heights above the water level as expected in our second hypothesis. Transplanting at higher levels did not lead to higher T. minima mortality despite a potentially higher competition for resources with later successional species [START_REF] Janssen | Fine-grained sediment deposition alters the response of plant CSR strategies on the gravel bars of a highly regulated river[END_REF] or drier abiotic conditions [START_REF] Shafroth | Woody riparian vegetation response to different alluvial water table regimes[END_REF]. Flood submergence and erosion could explain the survival rate gradient we observed. Along the riparian corridor, flood exposure drives vegetation turnover through erosion, accretion and immersion [START_REF] Arscott | Aquatic Habitat Dynamics along a Braided Alpine River Ecosystem (Tagliamento River, Northeast Italy)[END_REF][START_REF] Junk | The flood pulse concept in River -Floodplain systems[END_REF]) affecting riparian species expansion and survival rates [START_REF] Tealdi | Inter-species competition-facilitation in stochastic riparian vegetation dynamics[END_REF].

Optimizing biological material

We found that a high initial amount of transplanted biomass maximized spatial monopolization and colonization for T. minima from the first year after restoration; this confirmed our third hypothesis. More metabolic resources led to more space being colonized by T. minima during the first year, which undeniably enhanced the plant's ability to compete with other pioneer species that usually colonize riparian habitat [START_REF] Tealdi | Inter-species competition-facilitation in stochastic riparian vegetation dynamics[END_REF]. Two years later, stem production was equivalent for both medium and high transplanted biomass. Both amounts of biomass both improved vegetative colonization through the production of longer internodes. However, higher transplanted biomass also boosted inflorescence production and therefore improved colonization through sexual reproduction. In clonal plants, rhizomes act as storage organs besides serving in vegetative reproduction [START_REF] Klimešová | Belowground plant functional ecology: Towards an integrated perspective[END_REF][START_REF] Ott | The ecology and significance of below-ground bud banks in plants[END_REF]. Our results are consistent with previous studies, which have highlighted the positive feedback between initial rhizome biomass and clonal plant regenerative abilities (e.g. ramet number, survival) during vegetation recovery [START_REF] Luo | Burial depth and diameter of the rhizome fragments affect the regenerative capacity of a clonal shrub[END_REF][START_REF] Wang | The invasive stoloniferous clonal plant Alternanthera philoxeroides outperforms its co-occurring non-invasive functional counterparts in heterogeneous soil environmentsinvasion implications[END_REF]. Our results suggest using high initial biomass transplantation to optimize both clonal and sexual colonization, and using medium biomass to optimize clonal colonization only and to reduce costs (1115€ per 100m 2 vs 2580€ -3870€ per 100m 2 ).

Plot shapes also played a key role in T. minima colonization: greater clonal expansion occurred on linear strips with longer sides and more open habitat available for ramets. It has been acknowledged that ramet production and expansion in clonal plants are driven by resource availability [START_REF] Kettenring | Life on the edge: reproductive mode and rate of invasive Phragmites australis patch expansion[END_REF][START_REF] Reijers | Sediment availability provokes a shift from Brownian to Lévy-like clonal expansion in a dune building grass[END_REF]. We found that spatial monopolization (frequency) by T. minima was similar on linear strips and square plots during the first two years but regressed in width due to severe riverbank erosion the third year. Similar habitat destruction also occurred in the height experiment, especially at the lowest height above water. Frequent floods induce significant idiosyncratic significant bank erosion [START_REF] Gurnell | Changing river channels: the roles of hydrological processes, plants and pioneer fluvial landforms in humid temperate, mixed load, gravel bed rivers[END_REF][START_REF] Janes | Improving bank erosion modelling at catchment scale by incorporating temporal and spatial variability: Temporal and spatial variability within bank erosion modelling[END_REF]. Flooding occurrence should be therefore taken into account in the spatial designs for riparian species transplantation. Spreading the transplantations at different suitable heights and in multiple sites may constitute a bet-hedging strategy for successful transplantations [START_REF] Doherty | Increasing substrate heterogeneity as a bet-hedging strategy for restoring wetland vegetation[END_REF].

No facilitation effect by other pioneer riparian species on T. minima was evidenced in our results. Previous studies have demonstrated facilitation by Salicaceae or Poaceae species through their role in fine sediment accretion, stabilization and erosion resistance [START_REF] Corenblit | Control of sediment dynamics by vegetation as a key function driving biogeomorphic succession within fluvial corridors[END_REF][START_REF] Gurnell | Changing river channels: the roles of hydrological processes, plants and pioneer fluvial landforms in humid temperate, mixed load, gravel bed rivers[END_REF]. Salicaceae species could also have a facilitation effect on riparian pioneer vegetation though phytohormone production (i.e. abscisic acid (ABA) and gibberellins (GAs)) are involved in plant dormancy and growth [START_REF] Olsen | Mechanisms of dormancy regulation[END_REF]). Although the presence of these phytohormones in the immediate vicinity could improve seed germination and root growth [START_REF] Egorova | The technique of water extract preparation from goat willow leaves with allowance for circadian rhythm of their biological activity to stimulate scots pine seed germination[END_REF], our results did not allow us to detect this effect with T. minima.

To conclude, one limitation all of our transplanted banks had in common was that the initial environmental conditions were never exactly the same as those found on natural banks. The redesigned natural banks were artificially created for restoration purposes, some were sown to limit the arrival of exotic species and others were strongly affected by flow erosion due to a geomorphological imbalance with flow velocity [START_REF] Hagerty | Bank failure and erosion on the Ohio River[END_REF]). These restored banks can therefore be considered hybrids, or novel ecosystems, as the biotic conditions there were degraded and the ecological processes may be different from historical habitats [START_REF] Hobbs | Novel ecosystems: theoretical and management aspects of the new ecological world order[END_REF].

Perspectives for T. minima restoration

A lack of perspective and insufficient long-term monitoring often plague restoration projects [START_REF] Menges | Adaptive introductions: how multiple experiments and comparisons to wild populations provide insights into requirements for long-term introduction success of an endangered shrub[END_REF]. The next step toward improving T. minima restoration will be the long-term monitoring of restored patches, which will provide information on long-term population dynamics and ecological processes. Previous studies have shown that T. minima restoration can fail at the medium-term (5-10 years) [START_REF] Ansermet | Projet de restauration des berges de l'Arve (GE) en vue d'une réintroduction de la Petite massette (Typha minima Hoppe)[END_REF][START_REF] Werner | Recent évolution of Typha minima in the Alps and recommendations for river restoration[END_REF]. Nevertheless, T. minima being a riparian pioneer species, local extinctions are part of its natural population dynamics. Future work could focus on these long-term dynamics, including patch extinctions and emergence in natural sites related to the flood pulse concept [START_REF] Junk | The flood pulse concept in River -Floodplain systems[END_REF][START_REF] Boedeltje | Dispersal phenology of hydrochorous plants in relation to discharge, seed release time and buoyancy of seeds: the flood pulse concept supported[END_REF]. Moreover, another important issue is that most of the restored patches come from vegetative propagation of only a few clones. Connectivity between restored and natural patches should therefore be explored in terms of genetic structure and exchanges through sexual reproduction [START_REF] Proft | Making the connection: expanding the role of restoration genetics in restoring and evaluating connectivity: Incorporating connectivity into restoration genetics[END_REF].

Conclusion

Our results confirm that multiple hydrogeomorphological parameters affect riparian pioneer clonal plants (Typha minima Hoppe) and must be taken into account in restoration operations. We show that greater colonization by clonal expansion and sexual regeneration was achieved on redesigned bare banks compared to more artificial banks (riprap and mixed-technique banks). Transplanting at high and medium levels above the water line led to greater clonal expansion (in width and length) during the first years of growth, and initially higher biomass made it possible to maximize spatial occupancy (frequency) and colonization speed (number of inflorescences, internode length). To optimize biological material, linear strips proved to be the most suitable plot shape; they allowed greater vertical clonal expansion on the riverbank compared to square plots. We hope these results will

U N C O R R E C T E D P R O O F

Fig. 2 .

 2 Fig. 2. Effect of four transplantation heights (l2: 0.75 m, l3: 1 m, l4: 1.30 m and l5: 1.55 m above the average water level, X 2 = 8.96, df = 3, p = 0.03), monitoring year (X 2 = 193.29, df = 1, p < 0.001) and the interaction between the two (X 2 = 8.96, df = 3, p = 0.02) on T. minima clonal expansion in width monitored over 2 years (t + 1, t + 2) at site B3. Plot represents average width expansion and monitoring year with standard errors. Bars sharing a common letter are not significantly different (p < 0.05).

Fig. 3 .

 3 Fig. 3. Effect of transplanting height (l1: +0.47 m, l2: +0.75 m, l3: +1 m, l4: +1.30 m and l5: +1.55 m above average water level) on T. minima survival rate (% of total) for the first monitoring year at site B3 (ANOVA, X 2 = 3.53, df = 3 p = 0.001). Bars sharing a common letter are not significantly different.

  Fig. 4. Effect of three different amounts of initial biomass (high, medium and low, X 2 = 47.19, df = 2, p < 0.001), monitoring year (t + 1 and t + 2, X 2 = 23.05, df = 1, p < 0.001) and their interaction (X 2 = 10.77, df = 2, p = 0.005) on T. minima frequency at sites B1 and B2. Plot represents average frequency per initial biomass and monitoring year with standard errors. Bars sharing a common letter are not significantly different (p < 0.05).

Fig. 5 .

 5 Fig.5. Effect of two different initial plot shapes (linear strip or square) (X 2 = 5.90, df = 1, p = 0.01), monitoring year (X 2 = 49.22, df = 2, p < 0.001) and their interactions (X 2 = 24.30, Df = 2, p < 0.001) on T. minima expansion in width monitored over 3 years (t + 1, t + 2, t + 3) at site B4. Plot represents average expansion in width, per plot shape and monitoring year with standard errors. Bars sharing a common letter are not significantly different (p < 0.05).

Acknowledgements

The authors thank the Symbhi (Syndicat Mixte des Bassins Hydrauliques de l'Isère) for funding the restoration project and the Arbre Haie Forêt team for setting up the protocol in the field. We also thank Vincent Bourret, Vincent Breton, Nathan Daumergue, Camille Guilloteau, Delphine Jaymond, Marion Martinelli, Eric Mermin, Anaëlle Pinel and Margot Trinquier for their help with field data collection since the beginning of the restoration project.

Funding

This work was made possible and financially supported by the Symbhi (Syndicat mixte des bassins hydrauliques de l'Isère: https:// symbhi.fr/).

Credit author statement

Conceived and designed the experiments: MB, ED, AE and RJ. Implemented the experiment: MB and ED. Collected data: NP, GF, AE and RJ. Analyzed data: NP, YP and RJ. Wrote the manuscript NP. Contributed to draft versions: NP, YP, AE and RJ. Revised and approved the final version of the manuscript: all authors. et al., 2020et al., Olsen et al., 1994

Uncited references

McDonald

 Popoff et al. Ecological Engineering xxx (xxxx)xxx-xxx help managers and conservationists to design better restoration protocols and maximize restoration success. Supplementary data to this article can be found online at https:// doi.org/10.1016/j.ecoleng.2020.106130.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

All the transplanted sites had been monitored annually from their implementation and until the plots had merged and covered all open space (between 2 and 3 years). T. minima frequency was estimated by the pinpoint contact method (at least 100 points) implemented along two transects through the initial plots B1, B2 and B4, perpendicular and parallel to the river through the plot center. The internode length between two ramets was measured on ten rhizomes on each of plots B1 and B2. We randomly selected 10 ramets on each treatment by threwing a stone into a T. minima patch, dug down and extracted the first rhizome available and measured it. Clonal expansion was assessed through direct measurement of "plot width" perpendicular to the river and "plot length" parallel to the river at all the transplanted sites. Finally, the total number of inflorescences per plot was counted at sites B1 and B2. Area and clonal expansion data were calculated from plot dimension measurements. Plot area was approximated by multiplying the plot width and length of the square plots (B1, B2, B4). For the strip transplantations (B3, R1 and G1), a proxy for plot area was obtained by calculating an ellipse to better match the plot shape. Lastly, inter-annual clonal expansion was calculated in terms of plot area, plot width and plot length for all the transplanted sites (Expansion X t = X t -X t-1 ). Supporting data are available in supplementary material (Table S1).

We used the R software (version 3.5.1) to process the statistical analyses. We applied mixed models with transplantation protocol (bank type, transplantation height, initial biomass, plot shape, species association) and monitoring year as fixed factors, and site as a random factor. Following [START_REF] Hervé | RVAideMemoire: testing and plotting procedures for biostatistics[END_REF], we used either LMM or GLMM with different error distribution families or link functions. For all continuous variables, we built LMMs (Table S2) with a Gaussian error distribution (default) for five explanatory variables: area expansion (at sites G1, R1 and B3), width and length expansion (at site B3, for the height and species association protocols), width and length expansion (site B4) (I only see five variables: area exp., width exp., length exp., height and species). We built GLMMs with a Gamma error distribution and a logarithm link [lme4 package, [START_REF] Bates | Fitting linear mixed-effects models using lme4[END_REF]] for the continuous and strictly positive variables: internode length (B1-B2 site) and plot area (B3 site, elevation and association protocols; Table S2). We built two GLMMs with a Quasi-binomial error distribution and logit link for species frequency of occurrence (B1-B2 and B4 site; Table S2) [Matrix package, [START_REF] Bates | Matrix: Sparse and Dense Matrix classes and Methods[END_REF]]. Lastly, for over-dispersed count data, the number of inflorescences, we built a GLMM with a negative binomial error distribution (B1-B2 site; Table S2) [MASS package, [START_REF] Venables | Modern Applied Statistics with S[END_REF]]. Due to the limited number of replicates available for the lowest height above water line (l1: 0.45 m) at site B3 (Table S2), it was excluded from the analyses. We validated our models by assessing the independence between the model residuals and fitted values.

9.e1

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Bruno Bresson

Maude Portigliatti

Benoit Salvant

Christian Fretigny

Measuring Interdiffusion at an Interface Between Two Elastomers with Tapping-Mode and Contact-Resonance Atomic Force Microscopy Imaging

Keywords: atomic force microscopy (AFM), elastomers, interfaces, mechanical properties, miscibility

Measuring interdiffusion at an interface between two elastomers with tapping-mode and contact-resonance atomic force microscopy imaging

Bruno Bresson, Maude Portigliatti, Benoit Salvant, Christian

INTRODUCTION

The reliable measurement of polymer chain interdiffusion at an interface between two polymeric materials in contact is of great importance to many industrial applications. The description of composites materials based on a multilayered or blend elastomer structure, such as tires, requires its precise measurement. The interface between two polymers is a notion demanding precision. For example, two polymer mixtures can simply be put into contact, which leads to chain interdiffusion, or be submitted to a curing process, which leads to interdiffusion and crosslinking phenomena. In this study, butadiene rubber (BR) and styrene-butadiene rubber (SBR) were put into contact, and this BR/SBR couple was subsequently cured. The interphase between the two elastomers is defined by the region in which the value of a given physical property changes from one homogeneous region, with respect to that physical property, to the other. In this study, two atomic force microscopy (AFM) imaging modes were used to assess the interphase width: well-known tappingmode phase imaging and contact-resonance imaging.

In the tapping mode, the phase shift between the excitation of the cantilever and its response, which is dependent on the energy dissipation of the tip-sample system, 1,2 varies when the tip sweeps a surface with changing mechanical or chemical properties. Surprisingly, despite the common use of phase imaging to show the mechanical contrast in polymer blends, [3][4][5][6] almost no study has focused on the assessment of the interphase width. 7 Interphase width measurements are generally carried out on polymercharge composites 8,9 but not between two polymers. Moreover, the contrast phase inversion issue, pointed out and discussed in the literature, [10][11][12][13] can lead to a false assessment of the interphase width. Therefore, particular working conditions must be used. One aim of the article is to properly set some robust acquisition conditions and to discuss the effect of the experimental conditions on the assessment of the interphase width. Therefore, a contactresonance microscopy method [14][15][16] has been developed to validate the interphase width measurements; indeed, the agreement of the results obtained by both methods with very high and very weak mechanical solicitation ensures a proper assessment of the interphase width. In the literature, force or displacement modulation methods in the contact mode have been used for analyzing the contact stiffness. 17 Here, a resonant method has been used in which the resonance frequency of the cantilever is shifted because of the contact stiffness. 16,18

EXPERIMENTAL

Materials

The samples were bilayers, made of two elastomer layers 2.5 cm in diameter and 2 mm thick, that were put into contact and subsequently cured. They were supplied by the Michelin Technology Center (Clermont-Ferrand, France) and were studied as received. The polymers used were BR and SBR with respective number-average molecular weights of 120 and 240 kg/mol and respective glass-transition temperatures of 2105 and 2388C. Two SBR microstructures were chosen to modulate the miscibility of the SBR/BR couple: in the first sample (no. 1), the SBR/BR couple was immiscible, and in the second one (no. 2), the SBR/BR couple was miscible. The samples were prepared by the same procedure to minimize unwanted side effects: they were cut with a razor blade, just before being studied, to get samples with a typical size of 1 3 1 3 10 mm 3 presenting a clear interphase between the two elastomers in the center of the analyzed surface. The identification of the polymer on both sides of the interphase was then direct.

Tapping-mode imaging

Commercial silicon tapping cantilevers (BS-300, Budget Sensor) (Wetzlar, Germany) were used with a spring constant of about 40 N/m. The resonance frequency of the cantilever typically was 250 kHz. Tapping-mode AFM was performed with a Veeco Dimension 3100 atomic force microscope (Cedex, France). In this study, the excitation frequency, slightly below the resonance frequency of the free cantilever, was such that the ratio A(x)/A 0 (x) was equal to 0.8, where x stands for the excitation frequency, A stands for the amplitude of the cantilever, and A 0 stands for the free amplitude of the cantilever. The amplitude, given in nanometers, was obtained from approach-retract calibration of the cantilever in the tapping mode on a silicon wafer. Height and phase images were recorded simultaneously. The phase difference between the cantilever excitation at its resonance and the response of this cantilever was measured by an external lock-in amplifier. The input of the lock-in was the electrical signal arising from the diodes (deflection signal), and the reference signal was the driving excitation signal of the cantilever. It should, however, be noticed that most of the recent commercial instruments offer suitable build-in phase devices.

Contact-resonance microscopy

The contact-resonance experiments were performed with a home-built device. A silicon nitride V-shaped cantilever (Veeco NP) with an approximate stiffness of 0.58 N/m was in permanent contact with the sample surface. An electronic feedback loop excited the cantilever at its resonance frequency, whatever the contact conditions were. Excitation was performed via an electrostatic field 16 established between the sample holder and the grounded body of the microscope (Multimode, Veeco). The phase-controlled oscillator that we used was a simplified version of the feedback loops used in dynamic-mode force microscopy. 19 The large frequency shifts involved in the contact-mode resonance method allowed for a simpler design of the loop. The input signal of the home-built device was the electrical signal arising from the diode panel (deflection signal). It was first amplified to a constant amplitude (V 0 ) with an automatic gain control and was then phase-shifted. A constant voltage (V c ) was added, and this signal was driven to the sample holder, which was isolated from the ground. The resonance conditions of the loop were fulfilled when the frequency of the signal was identical to that of the cantilever and the phases were matched. The system is illustrated in Figure 1. The tip was embedded in an electric field proportional to the applied voltage, V c 1 V 0 cos(xt), where x is the frequency and t is the time. The dielectric tip was submitted to a polarization force proportional to the square of the applied tension {[V c 1 V 0 cos(xt)] 2 }. 20 This expression gave a term proportional to V c V 0 cos(xt), so that the magnitude of the driving force was controlled by the user. During the scan of the tip, the resonance frequency of the cantilever changed with the mechanical properties of the sample, and so did the quality factor.

The resonance frequency of the cantilever and the gain needed to keep the vibration amplitude of the cantilever constant were independently acquired during the scanning of the surface. The oscillation frequency of the first mode of the cantilever was about 40 kHz. In contact with an elastomer sample, the frequency of this first mode was shifted to a value ranging typically from 100 to 200 kHz, depending on the mechanical properties of the elastomer.

RESULTS AND DISCUSSION

Experimental conditions for tapping-mode phase imaging

As shown in the following, the experimental conditions had to be carefully chosen. Indeed, the artifacts in the phase images could prevent us from properly observing the interphase and therefore measuring its width. The experimental conditions of the phase acquisition in the tapping mode are discussed in the following to define robust imaging conditions.

As a first example, a topography image and a phase image of sample 1 are displayed in Figure 2. Only the phase image is split off in two contrasted areas with a sharp transition at the position of 5.5 lm.

Tapping-mode imaging conditions are of primary importance to get reproducible and coherent results. As the principles of the technique rely on the interactions between the tip and the surface, both the excitation frequency and the vibration amplitude determine the phase response of the oscillator. Two oscillation modes are possible: one is linked to an attractive tip-sample interaction, and the other is linked to a repulsive tip-sample interaction. 21 To point out the problems that can occur during the acquisition of a phase image, some phase profiles were acquired with different acquisition parameters. At first, the phase angle profile of the interface was recorded with two different free amplitudes and the same ratio of R sp 5 A sp /A 0 5 0.84, where A sp stands for the set point value and A 0 stands for the free amplitude value. The phase angle deviation, DF 5 F 2 F 0 , is displayed in Figure 3 for sample 2; F is the current phase angle, and F 0 is the reference phase angle. The result was obtained with a scanning range of 40 lm at a scan frequency equal to 0.5 Hz; the left part corresponds to BR, whereas the right part corresponds to SBR. The chosen phase reference (F 0 ) is equal to the mean phase of the BR (left) part. The contrast inversion suggests that the oscillation mode changed for SBR. For a weak value of the free amplitude (32 nm), the set point vibration amplitude can be reached in the attractive regime: van der Waals forces alone are able to reduce the amplitude of the cantilever to the working value. This regime is to be avoided because a weak mechanical response is expected. High driving amplitudes are then preferred for the interphase studies. In the following, the free amplitude is set to a value close to 180 nm.

To investigate the phase contrast when a phase image is recorded in the tapping mode, the phase profile of the interphase of sample 1 (narrower than the interphase of sample 2) was studied (see Fig. 4) with various values of the set point ratio and with a high value of the free amplitude (180 nm). The phase contrast increases with the R sp ratio decreasing. This is in agreement with the relation between the phase measurement and the energy dissipation during a tapping cycle, showing that increasing energy dissipation of the tip-sample interaction leads to an increasing value of the phase. 21 The relative phase between the two elastomers is kept constant whatever the set point values are, showing robust conditions in a regime of repulsive tip-sample interaction. Both a high driving amplitude and a low A/A 0 ratio ensured that we worked in the repulsive tip-sample interaction regime.

As mentioned previously, phase images are a measurement of the dissipation of the interaction between the tip and the surface. The origin of this dissipated energy can be found in adhesion or in the viscoelastic properties of the material. It has been recently shown 22 that, on elastomers, adhesion effects dominate. Then, one expects the tip radius and elastic modulus of the sample to play an important part in the observed contrasts. When the tip is damaged, a larger contact radius may increase the attractive part of the interaction. This may lead to poorer contrasts between both rubbers. Such an effect is exemplified in Figure 5. The profile acquired with a high set point ratio (0.99) is typical of an attractive regime. Increasing R sp induces a gradual evolution in which the contrast between the two elastomers disappears. In the interphase region, a nonmonotonic behavior can be observed, confirming the complex origin of the phase contrast in these intermediate imaging conditions.

To conclude this section, robust conditions could be found: a high free amplitude (180 nm) and a low A/A 0 ratio (<0.8). For an undamaged tip, these conditions guaranteed a good measurement of the interface between the two elastomers for most of the cases by favoring a repulsive interaction regime. These conditions were used to assess the interphase width for both samples: the interphase width is defined from the profiles by the distance between the two plateaus (Figs. 2 and3). Both samples were prepared with the same procedure. The only difference lies in the miscibility of the two polymers put into contact: the elastomers in sample 2 were miscible, whereas the elastomers in sample 1 were immiscible. The AFM signal shows an interfacial width of around 8 lm for the miscible couple, whereas the width of the immiscible couple was about 100 nm. In a recent study carried out on elastomer systems, 22 it was shown that in hard tapping conditions, the response of the tip can be affected by an inclusion 80 nm from the tip. This value is inferior to the measured interfacial width between the two elastomers (100 nm). This measurement is then believed to be the true value of the interfacial width. The confirmation of this argument is given in the next section.

It has to be stated that attenuated total reflection/ infrared spectroscopy was used on these samples to check that these micrometer-scale gradients measured by AFM indeed were linked to elastomer chain interdiffusion. The miscibility is a fundamental parameter of the interdiffusion of polymers, and a difference in the interfacial width between miscible and immiscible samples was expected. Measuring an interphase width of the order of 10 lm meant that macromolecules in these samples were able to cross distances equal to 1000 times their gyration radius ( 10 nm).

Interphase width measurements by contact-resonance microscopy

This section is devoted to the measurement of the interphase width by contact-resonance microscopy. Displayed in Figure 6 are the topography image, frequency image, and gain image of the BR/SBR interface of sample 2. These images were acquired with a scan size of 30 lm and a sweeping frequency of 0.1 Hz.

The main information extracted from these images is that only the frequency image and the gain image reveal the interphase between the two polymers (BR in the left part and SBR in the right part). Indeed, focusing on the frequency image, for example, we find that the contact-resonance frequency of the cantilever in the BR area is centered at 120 kHz, whereas it is centered at 132 kHz in the SBR area. The profiles extracted from these images in both cases give the same value of the interphase width, which is for sample 2 equal to 8 lm (Fig. 7): the frequency varia- tion is displayed with a frequency reference (120 kHz) equal to the mean frequency of the cantilever in the BR part (left).

It clearly appears that the resonance frequency on contact is essentially controlled by the mechanical properties of the elastomers. However, it is also observed that the topography, frequency, and gain images are correlated. This correlation between the three images is briefly discussed to properly assess the interphase width.

First, the examination of the profiles of each image indicates that a topography deviation as a sudden increase of the slope if the tip meets with a wall leads to a transient increase of the frequency and a transient decrease of the gain. The frequency and gain can then be changed without any modification of the mechanical properties of the material because of the scanning of the tip on a nonflat surface: the frequency and gain contrasts depend then on the roughness of the sample and the velocity of the tip; the frequency and gain are instead related to the derivative of the topography profile.

Second, for this reason, to obtain information independent of the topography, the mean resonance frequencies (mean gains) in the BR region on a flat area and in the SBR region on a flat area were compared. The comparison reveals unambiguously that the mechanical properties of the two elastomers are different. Moreover, it appears that the influence of the topography on the resonance frequency and gain variations is small compared with the influence of the nature of the elastomer: in the SBR part, the frequency variation is 2 kHz, and this value has to be compared to the frequency gap between BR and SBR (12 kHz).

Third, if the topography variations induce a gain change, it is possible to observe a gain or resonance frequency variation on a flat surface: close observation of the SBR part of each image shows, for example, that gain variations reveal more details than the topography images. Indeed, the gain variation is the result of a change for a fixed frequency of dissipated energy at the contact tip-sample.

In conclusion, even if the roughness and topography variation of the surface is strongly correlated to the gain and resonance frequency, the main source of the variation of the resonance frequency and the gain arises from the difference in the mechanical properties of the two elastomers. The roughness and topography induce only a second-order effect in comparison with the effect of the difference in the mechanical properties. It also should be noted that it is always possible to slow down the velocity of the tip on the surface, which decreases the topographyinduced contrast of the gain and frequency images.

In the topography, phase, and gain images of sample 1 (Fig. 8), it also appears clear that the frequency image and gain image provide good evidence for the interface. The profile extracted from these image gives an interphase width equal to 100 nm according to the result obtained by phase measurements. It should be noted that in comparison with the tapping experiment, the solicitation of the elastomer in a contact-resonance experiment is very weak, and this confirms that the interphase width of 100 nm obtained by the phase measurement under hard tapping conditions is the true width.

CONCLUSIONS

In this study, two methods have been presented to measure the interdiffusion at an interphase between two polymers in contact. The first is well-known tapping-mode AFM. Because of the frequently observed phase contrast inversion, it has been shown that both a high free amplitude (ca. 180 nm) and a reduced set point ratio are required to obtain good mechanical sensitivity and therefore a precise measurement of the interdiffusion. These particular conditions (hard mechanical solicitation) are allowed on very soft materials such as those studied. The interphase width has been precisely assessed between two miscible or immiscible polymers. These measurements have been confirmed by contact-resonance microscopy (very weak mechanical solicitation), in which the tip in contact with the sample is electrostatically excited at the resonance frequency of the cantilever. The gain and frequency imaging have allowed us to precisely measure the interphase width between the same polymers. The same interphase widths are obtained by both methods (weak and hard mechanical solicitation), and this confirms that the true interphase width is measured.

Figure 1

 1 Figure 1 Schematic diagram of the phase-controlled oscillator setup used for contact-resonance microscopy. G: Gain; AGC: Automatic Gain Controller.

Figure 2

 2 Figure 2 (a) Topography and (b) phase images of sample 1 acquired with a free amplitude of 175 nm, an R sp value of 0.85, and a sweeping frequency of 1 Hz. The left part corresponds to BR, and the right part corresponds to SBR. The Z-axis scale is displayed with the corresponding color for the topography image and phase image. The phase angle deviation (DF 5 F 2 F 0 ) is displayed in degrees with F 0 equal to the mean phase of the BR part.

Figure 3

 3 Figure 3 Two-phase profiles extracted from the twophase images of the interface of sample 2. The left part corresponds to BR, and the right part corresponds to SBR. A 0 and R sp are displayed. The phase angle deviation (DF 5 F 2 F 0 ) is displayed with F 0 equal to the mean phase of the BR part.

Figure 4

 4 Figure 4 Phase profile of the interface of sample 1 obtained in the tapping mode with a free amplitude equal to 180 nm, a scan frequency of 0.5 Hz, and different R sp values. The left part corresponds to BR, and the right part corresponds to SBR. The phase angle deviation (DF 5 F 2 F 0 ) is displayed with F 0 equal to the mean phase of the BR part.

Figure 5

 5 Figure 5 Sample 2 phase profile extracted from a phase image of the interface with a partially damaged tip. The left part corresponds to BR, and the right part corresponds to SBR. A 0 was equal to 178 nm. The different R sp values are displayed.

Figure 6

 6 Figure 6 (a) Topography, (b) frequency, and (c) gain images of sample 2 obtained with electrostatic excitation and with a sweeping frequency of 0.1 Hz.

Figure 7

 7 Figure 7 Sample 2 frequency variation profile extracted from the frequency image of Figure 6. The frequency variation is displayed with a reference frequency equal to the mean frequency of the cantilever in the BR part (on the left).

Figure 8

 8 Figure 8 (a) Topography, (b) frequency, and (c) gain images of sample 1 obtained with electrostatic excitation and with a sweeping frequency of 0.2 Hz.


Alexandre Saint

Anis Kacem

Kseniya Cherenkova
email: kcherenkova@artec-group.com

Konstantinos Papadopoulos

Julian Chibane
email: jchibane@mpi-inf.mpg.de

Gerard Pons-Moll

Gleb Gusev

David Fofi
email: david.fofi@u-bourgogne.fr

Djamila Aouada

Björn Ottersten

SHARP 2020: The 1st Shape Recovery from Partial Textured 3D Scans Challenge Results

The SHApe Recovery from Partial textured 3D scans challenge, SHARP 2020, is the first edition of a challenge fostering and benchmarking methods for recovering complete textured 3D scans from raw incomplete data. SHARP 2020 is organised as a workshop in conjunction with ECCV 2020. There are two complementary challenges, the first one on 3D human scans, and the second one on generic objects. Challenge 1 is further split into two tracks, focusing, first, on large body and clothing regions, and, second, on fine body details. A novel evaluation metric is proposed to quantify jointly the shape reconstruction, the texture reconstruction and the amount of completed data. Additionally, two unique datasets of 3D scans are proposed, to provide raw ground-truth data for the benchmarks. The datasets are released to the scientific community. Moreover, an accompanying custom library of software routines is also released to the scientific community. It allows for processing 3D scans, generating partial data and performing the evaluation. Results of the competition, analysed in comparison to baselines, show the validity of the proposed evaluation metrics, and highlight the challenging aspects of the task and of the datasets.

Introduction

Representing the physical world in 3D, including shape and colour, is key for industrial and research purposes [START_REF] Anguelov | Scape: shape completion and animation of people[END_REF][START_REF] Yang | Semantic parametric reshaping of human body models[END_REF][START_REF] Hasler | A statistical model of human pose and body shape[END_REF][START_REF] Pishchulin | Building statistical shape spaces for 3d human modeling[END_REF][START_REF] Bogo | Faust: Dataset and evaluation for 3d mesh registration[END_REF][START_REF] Xu | Multilevel active registration for kinect human body scans: from low quality to high quality[END_REF][START_REF] Bronstein | Numerical geometry of non-rigid shapes[END_REF][START_REF] Robinette | The caesar project: a 3-d surface anthropometry survey[END_REF]. It includes, for example, areas from virtual reality to heritage conservation, or from medical treatment to fitness, entertainment and fashion. 3D scanning allows to digitise the physical world, e.g. objects and humans. Acquired 3D scans vary in quality depending on the scanning system used, the properties of the target and the environment. For example, a high-end photogrammetric scanning system with a fixed camera array might capture high-quality data at a high frame rate but might be bulky, have a fixed structure, suffer from occlusion and limited in scanning volume. Other high-end systems such as hand-held devices might produce accurate results, while easily transported and easily oriented to limit occlusion, but cannot handle movable targets and are time-consuming. On the other hand, low-end scanning systems might be flexible and easy to manipulate but produce lowquality scans. Limiting factors due to the target or the environment include varying levels of details (e.g. finer anatomical parts), occlusion, non-rigidity, movement, and optical properties (e.g. fabric, material, hair and reflection). Moreover, for time-consuming acquisition systems or moving targets, it might be desirable or only possible to capture partial data. In this work, defective and/or partial acquisitions, are both viewed as data with missing information that must be completed.

The SHARP 2020 challenge for SHApe Recovery from Partial textured 3D scans is proposed to foster research and provide a benchmark on 3D shape and texture completion from partial 3D scan data. First, two new unique datasets of 3D textured scans are proposed to serve as reference data. These datasets contain thousands of scans of humans and generic objects with varied identities, clothing, colours, shapes and categories. One challenge is proposed per dataset, challenge 1 focusing on human scans and challenge 2 on object scans. Second, partial scans are generated synthetically, but randomly, to simulate a general pattern of partial data acquisition while still having access to ground truth data. Third, specific evaluation metrics are proposed to quantitatively measure the quality of the shape and texture reconstructions, and the amount of completed data. Fourth, reusable software libraries developed for the challenge are also made available. These contain routines to process 3D scans, to generate partial data, and to evaluate and analyse the submissions on the proposed benchmark. This paper summaries the SHARP challenge with a presentation of the proposed datasets, benchmark and evaluation method, as well as the results of the submitted methods and an analysis of the results. SHARP 2020 is the first edition of the challenge, held in conjunction with the 16th European Conference on Computer Vision (ECCV).

In the following, Section 2 describes the challenge and the proposed datasets. Section 3 describes the proposed evaluation protocol and, in Section 4, an extensive analysis on the results is presented. To conclude, the results and outcomes of the challenge are discussed in Section 5.

Challenges and Datasets

The SHARP challenge is split into two separate challenges: challenge 1 focuses on human scans, and challenge 2 focuses on generic object scans. Two corresponding datasets are introduced, 3DBodyTex.v2 for human scans, and 3DObjectTex for generic object scans. Table 1 describes the datasets with figures on the number of samples for different subsets, including the splits used in the challenges and categories of body pose and clothing type for 3DBodyTex.v2. 3DBodyTex.v2 is an extension of 3DBodyTex proposed by Saint et al. [START_REF] Saint | 3dbodytex: Textured 3d body dataset[END_REF]. See sample scans in Fig. 1. It contains about 3000 static 3D human scans with high-resolution texture. It features a large variety of poses and clothing types, with about 500 different subjects. Each subject is captured in about 3 poses. Most subjects perform the corresponding poses in both standard close-fitting clothing and arbitrary casual clothing. The faces are anonymised, for privacy reasons, by blurring the shape and the texture.

3DObjectTex is a subset of the viewshape [START_REF]Artec3D: viewshape: online repository of 3d scans[END_REF] repository. See sample scans in Fig. 2. It consists of about 1200 textured 3D scans of generic objects with a large variation in categories and in physical dimensions.

Both datasets encode the scans as 3D triangle meshes. The colour is encoded in a texture atlas with an independent and arbitrary UV mapping [START_REF] Zayer | Linear angle based parameterization[END_REF]

Challenge 1: Recovery of Human Body Scans

Challenge 1 covers the reconstruction of human scans, both with loose casual clothing and minimal close-fitting clothing.

Track 1: Recovery of Large Regions. Track 1 focuses on the reconstruction of large regions of human scans, excluding hands and head. Fig. 1 shows samples of the data, with ground-truth and partial scans. Both shape and texture are considered. These large regions are of relatively high quality in the raw reference data. The fine details (hands and head) are of unreliable quality and thus ignored in this track. The full 3DBodyTex.v2 dataset is used (see Table 1). Track 2: Recovery of Fine Details. Track 2 focuses on fine body details not considered in Track 1, i.e., hands, fingers, and nose. The raw scans are not of reliable quality for these details and the faces are not released due to privacy concerns. Thus, the reference data is generated synthetically from a body model [START_REF] Pavlakos | Expressive body capture: 3d hands, face, and body from a single image[END_REF] and the scans of 3DBodyTex.v2 in fitness clothing (see Table 1), where the fine body details are not occluded, to capture to the real distribution of rough poses and shapes. The reference data is generated in two steps: (1) fit a parametric body model to the scans to obtain the ground-truth data; (2) simulate the scanning process in software to obtain a synthetic scan (with simulated artefacts in the regions of interest, i.e. hands, ears...) from which the partial data is generated. The fitting is performed with the approach of Saint et al. [START_REF] Saint | Towards automatic human body model fitting to a 3d scan[END_REF][START_REF] Saint | 3dbodytex: Textured 3d body dataset[END_REF][START_REF] Saint | Bodyfitr: Robust automatic 3d human body fitting[END_REF]]. The texture is not considered in this setting as the raw data does not contain texture of reliable quality (and the parametric body model represents only the shape).

Challenge 2: Recovery of Generic Object Scans

Challenge 2 focuses on the shape and texture completion of generic objects. Fig. 2 shows some example objects.

Partial data

In all challenges, the partial data is generated synthetically by removing surface regions randomly, as shown in Fig. 1 and Fig. 2. This is done with a hole cutting operation following the steps below:

(1) take as input a central vertex v c and the number of vertices to remove k;

(2) select the k vertices closest to v c in Euclidean distance;

(3) remove the selected vertices and adjacent triangles from the mesh. The process is repeated 40 times, with k set to 2% of the points of the mesh. Most meshes in the datasets being regularly sampled, this is equivalent to defining a nearest-neighbour radius proportional to the size of the mesh. For challenge 1, the partial data is generated only in the considered regions (everywhere except hands and head for Track 1, and only on the hands, ear and nose in Track 2). The partial data is generated by the participants themselves. Additional methods for partial data generation were allowed if reported. Routines to generate the partial data were distributed in the provided software library.

Evaluation data

For evaluation, the partial data was generated by the organisers and shared with the participants. The reference data was held secret.

Evaluation Metrics and Scores

Entries to the challenge were ranked with an overall score, S, that considers jointly the quality of the shape and texture reconstructions, and the amount of completeness. It is based on the metrics proposed by Jensen et al. [START_REF] Jensen | Large scale multi-view stereopsis evaluation[END_REF], with modifications and extensions for the task of shape and texture completion. The main terms in computing the scores are a surface-to-surface distance accounting for missing data in determining correspondences, a measure of the texture distance (on top of the shape distance), surface area and hit-rate measures reflecting the degree of completion, and a mapping function to convert distances to scores, empirically adjusted from baseline data. Below, the ground-truth mesh is denoted, Y , and the estimated reconstruction, X.

Overall score. A single reconstruction is scored with,

S = S α S s + S t 2 ∈ [0, 1], (1)
where S a , S s and S t are independent scores for the surface area, shape and texture, respectively. All scores take as input the reconstructed and the groundtruth meshes, S = S(X, Y ), and map to the interval [0, 1]. A perfect reconstruction has a score of 1 and a poor reconstruction has a score tending towards 0. A submission to the challenge contains reconstructions for all the samples of the test set. The submission is ranked by averaging the individual scores into a final global score.

Surface area score. The surface area score,

S α = 1 -| ĀX -ĀY | ∈ [0, 1], (2)
penalises a reconstruction proportionally to the deviation of its surface area with respect to the ground truth. ĀX = A X A X +A Y is the normalised surface area of X with respect to Y . With a surface area lower or greater than the ground truth, S a decreases proportionally the overall score [START_REF] Anguelov | Scape: shape completion and animation of people[END_REF]. As the surface area approaches the ground truth, S a approaches 1, less affecting the overall score. The surface area of a mesh is computed in practice by adding the surface areas of all the individual triangles.

Surface-to-surface distance. Both shape and texture scores, S s and S t , are determined by estimating the directed distances, d XY and d Y X , between the ground truth mesh Y and the estimated reconstruction X.

The directed distance between mesh A and mesh B, d AB , is computed by sampling N points uniformly on the surface of A, finding the corresponding closest points on the surface of B, and averaging the associated distances.

For a point p A ∈ R 3 on A, the corresponding closest point on B is determined by computing the smallest point-to-triangle distance between p A and all triangles of B. The point-to-triangle distance, d = d 0 + d 1 , is made of two components. For a specific triangle in B, d 0 is the Euclidean distance from p A to the closest point p 0 on the plane of the triangle. d 1 is then the Euclidean distance from p 0 to the nearest point p 1 of the triangle (in the plane of the triangle). If the intersection p 0 is inside the triangle, it is denoted as a hit, otherwise it is a miss. In case of a hit, p 0 = p 1 , thus d 1 = 0 and d = d 0 .

Hit rate. When computing the surface-to-surface distance from mesh A to mesh B, the hit rate,

h AB = H AB N ∈ [0, 1], (3)
is the proportion of the N points sampled on A hitting B (see previous paragraph).

Shape score. The shape score,

S s = S XY s + S Y X s 2 = h XY φ s (d XY s ) + h Y X φ s (d Y X s ) 2 (4)
is a measure of the similarity of the shape of two meshes. The measure is symmetric by averaging the directed measures. The hit rates, h XY and h Y X , penalise overcomplete and incomplete reconstructions, respectively. In the directed shape score,

S XY s = h XY φ s (d XY s ), (5)
the mapping function φ s : [0, ∞] → [0, 1] converts the computed distance to a score in [0, 1]. It is defined by a normal distribution function with zero mean,

φ s (d) = 1 σ s √ 2π e -1 2 ( d σs ) 2 , (6)
where the standard deviation σ s is estimated from baselines, including the groundtruth data, the input partial data, additional perturbations thereof with local and/or global white Gaussian noise on the shape, and a baseline of shape reconstruction based on a hole-filling algorithm.

Texture score. The texture score,

S t = S XY t + S Y X t 2 = h XY φ t (d XY t ) + h Y X φ t (d Y X t ) 2 (7)
is similar in principle to the shape score, S s , except that the distance d t is computed in texture space for all point correspondences obtained by the surfaceto-surface distance. Additionally, the parameter σ t for the mapping function φ t specific to the texture is estimated from the ground-truth data, the input partial data, and additional perturbations with local and/or global white Gaussian noise, in both shape and texture. Below, the texture score is also interchangeably denoted colour score.

Results and Analysis

This section presents and analyses the submissions to both challenges. The challenge has attracted 32 participants with 9 validated registrations for Challenge 1 and 6 for Challenge 2. Table 3: Reconstruction scores (%) of the baseline and the proposed methods for both challenges. The baseline is the unmodified partial data.

Challenge 1 -Track 1

In challenge 1, track 1, the RVH-IF [START_REF] Chibane | Implicit functions in feature space for 3d shape reconstruction and completion[END_REF][START_REF] Chibane | Implicit feature networks for texture completion of 3d data[END_REF] approach ranks first with an overall reconstruction score of 86.75% (see Table 3). SnT-3DB comes second with 62%. RVH-IF surpasses the baseline unmodified partial data with an overall score of 46% higher and performs significantly better than SnT-3DB [START_REF] Saint | 3dbooster: 3d body shape and texture recovery[END_REF] with a score increment of 24%. RVH-IF-2 has similar shape and texture scores with differences of 2-3%, while SnT-3DB has a much higher texture score, 16% above the shape score. The RVH-IF-2 variant slightly improves the texture score over RVH-IF-1, with 88.26% instead of 87.69%, but the shape scores are identical. Fig. 3 shows the frequency distribution of the scores. RVH-IF appears relatively tightly located around the mean score 85% with a slight tail expanding in the lower scores down to 60%. SnT-3DB appears more spread for the shape score and with a tail reaching very low scores down to 10% below the baseline. Fig. 4: Challenge 1 -track 1: Correlation between shape and texture scores, for the baseline unmodified partial data, and all submissions, SnT-3DB and RVH-IF-{1,2}.

Fig. 4 highlights the correlation of the shape and texture scores. The baseline unmodified partial data is highly correlated, which is expected because the partial data available is exact. RVH-IF methods display a high correlation, with overall a tendency towards better texture scores than shape scores, except for a small proportion of grouped outlier samples with higher shape and lower texture scores. The SnT-3DB method displays the same tendency towards better texture than shape but with more dispersed results. Not a significant group of outliers is observed. The weaker correlation in SnT-3DB could be due to at least two factors: the sequential nature of the method, making the shape and texture reconstructions somewhat independent of each other; the mostly uniform colour of most clothing and of the body shape, resulting in good texture recovery even if the spatial regions are not matched correctly.

Fig. 5 and6 show the distribution of scores and the correlation between shape and texture scores for subsets of the 3DBodyTex.v2 dataset. The casual clothing subset (Fig. 5a) shows lower and more dispersed scores than the fitness clothing (Fig. 5b). This reflects the diversity in texture and shape in the casual clothing, which is challenging for all proposed methods. Moreover, to a small but noticeable extent, the reconstruction scores are higher and more correlated in shape and texture on standard poses (Fig. 6d) than on non-standard ones (Fig. 6c). As a qualitative assessment, the best and worst reconstructions are shown in Fig. 7 for both approaches SnT-3DB and the RVH-IF. The best reconstructions are for scans in fitness clothing and standard pose, as also observed quantitatively above. The worst reconstructions are for scans in casual clothing and non-standard sitting/crouching poses, containing more shape and texture variation. It could also be that the ground truth for this data is less reliable, biasing the results towards lower scores. the shape score. As in Track 1, and as visible in Fig. 8, RVH-IF is the highestperforming approach with a score of 83% compared to 60.7% for SnT-3DB and 41.1% for the baseline. The distribution of scores is also more concentrated around higher values for RVH-IF.

Challenge 2

Challenge 2 contains four submissions by a single participant with the RVH-IF method. As reported in Table 3, RVH-IF-2 achieves the highest score around 75%, which is more than 30% over the baseline. The RVH-IF-1 is the second best-performing approach, a few percent below. Fig. 9 shows the distribution of reconstruction scores. All approaches achieve high shape scores. For the texture, RVH-IF-{3,4} perform less well and overlap the baseline, not improving much on the unmodified partial data. Overall, the scores are widely spread, even for the baseline. This reflects the diversity of object classes in 3DObjectTex, making both the reconstruction and the evaluation tasks challenging. This is confirmed in the shape-texture correlation in Fig. 10 where the correlation is less than in Challenge 1.

As Fig. 11 shows, the best reconstructions are of meshes with a closed surface, and with both a smooth shape and a relatively uniform texture. The worst reconstructions are of meshes with complex shapes, i.e. non-convex and with holes, creases, sharp edges, steps, etc.

Conclusion

This paper presented the SHARP 2020 challenge for SHApe Recovery from Partial textured 3D scans held in its first edition in conjunction with the 16th European Conference on Computer Vision. The SHARP challenge proposes to foster research and provide a benchmark on 3D shape and texture completion from partial 3D scan data. With two aspects, the recovery of human scans and of object scans, two unique datasets of reference high-quality textured 3D scans were proposed and released to the scientific community. Moreover, new specific evaluation metrics were proposed to measure simultaneously the quality of shape and texture reconstruction, and the amount of completion. The results of the participants show the validity of the proposed metrics, the challenging nature of the datasets and highlight the difficulties of the task. The RVH-IF submission obtained the highest scores in both challenges with the Implicit Feature Networks for Texture Completion of 3D Data. The variation in clothing seems a major difficulty in Challenge 1, and to a lesser extent, the pose. The texture seems more easily reconstructed than the shape, probably due to it being mostly uniform on clothing. The reconstruction of fine details was more demanding than the reconstruction of the full body. Challenge 2 shows that the proposed dataset of generic objects contains a lot of variation that makes both the shape and the texture challenging to recover. As in Challenge 1, smooth objects were better reconstructed.

The SHARP 2020 challenge has thus promoted the development of new methods for 3D shape and texture completion. The addition of the texture aspect on top of the shape aspect makes the contributions stand out from the current scientific literature. As the proposed metrics show, there is still room for improvement. This will be the object of the next editions of SHARP challenges.

Fig. 1 :

 1 Fig. 1: Samples of 3DBodyTex.v2 in casual (top rows) and fitness (bottom row) clothing. For each person, ground truth scan (left), sample synthetic partial scan (right).

Fig. 2 :

 2 Fig. 2: Samples of the 3DObjectTex dataset (normalised in scale for visualisation). The objects vary widely in scale and categories. For each object, groundtruth scan (left), sample synthetic partial scan (right).

Fig. 3 :

 3 Fig. 3: Challenge 1 -track 1: Boxplots and frequency distributions of the reconstruction scores of the samples of the test set, for the baseline unmodified partial data, and all submissions, SnT-3DB and RVH-IF-{1,2}.

Fig. 5 :

 5 Fig.5: Challenge 1 -track 1: Boxplots and frequency distributions of the shape (top), texture (middle) and overall (bottom) scores on the test set, for subsets of 3DBodyTex.v2, and for the baseline unmodified partial data and all submissions, SnT-3DB and RVH-IF-{1,2}. Subsets (columns): casual and fitness clothing, non-standard and standard (A and U) poses.

4. 2 2 Challenge 1 -

 221 Challenge 1 -Track Track 2 targets the reconstruction of fine details on the hands, ears and nose, with only a shape ground truth. The only score evaluated is thus

Fig. 6 :Fig. 7 :

 67 Fig. 6: Challenge 1 -track 1: Correlation of shape and texture scores on the test set, for subsets of 3DBodyTex.v2, and for the baseline unmodified partial data and all submissions, SnT-3DB and RVH-IF-{1,2}. Subsets (columns): casual and fitness clothing, non-standard and standard (A and U) poses.

Fig. 8 :

 8 Fig. 8: Challenge 1 -track 2: Boxplots and frequency distributions of shape scores on the test set, for the baseline unmodified partial data and all submissions, SnT-3DB and RVH-IF.

Fig. 9 :Fig. 10 :Fig. 11 :

 91011 Fig. 9: Challenge 2: Boxplots and frequency distributions of scores on the test set for the baseline unmodified partial data, and all submissions RVH-IF-{1,4}.

Table 1 :

 1 Contents of the datasets and categorical subsets, along with associated challenge and track. The standard poses are the A and U rest poses. The other poses are varied, from a predefined list or arbitrary. The casual and fitness clothing types are shown in Fig. 1.

	for each

  Table2gives the number of valid submissions, received and accepted, and the number of submitted solutions.

	challenge track registrations submissions/participants
				received	accepted
	1	1	9	4/3	3/2
	1	2	9	2/2	2/2
	2	-	6	4/1	4/1

Table 2 :

 2 Figures on validated registrations and entries for the challenges of SHARP 2020.The accepted entries are Implicit Feature Networks for Texture Completion of 3D Data[START_REF] Chibane | Implicit functions in feature space for 3d shape reconstruction and completion[END_REF][START_REF] Chibane | Implicit feature networks for texture completion of 3d data[END_REF], from RVH (Real Virtual Humans group at Max Planck Institute for Informatics), submitted in several variants to both Challenge 1 and Challenge 2, and 3DBooSTeR: 3D Body Shape and Texture Recovery[START_REF] Saint | 3dbooster: 3d body shape and texture recovery[END_REF], from SnT (Interdisciplinary Centre for Security, Reliability and Trust at the University of Luxembourg), submitted to Challenge 1. In the following, the entries are interchangeably abbreviated RVH-IF and SnT-3DB, respectively. Table3shows the quantitative results of the submissions for both challenges. The scores are reported in percent in an equivalent way to the scores mapping to [0, 1] in Section 3. The methods are compared to a baseline consisting of the unmodified partial data. The rest of this section presents and analyses the results.

	challenge track method		score (%)
				shape	texture	overall
			baseline	38.95 ± 4.67	40.29 ± 4.24	39.62 ± 4.41
	1	1	SnT-3DB RVH-IF-1	54.21 ± 14.28 85.24 ± 5.72	70.55 ± 7.26 87.69 ± 5.96	62.38 ± 9.61 86.47 ± 5.38
			RVH-IF-2 85.24 ± 5.72	88.26 ± 5.46	86.75 ± 5.19
			baseline	41.1 ± 3.31	-	-
	1	2	SnT-3DB	60.7 ± 10.98	-	-
			RVH-IF	83.0 ± 4.87	-	-
			baseline	42.09 ± 4.99	41.64 ± 5.24	41.87 ± 4.74
			RVH-IF-1	72.68 ± 23.47	76.44 ± 14.33	74.56 ± 16.89
	2	-	RVH-IF-2 73.91 ± 22.85 76.93 ± 14.31 75.42 ± 16.68
			RVH-IF-3	72.68 ± 23.47	53.13 ± 18.21	62.91 ± 16.09
			RVH-IF-4	73.91 ± 22.85	53.73 ± 18.33	63.82 ± 16.01

Acknowledgements

We thank Artec3D for sponsoring this challenge with cash prizes and releasing the data for the 3DObjectTex dataset. This work and the data collection of 3D human scans for 3DBodyTex.v2 were partly supported by the Luxembourg National Research Fund (FNR) (11806282 and 11643091). We also gratefully acknowledge the participation, at different times, of all members of the Computer Vision, Imaging and Machine Intelligence (CVI 2 ) Research Group at the SnT, University of Luxembourg, including the moderation of the workshop event by Renato Baptista and the support of Pavel Chernakov in the development of the evaluation software. Finally, we express our appreciation to all the reviewers of the workshop submissions.