Katell Guizien
email: guizien@obs-banyuls.fr

Marco Ghisalberti

Living in the Canopy of the Animal forest: Physical and Biogeochemical Aspects

Keywords: Benthic boundary layer, flow instability, drag, micro-niche, spatial heterogeneity, gradients, filaments, biotic-abiotic interactions, ecosystem engineers

Long-lived hard and soft coral species that are able to develop dense patches with a complex, threedimensional structure form an animal forest canopy, similar to trees in terrestrial systems. Aside from the shelter provided by this canopy to other organisms, the animal forest can significantly modify the local physical and biogeochemical environment.

In the first part of this chapter, the modification of benthic boundary layer hydrodynamics in and above canopies is described, with a focus on the impacts of canopy density and flexibility. In the second part of this chapter, the structure of diffusive and advective mass transfer in canopies will be presented and discussed in relation to the biogeochemical transformations observed in animal forest canopies. Ongoing challenges in the conceptualisation of physical and biogeochemical processes in animal forest canopies are also exposed. In the third part of this chapter, we review the factors that form the basis of a mechanistic explanation of the development of micro-niches, which explain the large diversity hosted in animal forest canopies.

The concept of the 'marine animal forest' was initially introduced based on aesthetic similarities between trees and large erect colonial animal communities (e.g. corals, [START_REF] Bruno | Habitat modification and facilitation in benthic marine communities[END_REF] that cover some marine substrates (see Figure 1, as well as Gutt et al. in this book). Similarly to terrestrial forests, marine animal forests form a sheltered habitat by reducing the foraging efficiency of consumers [START_REF] Bartholomew | New dimensionless indices of structural habitat complexity: predicted and actual effects on a predators foraging success[END_REF][START_REF] Beukers | Habitat complexity modifies the impact of piscivores on a coral reef fish population[END_REF] and providing refuge for motile species like fishes or vagile invertebrates [START_REF] Ross | The fish fauna associated with deep coral banks off the southeastern United States[END_REF]. The similarities between marine and terrestrial forests extend beyond the provision of shelter, however, and include the manner in which these systems modify the local physical and biogeochemical environment. Despite differences in spatial scale and the properties (density, viscosity, heat capacity) of the fluid to which they are exposed, steady flows over atmospheric (O(10-100 m)) and aquatic canopies (O(0.1-1 m)) display a common characteristic flow structure, as detailed in Section 2. Because of such similarities, we use the terms 'forest' and 'canopy' interchangeably here. Organisms forming canopies are typically considered 'ecosystem engineers', a term which refers to organisms that, through causing changes in the local physical or biogeochemical conditions, directly or indirectly control the availability of resources (other than themselves) to other organisms and thus, modify, maintain or create habitats [START_REF] Lawton | What do species do in ecosystems ?[END_REF]. Autogenic engineers modify their environment through physical changes, while allogenic engineers do so through chemical transformations [START_REF] Jones | Positive and negative effects of organisms as physical ecosystem engineers[END_REF]). Six factors have been identified by [START_REF] Jones | Positive and negative effects of organisms as physical ecosystem engineers[END_REF] as defining the scale of impact of an ecosystem engineer: (1) the lifetime activity of individual organisms, (2) the population density and size, (3) the spatial distribution of the population, both at the local and regional level, (4) the length of time a population has been present at a site, (5) the durability of constructs, artifacts and impacts in the absence of the original engineer, and (6) the number and types of resource flows that are modulated by the constructs and artifacts, and the number of other species dependent upon these flows. On the basis of these factors, trees have always been considered the paradigmatic example of ecosystem engineers in terrestrial habitats [START_REF] Holling | Cross-scale morphology, geometry and dynamics of ecosystems[END_REF].

Marine animal forests have been shown to act as autogenic ecosystem engineers in marine systems through the provision of habitat, colonization opportunities and increasing habitat complexity. For corals, these effects are well-established in shallow tropical environments, but also recognized in temperate [START_REF] Scinto | Role of paramuricea clavata forest in modifying the coralligenous assemblages[END_REF][START_REF] Cerrano | Gold coral (Savalia savaglia) and gorgonian forests enhance benthic biodiversity and ecosystem functioning in the mesophotic zone[END_REF]) and deep-water environments [START_REF] Cordes | Coral communities of the deep Gulf of Mexico[END_REF]Freiwald and Roberts 2005). Animal forests also act as autogenic ecosystem engineers through modification of the mean and turbulent flow structure. The lower levels of turbulence inside the canopy increase sedimentation [START_REF] Luckenbach | Sediment stability around animal tubes: The roles of hydrodynamic processes and biotic activity[END_REF], causing the retention of propagules and enhancing larval settlement [START_REF] Eckman | Flow disruption by an animal-tube mimic affects sediment bacterial colonization[END_REF][START_REF] Smith | Species diversity in subtidal landscapes: Maintenance by physical processes and larval recruitment[END_REF][START_REF] Bruno | Whole-community facilitation through substrate stabilization by the intertidal grass Spartina alterniflora[END_REF]. At the top of the canopy, the enhanced turbulence generated by the large canopy roughness augments the delivery of food and critical metabolites by reducing the thickness of the diffusive boundary layer on organism surfaces [START_REF] Dennison | Effect of water motion on coral photosynthesis and calcification[END_REF]Thisle and Eckman 1990;Shashar et al. 1996).

Flow modification by marine forests encompasses a wide range of processes on a range of spatial scales (reviewed for coral reefs by [START_REF] Monismith | Hydrodynamics of coral reefs[END_REF] and it is now clear that the hydrodynamics of marine forests demonstrate strong similarities, regardless of whether the forest is comprised of plants (e.g. kelp forests or seagrass meadows, [START_REF] Eckman | Ecology of understory kelp environments. Effects of kelps on flow and particle transport near the bottom[END_REF][START_REF] Duarte | Marine biodiversity and ecosystem services: an exlusive link[END_REF] or animals. This flow modification likely leads to the creation of highly dynamic micro-environments, which ultimately select those organisms able to feed, grow and reproduce within the marine forest.

Animal marine forests can also act as allogenic ecosystem engineers, although in the opposite manner to vegetation canopies. Indeed, marine forests of autotrophic primary producers are expected to be carbon sinks (like their terrestrial counterparts) through atmospheric carbon fixation by photosynthesis [START_REF] Goreau | Control of atmospheric carbon-dioxide. Global environmental change -human and policy dimensions[END_REF]. In contrast, marine forests of heterotrophic consumers (except corals living in symbiosis with autotrophic algae) release inorganic carbon during organic matter assimilation in respiration. Nevertheless, the allogenic impact of the 'wall of mouths' of marine animal forests is expected to significantly alter the local biogeochemical conditions near the sea floor [START_REF] Fabricius | Scleractinian walls of mouths: Predation on coral larvae by corals[END_REF].

The objective of this chapter is to review the state-of-the-art understanding of the hydrodynamics and biogeochemistry of marine animal forests and their impact on living conditions inside the animal forest.

The hydrodynamics inside and above the marine animal forest

Marine animal forests can be found in both shallow and deep environments, exposing them to a range of hydrodynamic conditions in terms of the magnitude and steadiness of the flow. At the marine forest scale, steady flows include those generated by wind, buoyancy or tides, with surface waves (seas and swell) generating an unsteady flow. Flow in the oceanic bottom boundary layer is therefore often decomposed into a quasi-steady unidirectional component (the current) and a series of periodic components (waves). This decomposition is of utmost importance when considering the hydrodynamics inside and above the marine animal forest, as the bottom boundary layers associated with steady and unsteady flows differ greatly in their size and structure.

Structure of the turbulent boundary layer over flat beds in steady flows

The bottom boundary layer is the region where the flow velocity is impacted by the bed and where flows dissipate their energy into heat by viscous friction to reach a zero velocity at the bottom.

Under unidirectional steady flows, the thickness (of a turbulent boundary layer decreases with flow energy and is roughly given by ≈ 6000/u * (Wilcox 1992) where  is the kinematic viscosity and u * the bottom friction velocity(defined as the square root of the bed shear stress divided by fluid density). This yields a typical value of  ~ O(m) for u * ~ O(cm/s). The flow in a steady turbulent boundary layer exhibits a well-known vertical structure, with three distinct regions (Wilcox 1992):

(1) the viscous sublayer nearest the bed, where the velocity is low and viscous forces dominate inertial forces, (2) the logarithmic (or inertial) layer, where viscous forces are progressively overwhelmed by inertial forces, and (3) the outer layer, where the flow velocities are greatest, and exceed the bottom friction velocity by at least an order of magnitude. (Figure 2A). The viscous sublayer and logarithmic layer form the inner part of the boundary layer, where the flow velocity scales on the bottom friction velocity. In the viscous sublayer, velocity increases linearly with distance from the bed up to z  ≈ 30 /u * . In the logarithmic layer (of O(10 cm) in height for the typical flow considered above), the velocity increases logarithmically with distance from the bed according to the 'law of the wall' (Figure 2A). Over a rough bed, the viscous sublayer can vanish between roughness elements (Figure 2B). This is seen when u * k/> 70 [START_REF] Sleath | Sea bed mechanics (Ocean Engineering)[END_REF], where k is the average height of the roughness elements (k ≈ 30 z 0 , [START_REF] Nikuradse | Stromungsgesetze in glatten und rauhen rohren[END_REF] , and the law of the wall can be expressed as :

U(z) = u * / ln [z/z 0 ] for k N < z < z Log =600 /u* (1)
where  is the von Karman constant.

In the outerlayer, velocity do not have as a simple formulation as in the viscous and Log layers.

Structure of the turbulent boundary layer over large obstacles in steady flows: the canopy effect

When ocean beds are covered by large obstacles (i.e. a canopy) which extend into the theoretical logarithmic layer of the unobstructed flow, the classical boundary layer structure can be significantly modified when obstacles height is larger than 10 % of its drag length scale (see definition below, [START_REF] Nepf | Retention time and dispersion associated with submerged aquatic canopies[END_REF]. This is typically the case in animal forests formed by erect organisms larger than a few centimeters. The wakes produced by these obstacles create strong spatial variations in the flow, over a region (embedded within the boundary layer) known as the roughness sublayer (RSL, Figure 2C). In an homogeneous canopy (of elements of height h), the RSL is estimated to extend to approximately 2-3h above the bed (MacDonald 2000). Above the RSL, where the flow is horizontally homogeneous, there is again a logarithmic dependence of velocity on height; the profile in (1) is shifted upwards by a displacement height, d [START_REF] Raupach | A wind-tunnel study of turbulent flow close to regularly arrayed rough surfaces[END_REF]. Within the canopy (i.e. in the lower part of the roughness sublayer, below z = h), the vertical profile of horizontally-averaged flow velocity has been approximated by an exponential decay from its value at the top of the canopy (U h ) down to the bed (MacDonald 2000, Cheng and[START_REF] Cheng | Near wall flow over urban-like roughness[END_REF].

The mean flow velocity, U(z), inside and above animal forests is thus typically modelled as:

U(z) = u * / ln [(z-d) / z 0 ] for z > 2-3h (2) = U h exp [(z/h -1)] for 0 < z < h (3)
where z is the distance from the bottom, u * is the friction velocity (which can be related to the flow velocity far above the canopy through a drag coefficient)  is the attenuation coefficient of velocity within the canopy (which increases with canopy density, MacDonald 2000) and z 0 is the canopy roughness length. Many attempts have been made to relate the displacement height and roughness length of vegetation canopies to the packing density of the obstacles as well as their arrangement & shape (e.g. [START_REF] Wooding | Drag due to regular arrays of roughness elements of varying geometry[END_REF]. Similar studies are far less numerous for animal canopies, but similarly point out the difficulty in parameterizing drag and roughness in these systems [START_REF] Rosman | A framework for understanding drag parameterizations for coral reefs[END_REF]. The mean velocity between the top of the canopy and the bottom of the logarithmic layer has not been fully described, but has been shown to contain characteristic features that engender strong similarities across the range of canopy flows (as discussed below).

The proposed exponential decay of horizontally-averaged velocity within the canopy (equation ( 3))

is in fact a crude approximation to the highly-spatially-variable flow that develops in dense canopies. Figure 3

Inherent similarities of canopy steady flows

A key feature of the mean velocity profile in canopy flows is the characteristic inflection point (i.e.

a point of maximum velocity gradient) that is generated at the top of the canopy, the interface between the low speed in-canopy flow and high speed above-canopy flow. This inflection point yields the flow inherently unstable to Kelvin-Helmholtz-type vortices (Figure 4) that dominate the transport of mass and momentum across the top of the canopy (see, e.g., Ghisalberti andNepf 2005, 2009). predictive capability for the structure of the mean and turbulent flow in animal forests. For example, the thickness ( e ) of the region within the canopy where the vortices drive rapid transport (Figure 4) is shown to scale inversely with canopy density (given here as the canopy frontal area per unit volume, a), according to:

 e = 1/3 (C D a) -1 (4)
where C D is the drag coefficient of the obstacles in the canopy. (C D a) -1 is termed the canopy drag length scale. Similarly, the intensity of vertical turbulent fluctuations (w rms ) at the top of the canopy is directly related to the friction velocity:

w rms = 1.1 u * (5)
Canopy drag coefficients (as employed in (3)) are not typically known with a high degree of accuracy. Drag coefficients for certain (isolated) geometric shapes are well known, and simplifications have been made using morphological approximations. [START_REF] Vogel | Life in Moving Fluids[END_REF] reports drag coefficients of 0.74 for a rectangular solid, 0.76 for an erect cylinder and 0.32 for a hemisphere.

Such approximations may prove useful for some organisms in animal forests (e.g. hemisphere-like stony corals, Hench and Rosman 2013) but, in general, canopies present the additional complexities of (a) significant morphological complexity, including variation over height and (b) organisms potentially existing in the wake of upstream elements, which can greatly affect the drag coefficient.

Drag estimation becomes complicated further when animal forests are comprised of organisms with a range of ages, and hence a range of sizes and shapes, as is frequently observed in highly diversified tropical environments. Thus, quantification of canopy drag coefficients has remained elusive. Values of canopy drag coefficients ranging from 0.01 [START_REF] Reidenbach | Boundary layer turbulence and flow structure over a fringing coral reef[END_REF]

Variation of a steady flow with canopy flexibility

A significant complication in predicting the flow structure in animal forest canopies arises when dealing with flexible organisms like soft-corals [START_REF] Ghisalberti | The structure of the shear layer in flows over a rigid and flexible canopies[END_REF]. It has been seen that, eve in steady flows, flexible canopies exhibit a coherent, large-amplitude waving (Ghisalberti and[START_REF] Ghisalberti | The structure of the shear layer in flows over a rigid and flexible canopies[END_REF][START_REF] Ghisalberti | The limited growth of vegetated shear layers[END_REF], termed the monami in vegetation canopies [START_REF] Ackerman | Reduced mixing in a marine macrophyte canopy[END_REF]. The generation mechanism of the monami, although still under debate (Singh et al. 2015), has been explained by the passage of the vortices at the top of the canopy, which create strong sweeping motions as they pass [START_REF] Ghisalberti | The structure of the shear layer in flows over a rigid and flexible canopies[END_REF]. This coherent waving of flexible canopies significantly modifies the structure of the mean and turbulent flow above and inside the canopy, increasing (relative to rigid canopies) mean velocities inside the canopy and reducing the friction velocity (Ghisalberti and Nepf 2009).

Structure of the benthic boundary layer in oscillatory flows

Marine animal forests are not exposed only to steady unidirectional flows (i.e. currents), but also to oscillatory flows driven by wind-waves (shorter periods) and swell waves (longer periods). A complete description of wave-driven flow requires two parameters: the amplitude of the orbital velocity, U w , and the wave period, T. As in steady flow, a boundary layer forms near the bed, within which the wave orbital velocity decreases as the bed is approached.

In the absence of a canopy, boundary layers in oscillatory flow are considerably thinner than their unidirectional counterparts. While tidal boundary layers frequently extend over several meters, the boundary layer under a 10-second wave may extend over only a few centimeters. The thickness of a turbulent oscillatory boundary layer can be approximated by √❑ ❑ √ ν t T where  t is the eddy viscosity [START_REF] Nielsen | Coastal bottom boundary layers and sediment transport[END_REF]. With flow energy dissipated in such a thin layer, maximum bottom friction velocities are generally an order of magnitude larger in wave flows than in the corresponding unidirectional flow [START_REF] Jonsson | Wave boundary layers and friction factors[END_REF]). However, bottom friction velocities as all turbulent quantities within a wave boundary layer exhibit oscillatory variations at half the wave periodicity [START_REF] Sleath | Turbulent oscillatory flows over rough beds[END_REF]. As a consequence of these time variations, and in contrast with steady boundary layers in which turbulence intensity is fairly constant throughout fully developped boundary layers, timeaveraged turbulence intensity decay inversely with distance to the bed within a wave boundary layer [START_REF] Sleath | Turbulent oscillatory flows over rough beds[END_REF]). However, when velocities are phase-averaged i.e. keeping track of the flow phase along the periodic flow outside the boundary layer, the law of the wall (velocity log decay and linear increase of mixing length) applies along a large part of the wave cycle [START_REF] Jenssen | Turbulent oscillatory boundary layers at high Reynolds numbers[END_REF].

These experiments partly validated various quasi-steady modelling of wave boundary layer (e.g. [START_REF] Grant | Combined wave and current interaction with a rough bottom[END_REF]. However, describing with accuracy turbulent quantities within a turbulent oscillatory bounday layer, and particularly the phase lagging of turbulent quantities across it, motivated many more complex numerical modelling (reviewed by Fredsoe andDeigaard 1992, Guizien et al., 2003).

In the presence of a canopy, a wave boundary layer is considerably less affected than a steady flow boundary layer. The porous nature of the canopy, even at high densities, offers comparatively little resistance to pressure transmission within the canopy, and velocity reduction inside the canopy will be much smaller than in unidirectional flow [START_REF] Lowe | Oscillatory flow through submerged canopies. Part 1. Velocity structure[END_REF]. No simple description exists for the vertical profile of orbital velocity inside a canopy under wave-driven flow, although Lowe et al. (2007) have developed a unique model for prediction of the overall velocity attenuation of canopies in oscillatory flows. The model is based on wave energy dissipation from two sources, friction at the top of the canopy and canopy element drag. Ultimately, however, its use relies on estimation of friction and drag coefficients.

Similarly to steady flows, vortex generation at the top of the canopy is also observed under oscillatory flows. This occurs when two key dimensionless parameters, namely the Reynolds number and Keulegan-Carpenter number (the ratio of the timescale of flow oscillation to that of shear layer formation), exceed threshold values such that an unstable shear layer forms on each wave half-cycle [START_REF] Ghisalberti | Vortex generation in oscillatory canopy flow[END_REF]. This means that vortices are preferentially seen in long and energetic waves over dense canopies.

In summary, developing predictive capability for the structure of the mean and turbulent flow in real marine canopies remains challenging. Nevertheless, a qualitative classification of the effect of the canopy on flow velocity and mixing can be proposed for animal forests (Table 1).

Low population density High population density

Wave-dominated flow No significant attenuation of flow within canopy, enhanced mixing in canopy due to unsteady wakes.

Moderate flow attenuation within canopy, greatly enhanced mixing at top of canopy

Current-dominated flow

Flow speed reduced within canopy, fairly uniform rates of mixing through the canopy.

Flow speed strongly reduced within canopy, strong turbulent mixing in upper region of canopy, with reduced mixing near the bed.

Table 1: Summary of the key aspects of flow modification by animal forests.

The biogeochemistry inside and above the canopy of the animal forest

From a biogeochemical perspective, the analogy between terrestrial forests and marine animal forests is not straightforward given their opposite trophic pathways: trees as autotrophs synthesize organic matter from inorganic nutrients, absorbing CO 2 , while animals degrade organic matter into inorganic compounds, releasing CO 2 (N.B. the analogy works somewhat better with tropical corals whose symbiotic association with autotrophic algae put them in the category of semi-autotrophs).

Despite their reversed trophic pathways, an analogy between trees and marine animal forests can be based on their life-span; long-lived biota, either autotrophs or heterotrophs, act as carbon-sinks through carbon sequestration (albeit temporarily) as long as they grow, and thus influence the global carbon cycle in a similar manner. Furthermore, an increasing density of aquatic canopies is likely to shift their role in global biogeochemical cycles from carbon sink to carbon source. While the reduced flow and low turbulence deep in dense aquatic canopies can promote burial of undegraded particulate organic matter due to hypoxic conditions (carbon sink), higher levels of turbulence within canopies of intermediate density can maintain an oxygen supply sufficient to enhance the degradation of sedimenting organic matter (carbon source). The role of marine animal forests in global biogeochemical cycles is also linked to their stability and to the diversity they host.

Biogeochemical conditions are essential drivers of the growth of large organisms and cell division in micro-organisms. Therefore, it is critical that we understand how the regulation of mass transfer inside and above canopies controls the uptake of biogeochemical compounds necessary for the development of organisms living in or forming canopies, in order to predict their resilience to disturbances (Holling 1973).

Bulk mass transfer rates across canopy boundaries

At the canopy scale, turbulent mixing regulates the exchange of dissolved and particulate species across the top of the canopy boundaries. Indeed, mass transfer across the top of the canopy is typically related by analogy to turbulent momentum transfer, which is governed by the interfacial hydrodynamics. Turbulent momentum transfer (indicated by u * ) between the in-canopy and abovecanopy flows has been described through a momentum exchange velocity, U E [START_REF] Bentham | Spatially averaged flow within obstacle arrays[END_REF]:

u * 2 = U E (U ref -U c ) (6)
where U ref is the flow velocity at z = 2.5h (i.e. near the bottom of the logarithmic layer) and U c is the depth-averaged velocity inside the canopy.

By analogy, the rate of mass transfer (ф) of a dissolved compound across the top of the canopy is thought to be controlled by the same exchange velocity as momentum and expressed by :

ф = U E (C c -C ref ) / Sc ( 7
St = ф / [U ref (C c -C ref )] = U E /(U ref Sc), (8)
and depends only on the mean flow structure (and a Schmidt number correction). Given its practical utility, formulations of the Stanton number as a function of canopy drag coefficient (as used by [START_REF] Bilger | Anomalous mass transfer of phosphate on coral reef flats[END_REF] have been developed to avoid the necessity of explicitly measuring the in-canopy flow and mass transfer rate.

Uptake inside the canopy

For all the progress in understanding rates of mass transfer across canopy boundaries, downscaling bulk fluxes at the canopy scale to the micro-scale heterogeneity of concentration within the canopy remains a challenge. Within the canopy, transfer to organismal surfaces is expected to be regulated by molecular diffusion in the organism's diffusive boundary layer, which extends over a portion (approximately 10%) of the viscous sublayer. In canopies, the developed surface area where a diffusive boundary layer (DBL) can be present is considerably enhanced compared to uncovered beds and can reach 15 times the planar reef area [START_REF] Dahl | Surface area in ecological analysis : quantification of benthic coral-reef algae[END_REF].

With the thickness of the DBL proportional to the viscous sublayer thickness, it decreases with the local Reynolds number around the organism and will vary between canopy elements based on the local flow speed and turbulence intensity. The lower the Reynolds number, the thicker the DBL.

Hence, the DBL is likely thicker on the upstream face of organisms spacing is large than in the wake on the downstream face where turbulent detachment occurs and streamlines spacing is smaller (Figure 6, upper panel). Active motile cilia on the epidermis of an organism disrupt the viscous and diffusive boundary layers (Figure 6), increasing mass transport locally; up to a five-fold enhancement of mass transfer rates to organism surfaces has been observed due to vortical ciliary flows (Shapiro et al. 2014). Among cnidarians which often form animal forests, motile epidermal cilia are present in scleratinian corals [START_REF] Yonge | Studies on the physiology of corals. I. Feeding mechanisms and food. Great Barrier Reef Expedition 1928-29[END_REF], but absent in octocorals [START_REF] Lewis | Feeding behaviour and feeding ecology of the octocorallia (coelenterata: Anthozoa)[END_REF]. It is worth noting that not all erected species rely on the physical disruption of the diffusive boundary layer to increase mass transfer; many are active filter-feeders that create biomixing (Riisgard and Larsen, this book). In addition to the spatial heterogeneity of mass transfer inside the canopy, the canopy organisms contribute to strong concentration gradients through their consumption or production. Coral polyps (indicated by red dots in Figure 7A), where biogeochemical transformations take place through respiration, calcification, uptake and release of organic and inorganic forms of phosphorous and nitrogen, form a complex three-dimensional distribution of concentration (Figure 7B).

Relating bulk mass transfer across the canopy to local mass transfer limitations

An important application of the Stanton number characterisation of bulk mass transfer across canopies was in the demonstration that local nutrient uptake by coral reef organisms is frequently mass-transfer-limited, and not biologically-controlled. It has been shown that Stanton numbers for phosphate in experimental coral reefs (assuming infinitely rapid uptake, i.e., taking C c = 0) agree well with those estimated from engineering formulations that only consider the hydrodynamic influence of the reef roughness [START_REF] Bilger | Anomalous mass transfer of phosphate on coral reef flats[END_REF]. Other methods for quantifying the influence of fluid-canopy interactions on nutrient supply can be based on comparisons of timescales of nutrient consumption (if known) and canopy flushing (e.g. [START_REF] Kregting | Effects of a small-bladed macroalgal canopy on benthic boundary layer dynamics : implications for nutrient transport[END_REF]). Mass transfer limitation on reef flats has been shown for ammonia and nitrate, including under waves [START_REF] Falter | Mass-transfer limitation of nutrient uptake by a wavedominated reef flat community[END_REF]), demonstrating the high demand for these compounds in coral reefs. Similarly, mass transfer limitation has been shown for ammonia in seagrass and macroalgae canopies [START_REF] Cornelisen | Prediction and validation of flow-dependent uptake of ammonium over a seagrass-hardbottom community in Florida Bay[END_REF][START_REF] Stephens | Mass-transfer gradients across kelp beds influence Macrocystis pyrifera growth over small spatial scales[END_REF]. For heterotrophic forest-forming species, such as Mediterranean gorgonians, the validity of assuming mass transfer limitation for basic resources (oxygen and organic compounds) must be investigated.

Canopy uptake will not always be physically-limited, however; in such cases, direct measurements of mass transfer into the canopy are required. Eddy correlation techniques allow direct measurement of turbulent diffusive fluxes of a compound, provided a high-frequency, small-scale technique exists to measure the compound concentration and its turbulent fluctuations. In marine systems, such measurements can only be provided by micro-electrode sensors, which effectively limits the technique to quantification of fluxes of dissolved oxygen [START_REF] Berg | Oxygen uptake by aquatic sediments measured by a novel non-invasive eddy correlation technique[END_REF]. Importantly, eddy correlation techniques allow quantification of local fluxes under both wave-and current-dominated flows, unlike the exchange velocity model in ( 6), which only applies to steady flows. The eddy correlation approach was used to monitor spatial and temporal variability of respiration and photosynthesis rates over the slope and crests of a coral reef [START_REF] Long | In situ coral reef oxygen metabolism : an eddy correlation study[END_REF]. In this study, respiration rates increased with current velocity, suggestive of mass transfer limitation. Rates of respiration and gross primary production were higher on the reef crest (dominated by gorgonians and soft-corals) than on the reef slope (dominated by sand and pavement).

Living in the canopy of the animal forest

Habitat complexity has long been recognized as increasing biodiversity and biomass, explained through the provision of a diversity of niches [START_REF] Macarthur | Modelling the mean velocity profile in the urban canopy layer[END_REF]. Aquatic canopies built by flora or fauna display structural complexity and have been shown to host higher diversity and biomass than bare beds [START_REF] Benedetti-Cecchi | Predicting the consequences of anthropogenic disturbance: large-scale effects of loss of canopy algae on rocky shores[END_REF][START_REF] Emslie | Retention of habitat complexity minimizes disassembly of reef fish communities following disturbances : a large-scale natural experiment[END_REF]). Yet, the relationship between canopy complexity (measured through precise canopy descriptors) and the hosted diversity and biomass still needs to be defined. In a recent study, the overall fish population biomass (driven by large fishes) was positively correlated with the density of kelp stipes forming a canopy over temperate rocky reefs [START_REF] Trebilco | The rôle of habitat complexity in the size structure of a temperate reef fish community[END_REF]. The fish population structure, however, was more closely correlated to the roughness of the under-canopy rocky substratum. While this study is clearly a step towards more quantitative description of understorey species habitat, it highlights the lack of a mechanistic conceptualization of habitat complexity, one that integrates the effects of the underlying substratum roughness and the canopy to predict the overall flow structure. Moreover, although canopy density likely influences the living conditions of fishes inside the canopy, the increase of fish biomass with canopy density is not straightforward given the nonlinear effect of density on the canopy flow structure. Indeed, turbulence intensity first increases with density (as indicated by an increase in roughness length) but then suddenly decreases with the onset of skimming flow in dense canopies (a decrease in roughness length, [START_REF] Vogel | Life in Moving Fluids[END_REF].

Elucidating the functional role of canopies requires consideration of the combination of all physical and chemical factors that are (1) locally-or globally-modified within a canopy and (2) that define the fundamental niche of a hosted species. A fundamental niche (sensu [START_REF] Hutchinson | Concluding remarks[END_REF]) is defined as the set of abiotic conditions in which a species can live. Fundamental niche explorations should rely on different experimental or observational strategies according to the motility of hosted species.

For sessile species, fundamental niches should be sought with an Eulerian approach; that is, monitoring in fixed locations, determining regions where temporal variations in physical and chemical conditions are within acceptable ranges. For mobile species, fundamental niches should be sought with a Lagrangian approach; that is, monitoring conditions along potential organism paths.

Living in a sparse animal forest

In marine animal forests with low population density, the flow intensity will display localized variations, creating a dependence on organism arrangement of rates of mass transfer to organism surfaces. Hosted and more precisely-associated fauna and flora are expected to display a spatial structure reflecting the wakes developing behind each individual. In such open forests, mass transfer into the canopy will not be significantly affected and the biogeochemical conditions are expected to be similar to those in the absence of the animal forest(except in individuals wake), such that the physical conditions will be dominant in structuring the biota, particularly in determining colonization processes (settlement and post-settlement survival). Individual wakes should increase local larval retention and could potentially facilitate densification of the forest by self-recruitment of the canopy-forming species as long as intra-specific competition remains small. However, such densification may be slow compared to algal growth in photic areas, suggesting that shallow animal forests would be less resilient to perturbation than deeper ones.

Living in a moderately populated animal forest

In marine animal forests of intermediate population density, in which there is significant wake interaction, the patchiness of mass transfer into the canopy and flow intensity (together with some light penetration) should promote diversification of trophic niches, enabling the development of slow growing sessile autotrophs competing for space with sessile heterotrophs. In this context, despite high local retention of larvae by the animal forest, recruitment success will probably be low due to strong intra-and inter-specific competition. The settlement of sessile heterotroph larvae in these environments should be favored in regions of rapid mass transfer into the canopy. The larvae of some species are able to respond sufficiently quickly to turbulent fluctuations so as to change and adapt their locomotory behaviour to more precisely follow chemical cues to appropriate sites (Koehl et al. 2007). The ability of larvae with low motility to maintain themselves in the appropriate Lagrangian niche seems to depend on the larval sinking speed: only those larvae with a sufficiently high density or rapid behavioural changes (e.g. velum retraction, cessation of swimming) will settle rapidly enough. Patchy flow conditions and visual occlusion in less dense canopies should limit the size of highly mobile species (like fishes) seeking low-flow refuge in animal forests. In summary, marine animal forests of intermediate population density are expected to be characterized by (1) a high diversity of sessile species, autotrophic and heterotrophic, whose distribution could reflect the colonization ability of larvae advected from distant sites, and (2) strong intra-and inter-specific competition. Hosted mobile species are expected to be diversified, due to the variety of trophic resources associated with the diversity of sessile species and the spatial variability of the flow [START_REF] Finelli | Water flow controls distribution and feeding behavior of two co-occuring coral reef fishes : I. Field Measurements[END_REF]. Such hosted species are expected to be limited in number and size, depending on the size and shape of the canopy-forming organisms. In marine animal forests of intermediate density, the choice of spatial and temporal scales used to describe in-canopy conditions is incredibly important, as canopy-averaged values may differ greatly from those actually experienced by organisms. Upscaling procedure should take into account not only average but also variance and covariance descriptors. Quantile descriptors should also be considered as to express the proportion of time or space over which given conditions are experienced.

Living in a dense animal forest

In dense canopies (of either autotrophs or heterotrophs), the reduction of rates of mass transfer near the bed associated with the low in-canopy flow is expected to lead to the accumulation of compounds excreted by the canopy-forming species. Similarly, the consumption of compounds useful to the canopy-forming species can lead to their depletion. Local modification of the biogeochemical and mass transfer conditions below dense assemblages of macroalgae growing on sessile corals was found to be deletereous to the development of sessile corals, due to the reduction in oxygen concentration and increase in dissolved organic carbon concentration [START_REF] Hauri | Chemical and physical environmental conditions underneath mat-and canopy-forming macroalgae, and their effects on understorey corals[END_REF].

Combining limited diffusion and high rates of consumption, sessile species hosted in dense canopies are expected to be limited to those having a different trophic regime than the canopyforming species. However, near the bed in dense heterotrophic marine forests, low light conditions should also prevent the development of algae. In the absence of competition with algae in a low flow environment, bacteria associated with hypoxic environments will likely be favored, in turn leading to low biomass and a uniform composition of sessile species. One could expect a dense canopy to be monospecific, or at least formed by species sharing similar growth traits. Indeed, a canopy will adjust so as to have a large surface area in the the high-velocity, turbulent region of the canopy flow, where the DBL around the organism surface is thin. Such a mechanism was proposed recently to explain the existence of the oldest known marine animal forest in the deep ocean of the Precambrian era [START_REF] Ghisalberti | Canopy flow analysis reveals the advantage of size in the oldest communitiesof multicellular Eukaryotes[END_REF]). In the low-flow and nutrient-rich conditions of the Precambrian ocean, tall rangeomorphs could have grown up to 2 m relying on osmotic uptake only, due to an increased mass transfer to the organism surface resulting from a thinned DBL. As a consequence of limited diffusion and flow velocity in the lower part of the canopy, one can expect dense canopies to be cleared of smaller sessile species, freeing space for mobile species like fishes looking for shelter from predators and low flow conditions to rest. The amount of open space in the lower canopy might even increase as the canopy grows, as some canopy-forming species with a tree-like shape experience population density decay though a self-thinning mechanism [START_REF] Cau | Habitat constraints and self-thinning shape Mediterranean red coral deep population structure: implications for conservation practice[END_REF]. In this case, the hosted biomass is expected to increase with the growth of the canopyforming species. In summary, one could expect dense marine animal or vegetal forests to (1) be composed of sessile species of similar height, (2) host a diverse and large biomass of highly mobile species like fishes that are using the canopy as a refugia, and (3) a diverse microbiota subsisting on by-products of macrobiota function. .

Conclusions and Future directions

Local modification of the physical and biogeochemical environment by erect animals living on the sea floor has long been recognized as a key factor generating high biodiversity and biomass in the understorey. While there is a fairly comprehensive understanding in the environmental fluid mechanics community of the modification of the flow structure generated by these animal forests, these modifications are not well-known amongst the biological community studying these diverse assemblages. In this sense, marine animal forests are archetypal of ecosystems whose study requires more interdisciplinarity and reciprocal pedagogy to advance knowledge. Indeed, going beyond the term 'habitat complexity' to explain species associations in a unified framework to yield a typology of forest requires an understanding of physically-relevant parameters such as canopy planar and frontal density, roughness and drag coefficients, and non-dimensional parameters such as the Reynolds, Keulegan-Carpenter and Stanton numbers.

Research into the physical and biogeochemical environments around scleratinians has demonstrated the relevance of such an interdisciplinary approach in explaining species function. Drawing scientific attention to scleratinians in the last 40 years was possible given the climatic and overfishing threats that they face. However, other marine animals, such as gorgonians, soft-corals and sponges (Maldonado et al., in this book), form animal forests that may colonize places freed up by scleratinians and provide an alternative complex habitat for understorey species. The flexibility of soft-coral species contrasts with the stiffness of scleratinian species, making their hydrodynamic influence similar to that of vegetation canopies.

The ultimate goal of such interdisciplinary research should be to develop models of marine animal forest functioning, and to compare predictions and observations of niche extent in a metacommunity approach. Such models will then be useful in the prediction of biodiversity evolution under climatic and anthropogenic stresses, thereby assisting conservation efforts.

  hydrodynamics above and inside the marine animal forest 3. The biogeochemistry above and inside the marine animal forest 4. Living in the canopy of animal forest 5. Conclusions and future directions 1. Introduction

Figure 1 :

 1 Figure 1: The white gorgonian, Eunicella singularis, covering a boulder at 15 meters depth in Cap L'Abeille (Réserve Naturelle Marine de Cerbère-Banyuls, NW Mediterranean sea, Photograph by Katell Guizien).

Figure 2 :

 2 Figure 2: Schematic diagram of the vertical structure of the mean velocity in (A) a smooth-bottom boundary layer, (B) a rough-bottom boundary layer, and (C) a canopy boundary layer formed by obstacles of height h.

  Figure 3: (A) Vertical profiles (solid lines) of the non-dimensional temporally-and horizontallyaveraged longitudinal velocity (U(z)/U ∞ ) for a steady flow of strength U ∞ above rippled beds with different densities. Fits for the logarithmic layer and for the exponential decay of velocity within the roughness are indicated by the circles; clearly, the exponential fit breaks down deep within the roughness (B) The varying densities and geometries of the rippled beds (LD = low density, ID = intermediate density, HD = high density, from Moulin et al., 2007, with kind permission of EDP Sciences).

Figure 4 :

 4 Figure 4: The streamwise evolution of steady canopy flow. The coherent vortices are a characteristic hydrodynamic feature of canopy flows (from Ghisalberti 2009, with kind permissions of Cambridge University Press).

  to 0.8(MacDonald et al. 2006) have been estimated from flow measurements over coral reefs while values used in reef flow modelling ranged from 0.02 to 0.1[START_REF] Rosman | A framework for understanding drag parameterizations for coral reefs[END_REF]).Variation of a steady flow with canopy densityQualitatively, three regimes of flow within and immediately above animal forests have been identified. These regimes are distinguished by the packing density of the forest, and are schematized in two dimensions in Figure5(adapted from[START_REF] Vogel | Life in Moving Fluids[END_REF]. At low density, each individual in the forest is not in the wake of the closest upstream individual, and the forest impacts the mean velocity profile only in the vicinity of the individual canopy elements. Both the displacement height and roughness length remain small in this regime. As packing density increases, organism wakes begin to interact, such that individual wakes can no longer be identified. The in-canopy flow becomes strongly three-dimensional and local velocities depend strongly on the precise arrangement of organisms. The apparent roughness increases in this regime, but the displacement height remains small. As packing density increases further, forest drag produces a sufficiently strong blockage that a 'skimming' flow (where the strength of the in-canopy flow is minimized) occurs above the canopy. This corresponds to a decrease in the roughness length together with a rapid increase in the displacement height. Density thresholds delineating these three flow regimes in real canopies depend on the size of the wake that develops behind each organism, thus varying with organism size and shape as well as flow speed. In the case of atmospheric flows over vegetation canopies, the onset of skimming flows occurs for frontal area density (i.e. the canopy frontal area per unit bed area) larger than 0.2 (MacDonald 2000).

Figure 5 :

 5 Figure 5: Three typologies of flow modification in the vicinity of obstacles for increasing packing density (adapted from Vogel 1994).

)(

  [START_REF] Moulin | Impact of an invasive species Crepidula fornicata on the hydrodynamics and transport properties of the benthic layer[END_REF] where C ref is the compound concentration at z = 2.5h and C c is the depthaveraged concentration inside the canopy. The compound is characterized by its Schmidt number (Sc), equal to the ratio of the kinematic viscosity of sea water () to the diffusion coefficient of the compound in sea water (D). This characterisation of mass transfer can also be described in terms of the Stanton number (St), which represents the ratio of the mass transfer coefficient ф/(C c -C ref ) to fluid advection (U ref ):

Figure 6 :

 6 Figure 6: Streamlines (shown in blue) from numerical simulations of flow around a coral branch (diameter = 5 mm). Streamline spacing can be taken as proxy for DBL thickness: the greater the spacing, the thicker the DBL. Ciliary vortical flows (lower panel) significantly impact the flow topology and decrease the DBL thickness at low-to-moderate ambient flow velocities, relative to the no-cilia case (upper panel). The arrow marks the direction of the ambient flow. Streamlines shown in red are those passing within 50 μm of the branch (from Shapiro et al. 2014, with kind permission of PNAS Editions)..

  Mapping the micro-scale physical and chemical environment that organisms experience requires high-resolution, 3D measurements of both flow and concentration. The current capacity is limited to simultaneous 2D visualization of flow and concentration through a combination of Particle Image Velocimetry (PIV) and Particle Laser Induced Fluorescence (PLIF, e.g.Koehl and Reidenbach 2007, Figure7B). Significant advances should be sought to improve the 3D mapping of flow and concentration, which may come from medical (Positron Emission Tomography) or material science (Raman spectrometry,[START_REF] Du | Feasibility investigation on deep ocean compact autonomous Raman spectrometer developed for in-situ detection of acid radical ions[END_REF] technologies.

Figure 7 :

 7 Figure 7: Example of simultaneous PIV and PLIF measurements over Porites compressa coral in a wave-dominated flow (with a weak current present) in a flume. (A) A PIV frame, on which opening polyps are indicated by red dots. (B) A PLIF image of dye concentration released from the coral coating, recorded 0.02 s after the image shown in A. The velocity vectors during this interval are shown in blue (from Koehl and Reidenbach, 2007, with kind permissions of Springer).


Chinedu Innocent Nwoye
email: nwoye@unistra.fr

Nicolas Padoy
email: npadoy@unistra.fr

DATA SPLITS AND METRICS FOR METHOD BENCHMARKING ON SURGICAL ACTION TRIPLET DATASETS A BENCHMARK STUDY

Keywords: Surgical activity recognition, Tool-tissue interaction, Action triplet, CholecT40, CholecT45, CholecT50

In addition to generating data and annotations, devising sensible data splitting strategies and evaluation metrics is essential for the creation of a benchmark dataset. This practice ensures consensus on the usage of the data, homogeneous assessment, and uniform comparison of research methods on the dataset. This study focuses on CholecT50, which is a 50 video surgical dataset that formalizes surgical activities as triplets of 〈instrument, verb, target〉. In this paper, we introduce the standard splits for the CholecT50 and CholecT45 datasets and show how they compare with existing use of the dataset. CholecT45 is the first public release of 45 videos of CholecT50 dataset. We also develop a metrics library, ivtmetrics, for model evaluation on surgical triplets. Furthermore, we conduct a benchmark study by reproducing baseline methods in the most predominantly used deep learning frameworks (PyTorch and TensorFlow) to evaluate them using the proposed data splits and metrics and release them publicly to support future research. The proposed data splits and evaluation metrics will enable global tracking of research progress on the dataset and facilitate optimal model selection for further deployment.

Figure 1: An illustration of the dataset splits. Top: CholecT50 split as used in the Rendezvous [START_REF] Nwoye | Rendezvous: Attention mechanisms for the recognition of surgical action triplets in endoscopic videos[END_REF]. Middle: CholecT50 split as used in the CholecTriplet challenge [START_REF] Nwoye | Cholectriplet2021: a benchmark challenge for surgical action triplet recognition[END_REF]. Bottom: the official CholecT45 and CholecT50 cross-validation splits.

Introduction

The use of Artificial Intelligence (AI) techniques is increasingly driving research and development across many disciplines. Yet, there has been a delay in introducing large-scale data science to interventional medicine, partly due to the unavailability of large annotated datasets [START_REF] Maier-Hein | Surgical data science: Enabling next-generation surgery[END_REF]. While huge efforts have been made in creating small to medium scale datasets [START_REF] Nwoye | Rendezvous: Attention mechanisms for the recognition of surgical action triplets in endoscopic videos[END_REF][START_REF] Sznitman | Data-driven visual tracking in retinal microsurgery[END_REF][START_REF] Twinanda | Endonet: a deep architecture for recognition tasks on laparoscopic videos[END_REF][START_REF] Jin | Tool detection and operative skill assessment in surgical videos using region-based convolutional neural networks[END_REF][START_REF] Hajj | Cataracts: Challenge on automatic tool annotation for cataract surgery[END_REF][START_REF] Grammatikopoulou | Cadis: Cataract dataset for image segmentation[END_REF][START_REF] Nwoye | Recognition of instrumenttissue interactions in endoscopic videos via action triplets[END_REF][START_REF] Ross | Robust medical instrument segmentation challenge[END_REF][START_REF] Bawa | The saras endoscopic surgeon action detection (esad) dataset: Challenges and methods[END_REF], little or no effort has been made to standardize the data usage for tracking the global research progress. For instance, in laparoscopic and cataract surgeries, many published methods on the most prominent tasks of surgical phase [START_REF] Twinanda | Endonet: a deep architecture for recognition tasks on laparoscopic videos[END_REF][START_REF] Dergachyova | Automatic data-driven real-time segmentation and recognition of surgical workflow[END_REF][START_REF] Gao | Trans-svnet: Accurate phase recognition from surgical videos via hybrid embedding aggregation transformer[END_REF][START_REF] Funke | Temporal coherence-based self-supervised learning for laparoscopic workflow analysis[END_REF] and tool detection [START_REF] Garcia-Peraza-Herrera | Toolnet: holistically-nested real-time segmentation of robotic surgical tools[END_REF][START_REF] Vardazaryan | Weakly-supervised learning for tool localization in laparoscopic videos[END_REF][START_REF] Nwoye | Weakly supervised convolutional lstm approach for tool tracking in laparoscopic videos[END_REF] are reported on varying data splits of the same dataset, e.g: Cholec80 [START_REF] Twinanda | Endonet: a deep architecture for recognition tasks on laparoscopic videos[END_REF], Cataract [START_REF] Hajj | Cataracts: Challenge on automatic tool annotation for cataract surgery[END_REF], etc. Without a consensus data split, tracking research progress on these experimental datasets is not straightforward. Oftentimes, it complicates results comparison, making model selection for further clinical translation more challenging.

In this paper, we present standard data splits for the recently introduced CholecT50 dataset [START_REF] Nwoye | Rendezvous: Attention mechanisms for the recognition of surgical action triplets in endoscopic videos[END_REF]. The label formalism in the dataset provides comprehensive and fine-grained details on every tool-tissue interaction in any given surgical scene. A subset of the dataset, named CholecT45, was released after the CholecTriplet2021 challenge [START_REF] Nwoye | Cholectriplet2021: a benchmark challenge for surgical action triplet recognition[END_REF] while withholding 5 test set videos from public access. The remaining part of the dataset is planned to be released after the CholecTriplet2022 challenge.

The data split patterns, illustrated in Fig. 1, are fashioned on three criteria:

1. Reproducibility: to maintain consistent splits with the earlier published experiments that introduced the dataset, 2. Accessibility: owing that only a part of the dataset is publicly released to date, we consider a representative setup for its utilization and fair comparison, 3. Thoroughness: to counter the effect of class-imbalance predominant in a single test set by using a rigorous and exhaustive k-fold cross-validation approach, which enables alternating evaluation on the entire dataset.

Furthermore, we define and standardize the evaluation metrics for assessing the quality of triplet detection and recognition on the dataset. These metrics build on the evaluation setup used in earlier research [START_REF] Nwoye | Recognition of instrumenttissue interactions in endoscopic videos via action triplets[END_REF][START_REF] Nwoye | Deep learning methods for the detection and recognition of surgical tools and activities in laparoscopic videos[END_REF] on the dataset. In this work, we describe the evaluation algorithm and develop a standard metrics library, named ivtmetrics, for both triplet recognition and detection/localization evaluation. The metrics library is available online and can be installed via pip or conda package installers for method development and validation. The metrics library is usable in all python-based deep learning frameworks.

Finally, we re-implement our previously proposed deep learning methods for surgical action triplet recognition in two widely used deep learning frameworks: PyTorch and TensorFlow. The reproduced models are evaluated on the proposed data splits for CholecT45 and CholecT50 using the developed ivtmetrics library thus providing baselines for future comparison. By conducting this benchmark experiment on the newly introduced dataset, this study provides a definition of standard practice for the official data splits and an evaluation protocol to guide future research.

The CholecT45 dataset is released on http://camma.u-strasbg.fr/datasets. The evaluation metrics library is installable using python package and environment managers (pip and conda). The code and weights for the reproduced models are available on the CAMMA public GitHub https://github.com/CAMMA-public.

In the following sections, we present the proposed data splits and their constituting videos, followed by the evaluation protocols and the developed metrics library. Afterwards, we present the reproduced models, their performance across the proposed splits, and comprehensive per-category performance analysis on the two datasets.

Data Splits

CholecT50 [START_REF] Nwoye | Rendezvous: Attention mechanisms for the recognition of surgical action triplets in endoscopic videos[END_REF] is a surgical dataset for action triplet recognition. It is an extension of CholecT40 dataset [START_REF] Nwoye | Recognition of instrumenttissue interactions in endoscopic videos via action triplets[END_REF] with additional 10 videos. It contains 50 videos of laparoscopic cholecystectomy surgery annotated with 100 action triplet classes. Action triplet is a formalism to represent fine-grained activity in the form of 〈instrument, verb, target〉. In this dataset, they are composed from 6 instruments, 10 verbs, and 15 target classes resulting in over 161K triplet instances at 1 fps video frames.

In the CholecTriplet2021 [START_REF] Nwoye | Cholectriplet2021: a benchmark challenge for surgical action triplet recognition[END_REF] / CholecTriplet2022 challenges, the participants are given access to a subset of the CholecT50 dataset, also known as CholecT45. This subset is the first public release of the CholecT50 dataset available on http://camma.u-strasbg.fr/datasets. The videos of CholecT45 are part of the Cholec80 [START_REF] Twinanda | Endonet: a deep architecture for recognition tasks on laparoscopic videos[END_REF] dataset. The video indexes correspond between the two datasets with the prefix "video" in Cholec80 changed to "VID" in CholecT45.

The statistics of the CholecT45 dataset is presented in

VID15 VID26 VID40 VID52 VID65 VID79 VID08 VID06 VID51 VID02 VID18 VID27 VID43 VID56 VID66 VID92 VID12 VID10 VID73 VID04 VID22 VID31 VID47 VID57 VID68 VID96 VID29 VID14 VID74 VID05 VID23 VID35 VID48 VID60 VID70 VID103 VID50 VID32 VID80 VID13 VID25 VID36 VID49 VID62 VID75 VID110 VID78 VID42 VID111
To describe the official usage of CholecT45 and CholecT50 datasets, we present the different splits of the datasets in the following sections. We first present the data split of CholecT50 as used (a) in the Rendezvous paper [START_REF] Nwoye | Rendezvous: Attention mechanisms for the recognition of surgical action triplets in endoscopic videos[END_REF] that introduces the dataset and (b) in the CholecTriplet challenges [START_REF] Nwoye | Cholectriplet2021: a benchmark challenge for surgical action triplet recognition[END_REF] for reproducibility. Afterward, we present the official cross-validation splits of the CholecT45 and CholecT50 datasets.

Rendezvous (RDV) Split of CholecT50 dataset

This split is used in the original paper [START_REF] Nwoye | Rendezvous: Attention mechanisms for the recognition of surgical action triplets in endoscopic videos[END_REF] that introduces the dataset. It is presented for reproducibility of the earlier published methods on this task. In this setup, the dataset is split into three: (1) training, (2) validation, and (3) testing as presented in Table 2. The videos in each dataset split are distributed in the same ratio to include annotations from each of the (surgeon) annotators. This helps to minimize the effect of annotation bias on the learning algorithm.

CholecTriplet Split of CholecT50 dataset

This split is introduced by the organizers of the CholecTriplet2021 and CholecTriplet2022 challenges for surgical action triplet recognition and detection. Here, it is selected for consistency with the methods presented at the MICCAI 2021 EndoVis challenge. The dataset is split into two: (1) trainval, and (2) testing set, as presented in Table 3. During the challenge and for model hyper-parameter tuning, participants are allowed to further split the trainval split into training and validation subsets at their own discretion. All the videos in the trainval are drawn from the publicly available Cholec80 [START_REF] Twinanda | Endonet: a deep architecture for recognition tasks on laparoscopic videos[END_REF] dataset. Nevertheless, the testing set containing 5 videos are not in the public domain. The rationale for this data split is to ensure that the participants do not have access to the testing set of the challenge dataset for fairness in the competition.

Official Cross-Validation (CV) Splits for CholecT45 and CholecT50 datasets

K-fold cross-validation is known for its robustness in result analysis. As some of the triplet classes can be unrepresented in any testing set sampling, cross-validation is a more robust, and stable way of assessing the quality of model predictions on all observed triplet classes. This enables a result analysis that covers all the 100 class labels of the triplet datasets.

In this setup, the dataset is split into 5 equal subsets called folds. Different copies of a model are trained on different combinations of 4 out of 5 folds, each time leaving out one alternating fold for testing. The final result is averaged over the 5 hold-out testing splits.

To ensure that all folds have similar levels of complexity, the 50 videos of CholecT50 are sorted by their difficulty, determined by procedure duration. The sorted videos are divided into 10 clusters with each containing 5 videos of the same/similar complexity or duration. The videos in each cluster are randomly distributed to all the 5 folds split.

The CholecT50 CV split contains the full 50 video dataset divided into 5 folds with each fold containing 10 videos as presented in Table 4) (rows 1-10).

The CholecT45 CV split, on the other hand, contains 45 videos of the dataset divided into 5 folds with each fold containing 9 videos each as shown in Table 4) (rows 1-9). The CholecT45 excludes the test videos (row 10) of the CholecTriplet challenge. Hence, this split equally supports exhaustive cross-validation but only on the publicly released subset of the entire dataset.

Testing VID01 VID10 VID22 VID29 VID42 VID50 VID60 VID73 VID05 VID92 VID02 VID12 VID23 VID31 VID43 VID51 VID62 VID75 VID18 VID96 VID04 VID13 VID25 VID32 VID47 VID52 VID66 VID78 VID36 VID103 VID06 VID14 VID26 VID35 VID48 VID56 VID68 VID79 VID65 VID110 VID08 VID15 VID27 VID40 VID49 VID57 VID70 VID80 VID74 VID111
VID79 VID80 VID31 VID42 VID78 2 VID02 VID32 VID57 VID29 VID43 3 VID51 VID05 VID36 VID60 VID62 4 VID06 VID15 VID18 VID27 VID35 5 VID25 VID40 VID52 VID65 VID74 6 VID14 VID47 VID68 VID75 VID01 7 VID66 VID26 VID10 VID22 VID56 8 VID23 VID48 VID08 VID49 VID04 9 VID50 VID70 VID73 VID12 VID13 10 VID111 VID96 VID103 VID110 VID92
3 Metrics

Recognition Average Precision

Triplet recognition performance is evaluated using the Average Precision (AP) metric measured as the area under the precision-recall (p-r) curve per class:

AP = 1 0 p(r)dr. (1)
AP summarizes a p-r curve as the weighted mean of precisions achieved at each threshold, with the increase in recall from the previous threshold used as the weight. Video-specific AP score for evaluating surgical action triplet recognition is computed as follows:

i. per-category AP is computed across all frames in a given video.

ii. category AP is obtained by averaging per-category APs across all videos.

iii. mean AP is obtained by averaging N category AP, serving as the final score:

mAP = 1 N N i=1 AP i . (2)
The same process is followed when computing mAP for the individual components of the triplets. The predictive capacity of a model at recognizing correctly a triplet and its components is evaluated in two ways:

1. Component average precision: This includes three APs assessing the correct recognition of the instrument (AP I ), verb (AP V ), and target (AP T ) components of the triplets.

Triplet average precision:

This includes three APs assessing the correct recognition of tool-tissue interactions by observing different sets of triplet components, which includes: APs for instrument-verb (AP IV ), instrumenttarget (AP IT ), and instrument-verb-target (AP IV T ), which is the main metric.

Disentangling Action Triplet Prediction

This is introduced to support the evaluation of all triplet component prediction for models that produce

Y d = max d k ∈{i,v,t} Y ivt ∀ ivt ∈ IV T, k : 0 ≤ k < C d . (3)
This filtering algorithm [START_REF] Nwoye | Rendezvous: Attention mechanisms for the recognition of surgical action triplets in endoscopic videos[END_REF] directly translates to obtaining the probability of a given component class as the maximum probability value among all triplet labels having the same component class label in a video frame. Likewise, the groundtruths of the component labels can be obtained using the filtering setup.

Detection Average Precision

When evaluating the localization of the triplets as in CholecTriplet2022 challenge, AP metrics consider the overlap or Intersection of Union (IoU) of the predicted bounding boxes with the ground truth. The detection AP is evaluated in two ways:

1. Instrument Localization AP: In this metric, a detection is assigned a true positive (TP) if the degree of overlap between a predicted bounding box and the ground truth exceeds a certain threshold (usually 0.5) and the instrument ID is correct.

Triplet Detection AP:

This metric assess the correctness of every associated action triplet to every localized instrument. Here, a prediction is considered a TP if the predicted triplet ID is correct, assigned to the right instrument involved in the tool-tissue interaction, which must also be localized at a minimum IoU threshold with the ground-truth bounding box.

The missed predictions are marked as false negatives (FN) whereas false alarms are marked as false positives (FP). Following this, their corresponding precision (p) and recalls (r) are calculated as follows:

p = T P T P + F P , r = T P T P + F N , (4)
and using the computed p, r, the AP is calculated following Equation 1, averaged across videos.

In future, when target localization AP is considered, the triplet detection AP will take into account a satisfied bounding box IoU for both instruments and targets.

Metrics Library

To standardize the use of these evaluation metrics, we develop ivtmetrics library, which can be used in both training and inference mode. The library can be imported in a python-based script using import ivtmetrics with a prerequisite installation step: pip install ivtmetrics or conda install -c nwoye ivtmetrics. gives the mean AP across all frames in all seen videos. The component ∈ ("i", "v", "t", "iv", "it", "ivt") is a string argument that describes the respective sub-task's (instrument, verb, target, instrument-verb, instrument-target, instrument-verb-target) performance to be computed for. A top K performance is obtained by AP.topk(k: int) while top predicted class IDs are given by AP.topClass(k: int). More details and usage examples of the ivtmetrics can be found on GitHub https://github.com/CAMMA-public/ivtmetrics .

Benchmark Study Design

To provide a benchmark study on CholecT45 and CholecT50 datasets using our proposed data splits and metrics, we re-implement and reproduce three proposed methods in PyTorch and TensorFlow.

Methods

We summarize the reproduced methods as follows:

1. Tripnet: As shown in Fig. 2(a), Tripnet [START_REF] Nwoye | Recognition of instrumenttissue interactions in endoscopic videos via action triplets[END_REF] is a multi-task learning method that uses activation maps resulting from the instrument branch to enhance verb and target feature encoding in a new module known as class activation guide (CAG). It is followed by a 3D interaction space where relationships between instruments-verbs-targets components are resolved to triplets. Code and weights are publicly released on GitHub https://github.com/CAMMA-public/tripnet.

Attention Tripnet:

This is an upgrade of Tripnet with an attention mechanism. The main difference is the use of class activation guided attention mechanism (CAGAM) [START_REF] Nwoye | Rendezvous: Attention mechanisms for the recognition of surgical action triplets in endoscopic videos[END_REF] over CAG where the verb and target feature discovery are obtained by channel and position attention processes respectively. Code and weights are publicly released on GitHub https://github.com/CAMMA-public/attention-tripnet.

Rendezvous (RDV):

In this model [START_REF] Nwoye | Rendezvous: Attention mechanisms for the recognition of surgical action triplets in endoscopic videos[END_REF], the network encoder uses a weakly supervised approach to localize the instruments and the CAGAM module to detect the verb and target components of the triplets as shown in Fig. 2(b). The association part is achieved by both self and cross attention mechanisms in a new module known as multi-head of mixed attention (MHMA), and terminated by a simple classifier after 8 successive layers of association decoding. Code and weights are publicly released on GitHub https://github.com/CAMMA-public/rendezvous.

Implementation Details

We made few changes in the original implementations [START_REF] Nwoye | Rendezvous: Attention mechanisms for the recognition of surgical action triplets in endoscopic videos[END_REF][START_REF] Nwoye | Recognition of instrumenttissue interactions in endoscopic videos via action triplets[END_REF] as follows:

1. Output resolution: The original implementation lowered the strides of the last two blocks of the ResNet by one pixel to provide higher resolution (32 × 56) output. However, using original strides of size 2, we implement a faster version (size: 8 × 14), trading-off precise localization to speed.

Attention normalization:

The huge parameter layer-norms in the AddNorm layers of the attention module are replaced with batch-norms without affecting model accuracy.

Loss function:

We integrates warmup parameters within the auxilliary task' cross-entropies without requiring additional uncertainty loss balancing [START_REF] Kendall | Multi-task learning using uncertainty to weigh losses for scene geometry and semantics[END_REF] as in [START_REF] Nwoye | Rendezvous: Attention mechanisms for the recognition of surgical action triplets in endoscopic videos[END_REF]. This removes the excessive parameters introduced by the uncertainty loss. All the 100 triplet classes are evaluated in this setup. The benchmark results on the RDV split is presented in Table 5. The results follow the same trend as in the original paper [START_REF] Nwoye | Rendezvous: Attention mechanisms for the recognition of surgical action triplets in endoscopic videos[END_REF] as it is observed that the Attention Tripnet leverages CAGAM to improve the verb and target detections while Rendezvous utilizes its transformer-inspired MHMA to improve the triplet association performance. We show the performance across deep learning frameworks in Table 5.

Benchmark Results and Discussion

The PyTorch models approximates the performance of their TensorFlow counterparts (version 1). We observe that these results are comparable in some of the sub tasks.

Quantitative Results on CholecT50 using CholecTriplet Split

The challenge rule excludes the 6 null triplet classes (IDs: 94-99) from evaluation. The results are presented in Table 6. It is observed that AP IV T is higher than in the RDV split for each model, likely due to the reduced number of triplet classes (94 v 100). Also, the direct outputs (Y D ) for the individual components (i.e.:

Y I , Y V , Y T , Y IV or Y IT )
of the triplets (Y IV T ) are not provided by the challenge approaches, instead they are filtered from the main triplet predictions (Y IV T ) following the filtering formula in Section 3.2. As shown in Table 6, the AP performances on the filtered prediction are generally lower compared to AP on directly predicted probabilities of those components when provided, however, they are more informative and a better representation of how a model understands the triplet's composition. The benchmarking results on the CholecT50 cross-validation split are presented in Table 7 along with the standard deviation (std) over the folds. All the 100 triplet classes are evaluated in this setup. This presents a less biased and less optimistic estimate of the models with confidence intervals. Their standard deviation (std) spread shows the extent of performances approximation of the three models positioning Tripnet as the least and Rendezvous as the best in terms of performance. Similarly, the benchmarking results on the CholecT45 cross-validation split, presented in Table 8, justifies the use of attention mechanisms for surgical action triplet recognition. The analysis shows that the results obtained on the CholecT45 CV approximates the ones of the CholecT50 CV in all the sub-tasks, justifying its use/sufficiency in the absence of the complete CholecT50 dataset. We present the per-class performance for the triplet components (Tables 91011) and their association (Table 12) recognition using the cross-validation dataset splitting strategy on both CholecT45 and CholecT50. We observe similar performance pattern across the two datasets in all classes of each sub task showing the reliability of cross-validation split approach in model evaluation.

On instrument presence detection, as shown in Table 9, grasper and hook are the most detected owing to their highest occurrence frequencies in the dataset. However, hook is a little better detected than grasper owing to its uniqueness unlike the grasper which sometimes share some similarities with clipper, bipolar and scissor. The scissors and irrigator, on the other hand, are the least detected likely due to their low occurrence distributions in the datasets. For the verb recognition, grasp, retract, dissect, coagulate, clip, cut, and aspirate are better detect above 50% at all time as shown in Table 10. This is due to their strong affinities with unique instrument classes. Pack and irrigate are very challenging to discriminate from the dominant verbs of their instruments namely retract and aspirate. Null action, being a compendium of unconsidered actions, is the least recognized verb. The per-class target detection reveals the most interesting areas of improvement. The predominant targets such as gallbladder, liver, and specimen-bag are well detected above 70% as shown in Table 11. The main challenge comes in detecting tiny anatomical structures such as cystic-artery, peritoneum, cystic-plate, cytic-pedicle, etc. as against conspicuous structures such as liver, omentum, cystic-duct, fluid, etc. Some anatomies with no clear boundaries such as abdominal wall, cystic-artery, etc. are fairly detected. A presentation of class-wise results of the complete 100 triplet classes is only possible using the cross-validation approach. As shown in Table 12, the models recognizes the most important triplets such as grasper retracting gallbladder or grasping specimen-bag, hook dissecting either gallbladder or omentum, bipolar coagulating liver, clipper clipping cystic-artery and -duct with scissors cutting the same, and irrigator aspirating fluid or irrigating the cystic-duct. The good performance on these specific triplets are expected from the models' high performance on their specific triplet component classes. Surprising, the irrigator rare use in dissecting cystic-pedicle is well detected by RDV model.

Conclusion

With the public release of the CholecT45 dataset to support research on surgical action triplet recognition, we present in this paper a standard practice for splitting the dataset to enable a uniform comparison of research methods. These splits will remain relevant in the planned future release of the entire CholecT50 dataset. We also design, implement, and publicly release a python packaged metrics library, ivtmetrics for the evaluation of surgical action triplet recognition and localization on the dataset. For the benchmark study, we re-implement the current state-of-the-art models in two predominant deep learning frameworks, PyTorch and TensorFlow, and then train and evaluate them on the proposed data splits. Owing to the well-articulated rationale for dataset splits and exhaustive cross-validation, results obtained reflect better the generalization capability of the models. This study sets a rich foundation for fair comparison of methods researched on the CholecT45 and CholecT50 datasets using the same data splits and metrics. Future work will extend the metrics library to include more statistical evaluations.

  only the final triplet (Y IV T ) probabilities. If IV T represents all the triplets in a single image, and D = {I, V, T, IV, IT } is a set of the triplets' components and their possible combinations, then, ∀d ∈ D, the indirect component's output vector Y d of class size C d (e.g. for d = I, C d = 6 as there are 6 instrument classes) can be filtered from Y IV T following Equation 3:

Figure 2 :

 2 Figure 2: Reproduced models for surgical action triplet recognition: (a) Tripnet [9], (b) Rendezvous [1].

Table 1

 1

Table 1 :

 1 Statistics of CholecT45 Dataset

	Videos	Frames	Instances	Instruments	Verbs	Targets	Triplets
	45	90489	127385	6	10	15	100
	Table 2: CholecT50 dataset split as used in Rendezvous publication [1].
			Training		Validation		Testing
	VID01

Table 3 :

 3 CholecT50 dataset split as used in CholecTriplet2021 [2] & CholecTriplet2022 challenges. Trainval (= CholecT45)

Table 4 :

 4 Official cross-validation data splits of CholecT45 and CholecT50 datasets.

			Fold 1	Fold 2	Fold 3	Fold 4	Fold 5
	1	CholecT50 Cross-Val. splits	CholecT45 Cross-Val.

  The library provides metrics classes for triplet recognition: AP = ivtmetrics.Recognition(N : int) and triplet detection AP = ivtmetrics.Detection(N: int), as well as an internally implemented triplet component filtering AP = ivtmetrics.Disentangle(N: int), where N = number of triplet classes. Invoking the metrics class initializes the metrics accumulators by a AP.reset(). This reset function is to be called at the beginning of every training epoch. Other reset options include AP.reset_video() to reset scores accumulated for all seen videos, and AP.reset_global() to reset every accumulator. The metrics update function takes in the predicted and target labels over each iteration by calling AP.update(targets: array, predictions: array). If a video-specific AP is needed, AP.video_end() must be called at the end of each video. The AP scores from a current time up to the last reset() call are obtained via AP.compute_AP(component : str). The mean AP average across videos is obtained by calling AP.compute_video_AP(component : str) while AP.compute_global_AP(component : str)

Table 5 :

 5 Benchmark triplet recognition AP (%) on CholecT50 dataset for different frameworks using RDV split.

	Framework Method	Component detection	Triplet association
			AP I	AP V	AP T	AP IV	AP IT	AP IV T
		Tripnet [9]	92.1	54.5	33.2	29.7	26.4	20.0
	TensorFlow	Attention Tripnet [1]	92.0	60.2	38.5	31.1	29.8	23.4
		Rendezvous (RDV) [1]	92.0	60.7	38.3	39.4	36.9	29.9
		Tripnet [9]	88.7	59.2	39.3	31.9	27.9	21.6
	PyTorch	Attention Tripnet [1]	87.9	59.7	40.6	34.2	29.0	23.2
		Rendezvous [1]	89.1	62.3	43.8	40.0	35.8	29.5
	5.1 Quantitative Results on CholecT50 using Rendezvous Split

Table 6 :

 6 Benchmark triplet recognition AP (%) on CholecT50 dataset using CholecTriplet split.

	Framework Method	Component detection	Triplet association
			AP I	AP V	AP T	AP IV	AP IT	AP IV T
		Tripnet [9]	74.6	42.9	32.2	27.0	28.0	23.4
	TensorFlow	Attention Tripnet [1]	77.1	43.4	30.0	32.3	29.7	25.5
		Rendezvous [1]	77.5	47.5	37.7	34.4	38.2	32.7
		Tripnet [9]	73.9	41.6	32.1	28.8	29.2	27.4
	PyTorch	Attention Tripnet [1]	73.7	43.7	35.3	31.6	31.9	27.7
		Rendezvous [1]	75.9	46.0	38.7	35.9	37.1	32.8
	5.3 Quantitative Results on CholecT50 using Cross-Validation Split

Table 7 :

 7 Benchmark triplet recognition AP (%) on CholecT50 dataset using the official cross-validation split.

	Method (in PyTorch)	Component detection	Triplet association
		AP I	AP V	AP T	AP IV	AP IT	AP IV T
	Tripnet [9]	89.1±1.7 58.8±3.1 38.4±1.3	32.7±2.4 29.0±0.8 25.3±2.4
	Attention Tripnet [1]	88.7±1.3 61.1±2.0 40.7±3.2	33.1±2.7 30.3±1.6 27.2±2.9
	Rendezvous [1]	89.4±2.0 60.4±2.8 40.3±2.2	34.5±2.8 31.8±1.0 29.4±2.5
	5.4 Quantitative Results on CholecT45 using Cross-Validation Split

Table 8 :

 8 Benchmark triplet recognition AP (%) on CholecT45 dataset using the official cross-validation split.

	Method (in PyTorch)	Component detection	Triplet association
		AP I	AP V	AP T	AP IV	AP IT	AP IV T
	Tripnet [9]	89.9±1.0 59.9±0.9 37.4±1.5	31.8±4.1 27.1±2.8 24.4±4.7
	Attention Tripnet [1]	89.1±2.1 61.2±0.6 40.3±1.2	33.0±2.9 29.4±1.2 27.2±2.7
	Rendezvous [1]	89.3±2.1 62.0±1.3 40.0±1.4	34.0±3.3 30.8±2.1 29.4±2.8
	5.5 Class-wise Performances of the Benchmark Models

Table 9 :

 9 Per-class instrument presence detection AP (%) on cross-validation splits (Method in PyTorch)

	Classes		CholecT45			CholecT50
		Tripnet	Attention Tripnet	RDV	Tripnet	Attention Tripnet	RDV
	grasper	96.5±0.4	96.4±0.7	96.6±0.6	96.4±0.7	96.5±0.6	96.6±0.6
	bipolar	88.4±4.2	86.0±4.2	87.4±4.7	89.0±3.4	88.2±4.2	88.5±4.1
	hook	97.5±1.6	97.1±1.3	97.4±1.5	97.5±1.3	97.3±1.3	97.6±1.3
	scissors	80.3±6.0	79.6±8.4	78.4±5.4	82.8±4.9	81.3±5.8	82.6±6.5
	clipper	91.2±3.9	90.1±3.9	90.9±3.8	89.6±5.6	89.8±5.8	89.9±5.0
	irrigator	86.0±4.1	85.3±2.8	84.5±6.8	79.6±6.5	79.1±5.7	81.3±4.9
	Mean	89.9±1.0	89.1±2.1	89.3±2.1	89.1±1.7	88.7±1.3	89.4±2.0

Table 10 :

 10 Per-class verb recognition AP (%) on cross-validation splits (Method in PyTorch)

	Classes		CholecT45			CholecT50
		Tripnet	Attention Tripnet	RDV	Tripnet	Attention Tripnet	RDV
	grasp	70.5±5.8	60.5±9.9	69.8±3.7	67.1±3.4	66.1±5.4	68.3±3.0
	retract	90.5±5.4	84.0±9.8	89.7±7.2	86.7±5.1	85.8±5.4	86.7±5.8
	dissect	93.0±2.8	86.5±9.9	93.2±3.9	90.9±2.4	90.6±2.4	91.0±3.3
	coagulate	67.2±6.1	56.5±9.9	68.7±5.5	67.9±5.0	68.5±6.2	69.7±6.1
	clip	85.4±6.4	67.8±9.8	85.5±3.7	85.5±6.3	86.1±5.4	86.5±5.5
	cut	70.5±9.1	57.7±9.9	72.0±4.8	74.9±3.4	72.3±6.1	74.9±7.6
	aspirate	60.7±9.2	47.1±9.9	57.8±9.9	57.4±4.9	57.1±7.3	56.7±5.5
	irrigate	29.6±8.2	17.4±9.7	25.7±5.8	27.6±9.4	25.4±7.9	25.1±9.2
	pack	32.1±9.9	25.8±9.9	31.2±9.9	26.8±9.9	33.2±9.9	20.0±9.9
	null-verb	23.0±2.4	21.1±5.0	24.0±4.1	24.5±1.8	25.5±4.0	24.9±2.6
	Mean	59.9±0.9	61.2±0.6	62.0±1.3	58.8±3.1	61.1±2.0	60.4±2.8

Table 11 :

 11 Per-class target recognition AP (%) on cross-validation splits (Method in PyTorch)

	Classes		CholecT45			CholecT50
		Tripnet	Attention Tripnet	RDV	Tripnet	Attention Tripnet	RDV
	gallbladder	93.6±1.1 91.2±6.5 93.7±1.2	93.6±1.3 93.8±1.0 93.6±1.6
	cystic-plate	11.6±3.9 10.1±2.0 11.0±3.5	11.1±2.2 11.2±2.7 09.9±3.3
	cystic-duct	47.2±5.8 41.9±9.9 47.1±2.8	47.6±5.6 48.1±3.1 47.2±3.9
	cystic-artery	31.9±3.7 29.6±9.7 31.2±2.2	35.0±4.7 34.6±2.8 35.6±4.6
	cystic-pedicle	04.0±2.4 08.7±6.0 13.4±7.8	10.3±5.0 06.9±8.2 10.4±6.5
	blood-vessel	08.4±5.6 15.6±9.9 06.7±6.2	12.7±9.9 23.5±9.9 18.7±9.9
	fluid	58.4±9.2 48.9±9.9 58.0±9.9	56.3±5.1 54.5±6.8 57.0±5.1
	abdominal-wall/cavity	30.0±4.6 20.4±9.9 25.9±7.2	25.7±3.4 28.5±5.0 31.3±9.9
	liver	71.8±5.5 65.3±9.9 72.9±2.5	72.7±6.5 73.5±4.4 74.8±4.2
	adhesion	04.2±0.3 13.9±3.3 07.2±0.5	05.2±0.0 33.3±9.9 11.3±2.8
	omentum	46.7±8.6 44.4±9.9 48.0±9.9	45.8±8.0 45.8±9.9 46.2±9.9
	peritoneum	17.7±5.5 24.1±9.9 26.6±4.5	19.5±9.9 28.8±9.9 25.7±8.1
	gut	10.7±7.7 09.6±6.9 09.5±6.9	13.6±8.3 14.4±6.6 15.5±7.4
	specimen-bag	85.8±2.5 70.1±9.9 84.4±1.2	85.5±1.8 84.1±1.3 84.6±1.2
	null-target	22.8±2.3 21.1±5.4 23.5±4.1	24.5±2.1 25.5±3.9 25.2±2.6
	Mean	37.4±1.4 40.3±1.2 40.0±1.4	38.4±1.3 40.7±3.2 40.3±2.2

Table 12 :

 12 Per-class triplet recognition AP (%) on cross-validation splits (Method in PyTorch)

	Classes	CholecT45			CholecT50	classes		CholecT45			CholecT50
	Tripnet	Attention Tripnet	RDV	Tripnet	Attention Tripnet	RDV	Tripnet	Attention Tripnet	RDV	Tripnet	Attention Tripnet	RDV
	grasper,dissect,cystic-plate

CholecT45 & CholecT50 Dataset Splits and Metrics

Acknowledgements:

This work was supported by French state funds managed within the Investissements d'Avenir program by BPI France (project CONDOR) and by the ANR under references ANR-11-LABX-0004 (Labex CAMI), ANR-16-CE33-0009 (DeepSurg), ANR-10-IAHU-02 (IHU Strasbourg) and ANR-20-CHIA-0029-01 (National AI Chair AI4ORSafety). It was granted access to the HPC resources of Unistra Mesocentre and GENCI-IDRIS (Grant 2021-AD011011638R1). The authors also thank the IHU and IRCAD research teams for their help with the initial data annotation during the CONDOR project.