Mohamed Becha Kaaniche
email: mohammed-becha.kaaniche@sophia.inria.fr

Francois Bremond
email: francois.bremond@sophia.inria.fr

Monique Thonnat
email: monique.thonnat@sophia.inria.fr

Monitoring Trichogramma Activities From Videos An adaptation of cognitive vision system to biology field

This paper describes a new adaptation of a cognitive vision system in biology field. Our goal is to monitor Trichogramma activities from image sequence. More precisely we aim at recognizing several scenarios of the parasitoid behavior when it parasites the eggs of the Mediterranean flour moth Ephestia kuehniella Zeller (crops-harmful butterfly). The main advantage of our current work is the use of accurate features for characterizing mobile objects shapes. We first establish different requirements to describe Trichogramma activities involved in the laboratory experiment context. We second explain the steps taken to adapt a general video understanding framework containing a scenario recognition algorithm to reach our objective.

Introduction

Activity monitoring is an important field of research but it usually deals with human activities. We are interested in applying it to the biology field. Trichogramma species are recognized as important biological control agents to substitute pesticides in field crops, forests and fruits. As a parasitoid of caterpillar pests, it protects several vegetables such as corn, rice and sugarcane. Current studies are focused on analyzing the variations of handling-time and on understanding their foraging mechanisms for screening better agents for biological control and improving their efficiency to control their hosts when they are released in the field. To conduct this works, it is essential to understand the parasitoid behavior. Currently, the video sequences of laboratory experiments (see Fig. 1 for sample) are analyzed manually by experts. Due to the hugeness of the data to collect from plentiful video sequences, we are interested on automating this task by using scenario recognition techniques.

Unfortunately, video understanding is focused generally on recognizing human activities. Furthermore, behaviors are usually recognized through the study of trajectories and positions of studied objects and using a priori knowledge about the scene. This is quite sufficient when we deal with scenes having large field of view and simple human activities. But, we often do not have enough information to accurately determine more complex behaviors and especially non-human activities. Moreover, we need to process visual features characterizing the shape of the mobile object so that we can identify its behavior.

Our aim is to adapt an automatic video interpretation system to recognize Trichogramma behaviors which is composed of a vision module and a scenario recognition module. The system takes two types of inputs: (1) a video stream acquired by camera(s) and (2) a priori knowledge concerning scenario models predefined by experts and the 3D geometric and semantic information of the observed environment. The output of the system is the set of recognized scenarios at each instant.

In general words, the system performs through three steps. First, a low-level image processing algorithm subtracts the current frame with the background frame and detects moving regions. Then a tracking algorithm tracks the detected regions and computes their trajectory. Finally, the scenario recognition module identifies the tracked moving regions as mobile objects and interprets the scenarios that are relative to their behaviors.

To reach our goal, we use VSIP (Video Surveillance Intelligent Platform), described in [START_REF] Avanzi | Design and Assessement of an Intelligent Activity Monitoring Platform[END_REF], including a scenario recognition module based on [START_REF] Vu | Automatic Video Interpretation: A Novel Algorithm based for Temporal Scenario Recognition[END_REF]. We also integrate a module to handle Trichogramma specific behaviors. In this paper we focus on the wrapper module and on the set of parameters required for tuning the vision module. We first present the state of art in the related fields. Second, we introduce the proposed method. Third, we show the early results and discuss them. Finally, we conclude by summarizing the contributions and exposing our future work.

State of Art

Shape Features

There are two main categories of methods studying the visual features of the shape of a mobile object: methods based on 2D appearances and methods using 3D models. The majority of the methods based on 2D appearance use the same schema. First they detect the principal extremity parts of the body. Then, based on these detections, they search for the secondary parts of the body which are the articulations. The method proposed by [START_REF] Iwasawa | Realtime Estimation of Human Body Posture from Monocular Thermal Images[END_REF] proceeds in three steps: determining the center of gravity of the human silhouette, computing the orientation of the upper half of the body and finally estimating the significant points such as feet, hands, elbows and knees by using a heuristic contour analysis of the human silhouette. Reference [START_REF] Wren | Pfinder: Real-time tracking of the Human body[END_REF] is a real time system which uses a multi-class statistical model of color and shape to obtain a 2D representation of head and hands in a wide range of viewing conditions.

Another approach, described in [START_REF] Haritaoglu | Ghost: A Human Body Part Labelling System Using Silhouettes[END_REF], segments the silhouette from the background and computes the vertical and horizontal projections of the silhouette to determine the global posture of a person (standing, sitting, crawling-bending and laying) and his/her orientation relative to the camera (front view, left side view and right side view). To recognize the posture the system compares the current projections to the model of projections realized for a set of predefined posture and point of view. Then it determines the body parts by analyzing the contour of the silhouette. The principal drawbacks of these methods are the dependency on the point of view and their focus mostly on human-shapes.

Concerning methods using 3D models, a model is defined as a set of geometrical objects such as parallelepipeds, spheres or truncated cones and parameters which define the relations between these objects such as spatial constraints. This model is defined in a high dimensional phase space (dimension depends on the degrees of freedom of the model). Several pre-established and known 3D Models are used as a priori knowledge in such methods. In [START_REF] Moeslund | 3D Human Pose Estimation using 2D Data and an Alternative Phase Space Representation[END_REF], an alternative representation of the phase space which supports a more efficient use of the different constraints is proposed. This method needs a frontoparallel view of the camera.

To handle ambiguities in such methods and to estimate precisely the depth, several cameras may be used. For instance, [START_REF] Iwasawa | Real-time, 3D Estimation of Human Body Postures from Trinocular Images[END_REF] proposes a system using three cameras all around the person. The method compares the projections of 3D model of a person on an image with the detected silhouettes. This process is iterated by computing a force that will move the 3D model towards the current silhouette. The final parameters of the 3D model constitute an estimation of the real posture. The main drawbacks of these methods are the utilization of too many parameters difficult to tune and the requirement of several cameras to obtain a better precision.

In this work, we combine the 2D methods described in [START_REF] Iwasawa | Realtime Estimation of Human Body Posture from Monocular Thermal Images[END_REF] and [START_REF] Haritaoglu | Ghost: A Human Body Part Labelling System Using Silhouettes[END_REF] to extract features characterizing a non-human shape. Methos using 3D models are ill-adapted since only one camera has been provided in the experiment and no Trichogramma 3D model is available for the current time.

Scenario Recognition

Automatic Video Interpretation has been a problem of focus in cognitive vision in the last decade. The last years witnessed a more practical and user-centered development of this field. However, it remains focusing on people and vehicle tracking. Through several approaches which aim at recognizing temporal scenarios we can retain two main categories based on (1) a probabilistic/neural network combining potentially recognized scenarios and (2) a symbolic network.

As a computer vision researcher, the probabilistic/neural network [START_REF] Oliver | Graphical Models for Driver Behaviour Recognition in a Smartcar[END_REF] is an adequate approach. The nodes of such network correspond usually to scenarios that are recognized at a given instant with a computed probability. For example, [START_REF] Howell | Active Vision Techniques for Visually Mediated Interaction[END_REF] proposed an approach to recognize a scenario based on a neural network (time delay Radial Basis Function). Reference [START_REF] Hongeng | Representation and Optimal Recognition of Human Activities[END_REF] proposed a scenario recognition method that uses concurrence Bayesian threads to estimate the likelihood of potential scenarios. These probabilistic methods are useful, in the case of noisy images, to give an interpretation of the scene while taking into account the stochastic variations of the analysis. For our work, we choose classical filtering techniques to get rid off these variations and to obtain coherent data that can be associated with symbolic values.

In artificial intelligence, researchers use symbolic networks; their nodes correspond usually to the boolean recognition of scenarios. For example, [START_REF] Rota | Activity Recognition from Video Sequences using Declarative Models[END_REF] used a declarative representation of scenarios defined as a set of spatiotemporal and logical constraints. To reduce the processing time for the recognition step, they proposed to check the consistency of the constraint network using the AC4 algorithm.

More recently, [START_REF] Gerber | Deriving Textual Descriptions of Road Traffic Queues From Video Sequences[END_REF] defined a method to recognize a scenario based on a fuzzy temporal logic. Concurrently, [START_REF] Vu | Temporal Constraints for Video Interpretation[END_REF] present an approach to optimize the temporal constraint resolution by ordering in time the sub-scenarios of the scenario to be recognized. The common characteristic of these approaches is to store all totally recognized scenarios (recognized in the past).

Another approach consists in using a symbolic network and to store partially recognized scenarios (to be recognized in the future). For example, [START_REF] Ghallab | On Chronicles: Representation, On-line Recognition and Learning[END_REF] has expressed a temporal scenario as a chronicle which is represented as a set of temporal constraints on time-stamped events. The recognition algorithm keeps and updates partial recognition of scenarios using the propagation of temporal constraints based on the RETE algorithm. The applications are dedicated to the control of turbines and telephonic networks. Reference [START_REF] Chleq | Real-time Image Sequence Interpretation for Video Surveillance Applications[END_REF] made an adaptation of temporal constraints propagation for video surveillance. In the same period, [START_REF] Pinhanez | Human Action Detection using PNF Propagation of Temporal Constraints[END_REF] have used Allen's interval algebra to represent scenarios and have presented a specific algorithm to reduce its complexity.

Therefore, we extend the method shown in [START_REF] Vu | Automatic Video Interpretation: A Novel Algorithm based for Temporal Scenario Recognition[END_REF] by adapting the ontology used by the scenario recognition algorithm as described in [START_REF] Bremond | Ontologies for Video Events[END_REF] in order to recognize Trichogramma behaviors. Our choice is justified by the ability of this method to limit the amount of scenarios stored by symbolic network based methods.

Proposed Method

In VSIP, an image processing module detects the moving regions and computes several measures (e.g. their size, location). Then a tracking module tracks the detected regions within the whole video. Because of detection errors, a moving region can either correspond to a noise, to a part of a mobile object (e.g. part of the wings of a Trichogramma) or to a mobile object (e.g. a Trichogramma). Then the scenario recognition module generates hypothesis to consider the tracked moving regions as a mobile object composed of one or more regions. Finally the scenario recognition module computes the properties of mobile objects and analyzes the scenarios relative to the behavior of the mobile objects based on their properties. Scenarios are recognized in a recursive manner. At level 0, an elementary scenario (i.e. primitive state or event) is recognized directly from the associate mobile object properties. At level n, a scenario is recognized through a combination of sub-scenarios recognized at level n-1. To describe a scenario we use a modeling formalism as proposed by [START_REF] Bremond | Ontologies for Video Events[END_REF].

Before the current work, the system could only handle human activities and detect only human and vehicles. Up to eight mobile object properties were computed: height, width, speed, motion direction, current location, trajectory (set of previous location), the distance to a reference object and the number of moving regions that compose the mobile object. To adapt this video understanding platform to Trichogramma behavior recognition, we have performed three tasks. First, we have tuned the vision module parameters and a priori knowledge to adjust the context initialization and the segmentation process. Second, we have designed a visual feature algorithm dedicated to the recognition of parasitoid (such as Trichogramma) and to the computation of its specifics properties. Finally, we have extended the scenario recognition module (as shown on Fig. 2) to take into account the visual feature module outputs.

Trichogramma Behavior Description

Studies on parasitoids behaviors are conducted since the sixties. Reference [START_REF] Wajnberg | Analysis of Variations of Handling-time in Trichogramma Maidis[END_REF] shows one of the researches on Trichogramma behavior which analyses the variations of handling-time in the parasitoid activities. The experiment consists in offering groups of host eggs to isolated Trichogramma females that one observed under a microscope until all host eggs are parasitized. The output of the microscope is digitalized and stored as a video stream. Our goal is to build the history of six Trichogramma activities. First, we detect every entry ("Enter" event) and exit ("Exit" event) in an experimental zone surrounding the host eggs; if the Trichogramma female exits from this zone and stays out more than sixty seconds, the tracking is stopped. Then, we recognize the "Walk" event which corresponds to the walking of the Trichogramma females in the experimental zone between host eggs. Finally, we focus on the duration and time-bound of the three phases of egg laying behavior. The three phases are: (1) antennal drumming, (2) ovipositor drilling and (3) oviposition.

The first three actions can be easily detected in VSIP because they can be computed using only mobile object position. However, the three phases of egg laying behavior are specific to the Trichogramma activities. Thus, local descriptors are needed to identify these three phases. First, we focus on the antenna positions and movements to identify the antennal drumming phase. Second, we detect the quasiimmobility of the Trichogramma female during the drilling and the oviposition phases. Finally, we distinguish between these two later phases by detecting the slight vibration of the Trichogramma abdomen to insert, completely, its egglaying organ (i.e. ovipositor) into the host egg.

Nonetheless, due to the delay needed by a Trichogramma to be interested in host eggs, the experiment begins with a phase where a glass dish is reversed to prevent Trichogramma from escaping. If the Trichogramma is not interested in the host eggs, the experiment is stopped. The glass dish reversing phase introduces a background modification in the image sequence, thus the video understanding process starts only after this phase. To extend the automate analysis through the whole video, we need to modify the experiment steps.

Detection and Tracking of Trichogramma

Basically, in case of one static observing camera, the vision module contains four main components: the acquisition component, the context and background component, the segmentation component and the frame to frame (short term) tracking component.

The acquisition component manages the source of the video, the format of the captured image sequence and its frame rate (typically between 4 and 25 frames/second). It provides the current frame of the video to process at the current iteration.

The context and background component detects the host eggs (using contextual information) and the mobile object (using background information) in the current frame. This component was adapted to treat sequences captured from a camera view point enabling the computation of mobile object height. However, in the experiment, the image sequences are captured by a vertical camera with a non-focal lens. So, we have extended this component to handle this situation where only two dimensions can be observed.

The segmentation component detects the moving regions by subtracting the current image from the background image. These moving regions, associated with a set of 2D features like moving pixel density or region position, are called BLOBS. The 2D features correspond to image dimensions measured in pixels. After noise removing, a set of 3D features like 3D position, width and height, are computed for each blob. The 3D features correspond to the physical world dimensions measured, in the current case, in micrometers.

The blobs associated with their 3D features are called MO-BILE OBJECTS. We have adjusted the segmentation component parameters to adapt the quality of the segmented mobiles in the scene observed through microscope equipment which implies a strong light intensity due to the experimental conditions.

The short-term tracking component links from a frame to the next frame all detected mobile objects. The output of this module is a graph containing the detected mobile objects updated over time and a set of links between blobs detected at time t and blobs at time t-1.

Trichogramma Visual Feature Algorithm

To identify the three phases of the Trichogramma egg laying behavior, we need to extract the visual features characterizing the insect shape and interpret them as events. Hence, we have designed an algorithm in order to handle these aspects. The Trichogramma Visual Feature Algorithm first classifies the segmented mobile object as a Trichogramma female by controlling the already computed features such as width and height. Then, it detects the antennas and the ovipositor of the Trichogramma. Finally, it determines their events (e.g. Drumming, Drilling) by computing their positions and monitoring their movements.

The Visual Feature Algorithm classifies the detected mobile object into two classes: Trichogramma or unknown. We have defined a specific probabilistic model which learns the 3D size of the insect in a preprocessing phase. Trichogramma female is recognized by comparing the current 3D features to the predefined model. Then, the algorithm computes additional visual features to be used by the scenarios recognition module.

In order to detect the parts of the body of the parasitoid, we proceed through five steps. First, we compute the center of gravity of the mobile object recognized as the Trichogramma body. Second, we compute its orientation by calculating autocorrelations of pixels through x axis (C x 2 ) and y axis (C y 2 ) and their intercorrelation (C xy ): the orientation is deduced by applying [START_REF] Avanzi | Design and Assessement of an Intelligent Activity Monitoring Platform[END_REF]. Third, we normalize the blob corresponding to the parasitoid body with a rotation to position it horizontally in order to obtain a self-referential of the insect. Fourth, we calculate the main axis and orthogonal axis projections of the insect (self-referential) by counting the number of pixels of each axis as shown by Fig. 3.

θ = arctan Cxy C x 2 -C y 2 + (C x 2 -C y 2 ) 2 + C 2 xy (1)
Finally, we determine the length and the position (in the projections) of the antennas and the ovipositor by matching the extremities of the projections with a 3D template corresponding to their average size. After that, we can locate these body parts in the blob and retrieve their positions in the scene. To generate the antenna drumming and ovipositor events, we maintain a history of the positions of the antennas and the ovipositor. By analyzing this history, we can monitor the movements of these parts of the insect and determine if the insect is in a drumming phase, in a drilling phase or in an oviposition phase.

Recognition of Scenarios Revision

The scenario recognition module, given a priori knowledge of the scene and the scenario models, has to detect which scenario is happening from a stream of observed individuals tracked by a vision module at each instant.

The scenario models are based on the concepts of "state", "event" and "scenario". A state is a spatio-temporal property valid at a given instant or stable on a time interval. An event is a meaningful change of state. A scenario is any combination of states and events and is represented as a constraint network whose nodes correspond to sub-scenarios and whose edges correspond to temporal constraints. Temporal constraints are propagated inside the network to avoid an exponential combination of previously recognized subscenarios. The scenarios are modeled in terms of "physical objects" (individual or zones of interest etc.), "components" (which can be primitive-states, composite-states, primitiveevents or composite-events) and "constraints" between the physical objects and/or the components (constraints can be temporal, spatial or logical). To describe the scenarios relative to the Trichogramma behavior, we use a declarative language specifying generic events which are defined in the video event ontology detailed in [START_REF] Bremond | Ontologies for Video Events[END_REF].

In order to recognize the phases of the egg laying behavior, we have matched the visual features computed by the Visual Feature Algorithm with three new primitive-states. Figure 4: An extract from the description of the scenario models representing the three phases of the egg laying behavior.

We have extended the scenario description language by adding these states. The first state indicates whether the Trichogramma antennas are drumming a host egg. The second state corresponds to the quasi-immobility of the insect during the drilling and oviposition phases. The last state is relative to the slight movement of the ovipositor discriminating the two last phases of the egg laying behavior. Fig. ?? shows an extract from the description of drumming, drilling and oviposition scenario models which define the three added states. For instance, in Drumming scenario, two physical objects are involved: an insect "tricho" and a zone of interest z corresponding to an egg. To recognize this scenario, one component (sub-scenario) has to be recognized indicating that the Trichogramma is close to the egg to parasitize and two constraints needs to be verified: First that the Trichogramma remains in motion and second that their antennas are in movement.

The algorithm, part of the scenario recognition module, performs the recognition of the scenarios in two steps: (1) recognition of elementary scenarios (primitive-states and primitive-events) and (2) recognition of composite scenarios (composite-states and composite-events).

During the first step, all elementary scenarios are recognized. To recognize a given elementary scenario model, a loop is performed on all possible sets of physical objects followed by a verification of the corresponding atemporal constraints until all combinations of physical objects have been tested. Once a set of physical objects satisfies all constraints, the elementary scenario is recognized and a scenario instance p is generated and attached with the corresponding scenario model, the set of physical objects and the recognition time t. The scenario instance is then stored in the list of recognized scenarios. If at the previous instant, a scenario instance p of same type (same model, same physical objects) was recognized on a time interval [t 0 , t -1], the two scenario instances are merged into a scenario instance recognized on the time interval [t 0 , t].

For the second step we define a composite scenario as a set of sub-scenarios ordered in time, as described in [START_REF] Vu | Automatic Video Interpretation: A Novel Algorithm based for Temporal Scenario Recognition[END_REF]. Each sub-scenario corresponds to a temporal variable in the corresponding scenario model. To speed up recognition process, a scenario model is decomposed in a preprocessing phase into a set of simple scenario models containing at most two sub-scenarios. The recognition of a composed scenario model S c is triggered by a scenario template, which has been generated when the last sub-scenario p e terminating S c has been recognized. The scenario template contains S c and the scenario instance p e with its list of physical objects that partially instantiate S c . As S c is composed of two sub-scenarios, only one sub-scenario p s starting S c remains to be found. If such scenario instance already exists in the past and p s and p e satisfy S c constraints, the scenario S c is recognized and stored in the list of recognized scenarios.

Evaluation and Discussion

To validate our work, we have conducted tests under rigorous conditions. This section describes and discusses the experimental results. First, we describe the system and the test set characteristics and the criteria for experimental evaluation. Second, we show our early results. Finally, we discuss our proposed method and its results.

Implementation Details

The results are computed on a PC based on an Intel Pentium IV processor and Linux operating system. Our test set consists of a long video (46 minutes) representing a typical laboratory experiment. The image sequence was captured by a digital camera (color image 720x576 pixel at rate of 25 frames/second) placed at the front-end of a microscope. As already explained, we truncate the first five minutes of the video to avoid the background modification caused by the glass dish reversing phase. The acquired video is annotated manually by a human expert. These results are confronted to those obtained automatically by the extended cognitive vision system. For each behavior we compute two indicators: the precision and the sensibility. The precision is the

Results

The outputs of the four components of the vision module at an instant t are shown in Fig. 5: (a) The context and the backgroud image, (b) the cuurent frame to handle, (c) the segmented current frame (blob identified) and (d) the tracked mobile object. Fig. 6 shows the ouput of the scenario recognition module at two intants: When it recognize a Walk scenario (a) and when it recognize a Drilling scenario (b). As shown in table 2, we have obtained acceptable results as feasibility proof. The miss detection of Drumming and Oviposition activities is first due to the segmentation. Besides, the distinction between these two phases is even difficult for expert human. However, we have a low sensiblity which means that the system detects too many false positive scenarios. This is due to the approximative definition of the scenario models. A finer design of these models is currently under development.

Discussion

The first problem in this application is to discriminate the egg laying phases which is not even possible for experts in some cases. Moreover, when expert are able to distinguish this phases, they are not always able to explain how they manage to do it. Thus, there is a main problem of the modelisation of the scenarios of interest. Another problem in this method is the segmentation process. It still has some imperfections: the anteneas and the ovipositor are sometimes not segmented which are the main causes of the detection problem of the three phases of egg laying behavior. In addition, the descriptors of the walk behavior are not accurate: it is defined by the transition between two states which are Trichogramma is close to egg i and then Trichogramma is close to egg j. Another definition of the walk behavior, corresponding more to the expert definition, is that the Trichogramma is in motion and is not overlap any egg zone.

Conclusion and Future Work

We have extended a cognitive vision system to monitor Trichogramma activities. Our approach computes the visual features characterizing mobile object shape to distinguish between the three phases of the egg laying behavior and allow the recognition of the global activities. After extending the vision module of this system, we have concieved a module which extracts these visual features and bind them to a scenario recognition module. In this paper, we have shown that this behavior recognition approach can be extended over physical objects than human beings. The main challenge is to be able to detect shape features characterizing the body parts of physical objects. As a feasibility proof, we have obtained acceptable results according to the complexity of the egg laying behavior. Previous work has concentrated on studying human behaviors. This paper summarizes an attempt to generalize the utilization of cognitive vision system to monitor non-human activities such as insect parasitoid activities. This work can be improved by developing the following aspects. First, we plan to improve the segmentation algorithm in order to have a better determination of the three egg laying behavior phases. Currently, we focus on applying program supervision techniques to dynamically tune the parameters of the segmentation algorithm. A second task consists in refining the definition of the walk activity by a better understanding of the knowledge of th expert. Third, in order to develop an operational system, we shall automate the description of the context of the scene. For instance, we have, now, to define the context of each new experiment due to the variations of the background. We are planning to develop a learning module for automating the acquisition of the experimental context which will define the context of the scene without expert help. Finally, in the long term, we also plan to add a new front-end tool which will collect the output of the scenario recognition module for all experiments and mine these outputs to deduce the frequent activities and their probabilistic law: it is claimed that the behavior of the Trichogramma while selecting a host egg can be described by the dynamic game theory.

Figure 1 :

 1 Figure 1: The figure shows the background of a sample image sequence and a sample frame from the video. Image (a) illustrates the nine hosts eggs and their shadows. Image (b) illustrates a Trichogramma female in drilling phase.

Figure 2 :

 2 Figure 2: Flowchart of the proposed Automatic Video Interpretation System.

Figure 3 :

 3 Figure 3: Main axis projection of the Trichogramma in its self-referential

  tricho : Insect),(z : Zone)) Components((close : PrimitiveEvent close to zone(tricho,z))) Constraints((!IsStopped(tricho)) (AntennaeMovement(tricho)) ) Alarm(AText("Trichogramma is Drumming in " + z-¿Name)...) ) # Drilling Scenario CompositeEvent(Drilling, PhysicalObjects((tricho : Insect),(z : Zone)) Components((close : PrimitiveEvent close to zone(tricho,z))) Constraints((IsStopped(tricho))) Alarm(AText("Trichogramma is Drilling in " + z-¿Name)..tricho : Insect),(z : Zone)) Components((drilling : CompositeEvent Drilling(tricho,z))) Constraints((!IsOvipositorMoving(tricho))) Alarm(AText("Trichogramma is in Oviposition in " + z-¿Name)...) )

Figure 5 :

 5 Figure 5: Outputs of the four main components of the vision module.

Figure 6 :

 6 Figure 6: Output of the scenario recognition module.

Table 1 :

 1 Number of Occurence of the Parasitoid Activities in the Test Video

	Behaviors	Number of occurence
	Enter	18
	Exit	19
	Walk	49
	Drumming 42
	Drilling	25
	Oviposition 21
	Total	194

Table 2 :

 2 Trichogramma

		Behavior Detection Results
	Behaviors	Precision Sensibility
	Enter	100%	0%
	Exit	100%	0%
	Walk	100%	0%
	Egg laying behavior phases 85%	15%
	Drumming	70%	5%
	Drilling and Oviposition	15%	10%
	ratio between the numbers of instances well detected au-
	tomatically and the number of instances detected manually
	(Ground Truth). The sensibility is the ratio between false-
	detected instances and manually-detected instances. The
	content of the test video is resumed by table 1.


Pierre Guiraldenq
email: pierre.guiraldenq@orange.fr

New comments on the Melting Entropy of Binary Eutectic Alloys without solid state solubility

Keywords: eutectic transition, melting entropy, diffusion in the solid state, interfaces, amorphous phases, vibration frequencies

A new approach is given for the solid -liquid transition at the melting temperature for a family of well known binary eutectic alloys, problem which has been introduced in a preceding paper in 2020.

In a first time, a mechanism is described for the beginning of the melting process, with the role played by the interfaces between the two lattices. A second question concerns the vibration frequencies of atoms at that time for the two components in relation with the self diffusion constants. At the end, it is proposed an orderdisorder model by damped oscillations of the entropy before the final stabilized amorphous liquid state.

A RECALL ON THE PRECEEDING RESULTS :

In a previous paper [START_REF] Guiraldenq | A new approach to the solid-liquid transition for simple binary eutectic systems in relation to the melting entropy and the periodic Table[END_REF], we have focused on a singularity about a small group of binary eutectic alloys (without solid state solubility) and for which the solidliquid transformation at the eutectic temperature is characterized by an excess of entropy, compared to other thermodynamic systems (at the atmospheric pressure). This small group contains nine binary diagrams ;

Si -Au, Ge-Au, B-Pt, Ge-Al, As-Pb, Ge-Ag, Cd-Bi, Si-Ag, Si-Be which corresponds to a simple binary semi-conductor -metal family.

For this family, it has been noted a linear relation between an entropy excess during the melting process, ∆𝑺𝑬, with a specific parameter taking in account the self diffusion properties of each component (m1, m2) by the cumulative ratio of the eutectic temperature TE compared with the two melting temperatures (Tm1, Tm2) according the relation ;

∆𝑺𝑬 ∝ ( TE / Tm1 + TE / Tm2 )

The Figure 1 shows a linear relationship for this binary alloys family seen before, with a slope which value is 3 kB NA, with kB the Boltzmann Constant and NA the Avogadro Number. Other results with a very low level for ∆ S E are not taken into account here (Ag -Bi, Al -Sn, Be -Al, etc).

We note with surprise the same property defined a very long time ago by Albert Einstein for the solid state heat capacity corresponding to one simple perfect solid, in which all the atoms have at the end the same vibration frequency (2) (3). The problem is presently clearly different because it concerns, at the same time, two solid phases in equilibrium and in contact, with the classical lamellar eutectic structure giving at the end only one liquid phase, at the same temperature TE, like a pure metal. To obtain an analysis of this singular state, we have considered two complementary approaches : the first one by a structural analysis at the interfaces between the two components and, in a second way, by a quantitative description of the vibration frequencies calculated with the self diffusion coefficients in the solid state.

A STRUCTURAL REGARD TO THE EUTECTIC TRANSITION AT A NANOSCOPIC SCALE :

We have described before in (1) the role played by the interfaces between two lamellar phases as simple diffusion couples : We know that several diffusion processes may be present and in which the interfacial diffusion process is preponderant when the ratio T Eutectic / T m is low (TE /Tm1 and TE / Tm2 under 0,5) and, on the contrary, in relation with a bulk diffusion when the ratio TE / Tm is larger than 0,6-0,7.

At the beginning and at a very low temperature, before the heating process to the melting temperature TE, and taking into account the crystallographic properties of each element, we can consider possible crystallographic coincidences sites between the two systems, as described a long time ago by Aust and Chalmers (4), Smith (5) in 1951, then later by Spaepen in 1975 to describe the liquid transition with an amorphous phase [START_REF] Spaepen | A structural model for the solid-liquid interface in monoatomic systems[END_REF].

In a first time, applied to the eutectic Si-Au system, the figure 2 gives a possible equilibrium coincidence sites, taking for instance the same simple (100) plane and the same axis <100 >, with the crystallographic parameters for each element.

By a rotation of 20° around one axis < 𝟎𝟎𝟏 > for the Au lattice, it appears for example, at the interface, coincidence sites for Au(F.C.C) and Si (D.C.) every eight atomic positions, the other places being with possible local or other disturbing defects (dislocations, etc) For very high interfacial energies which characterize the diffusion process, with an increasing temperature and new atomic configurations, we can imagine a progressive structural instability like in Figure 3. The new transitory medium, presented here, like an amorphous zone, should be the progressive evolution toward the liquid state from the initial quasi-ordered structure between the two lamellar phases, giving so an higher transitory entropy compared to the self melting entropy alone.

ANALYSIS OF THE ATOMIC VIBRATIONS WITH THE DIFFUSION CONSTANTS IN THE SOLID STATE

As said before in (1), the atomic diffusion processes are defined for each element in a binary system by Arrhenius laws giving the diffusion coefficients in the bulk, or in the grain boundaries and interfaces at lower temperatures.

In the present case, we consider only the bulk diffusion coefficients through the Arrhenius law because this mechanism is always present at the same time in the transverse directions of the interfaces at medium temperatures (TE / Tm higher than 0. In the present case, the entropy which characterizes all the defects present during the transition at TE, is the excess of entropy ∆𝑺𝑬 which has been calculated in the preceding paper at the melting temperature of the eutectic alloys with this singular property (Figure 1).

So, taking the values of the frequency factor D o and the crystal parameters '' a '' (taken constant at low temperature), we can define an average frequency '' v E '' for each element corresponding at the end to the solid-liquid transition. We have noted that the two atomic concentrations for CE (with CE = C1 + C2.) at TE have no importance at this level because this factor disappears at the atomic scale for the two elements without solubility (each element has the same concentration (100 at. per cent) on each side of the interfaces at low temperature, before heating to T E. Between these different binary alloys, we note a decreasing ratio of the vibration frequencies which values are in coherence with many other physical properties. It is certainly the expression of different atomic interactions during the solid-liquid transition at TE between the structure of a semi-conductor (Si or Ge) with a classical noble metal (Au or Ag). These same components have been a long time ago studied at an atomic level for electronic devises [START_REF] Brillson | The structure and properties of metal -semiconductors interfaces Surface Science reports nov[END_REF] and for the vibration frequencies in the crystalline or amorphous states by P. Dean [START_REF] Dean | Atomic vibrations in Solids[END_REF] and A.T. Willis and A.W. Prior [START_REF] Willis | Thermal vibrations in Crystallography[END_REF].

In the present case, the vibration frequencies vE have been obtained only in relation with the diffusion mechanisms and it should be interesting, with new other methods, like Laser Spectroscopy, to obtain in situ confirmation of these results. The other cases, seen in the Figure 1, should be also discussed, but with some difficulties according their different crystalline structures (B, Be, Sn, As, Bi, Th) and the best rigorous values obtained for the self diffusion constants Do, as said before.

At the end and for the progressive evolution of the micro structure of such eutectic alloys to the amorphous liquid state at TE, it is possible to imagine a damped oscillations process, starting from the interfaces toward the bulk, like in the figure 3 with new transitory configurations. A such decreasing evolution of the ordered duplex lamellar structure should be so described by a Fourier series model [START_REF] Angot | Compléments de Mathématiques à l'usage des ingénieurs de l' Electrotechnique et des Télécommunications[END_REF] for the entropy ∆ S E before the final liquid eutectic state (Figure 4).

FINAL CONCLUSION :

Using the simple thermodynamic concepts, a new analysis has been suggested with a singular family of binary alloys, characterized by an insolubility in the solid state.

It has been noted a set of such alloys which match this property with a singular entropy corresponding to the melting temperature in relation with a factor 3kN, which has been formerly taken as a reference to define the upper solid state heat capacity.

This historical review inside the Materials Science chapter, particularly with only the self diffusion constants to define the atomic vibrations, has shed some light at a nano scale level of a singular new alloys family concerning the order-disorder phenomena during the solid-liquid transitions.

during the final solid → liquid transformation, like for a pure metal in the grain boundaries at its melting temperature and according the Gibbs phases rule.

The other cases seen before, with high transitory entropy and with high difference between the frequencies (the best case is Au-Si), are explained by quasi amorphous disordered structures during the melting process.

5 )

 5 The literature gives a large panel of results obtained with radiotracers or other physical methods, giving the frequency factor D 𝒐 by the well known relation : D o = a 2 v exp ( -∆𝑺/𝒌 ) equ. a '' the lattice parameter taken at low temperature (for F.C. C., C. C. and D.C. cubic structures)

FIGURES 1 to 4 (pages 9 to 10 )Figure 1 :

 4101 FIGURES 1 to 4 (pages 9 to 10)

Figure 2 :

 2 Figure 2 : Coincidence sites at the interface between the two elements Si and Au in the same plane (100) and a rotation of 20 degrees for Au lattice around an axis <001> (parameters ref. (9))

Figure 3 :

 3 Figure 3 : The possible first evolution of the interface between the two lattices of Au and Si, for the same plane (100) without rotation and with several local distortions of the two lattices under the influence of vibration frequencies and short range diffusion at TE.

Figure 4 :

 4 Figure 4 : Evolution of the entropy excess at TE, growing from the interfacial zones by a damping oscillations process during the progressive transformation of the eutectic structure to the final amorphous liquid state.

  So, we have taken only four typical diagrams covering high and low values for ∆𝑺 𝑬 (with cubic structures and with well defined Do values)The table gives below the frequencies vE obtained by this way from equ.1

		Si -Au	Si -Ag	Ge -Au	Ge -Ag
	For each case, the best Do experimental values have been chosen in the literature
	(7) (8) and the lattice parameters from the classical Charles S. Barrett book (9) :
	Au	Do = 0.09 . 10 -4 (m2 / sec)	a = 0,4078 n m
	Ag	Do = 0.44 . 10 -4	''	a = 0,4085	''
	Si	Do = 2	. 10 -1	''	a = 0,5422	''
	Ge	Do = 7. 8 . 10 -4	''	a = 0,5658	''
	Alloy	T E ( K )		TE/Tm1 + TE/Tm2	v E ( Hz )	v1/v2 ≈
	Si	643		0,85		2.9 . 10 +16	10+4
	Au	''		''		2.3 . 10 +12
	Si	1103		1,54		2.9 . 10 +16	10+3
	Ag	''		''		1.1 . 10 +13
	Ge	629		0, 98		1 . 10 +14	10+2
	Au	''		''		2.3 . 10 + 12
	Ge	924		1,5		1 . 10 + 14	10+1
	Ag	''		''		1.1 . 10 + 13

Conflicts of interest : the author declare no conflict of interest ACKNOWLEDGEMENTS : to Dr Jean Marie Dubois, Emeritus Director of CNRS at the Institut Jean Lamour (UMR CNRS 7198) -Nancy University -for his encouragements, discussion in detail and corrections.

FINAL IMPORTANT REMARK

The Al-Be eutectic system has been taken here as an example with a very small ∆S E value (near zero).

As said before, taking into account the crystallographic parameters and the bulk self diffusion constants Do given by the literature (9) ( 14 For Be, the self-diffusion results have been obtained with single crystals along two directions (along the // (c axis), and the ꓕ (basic plane) ( 14)).

So, the vibration frequencies obtained with the frequency factors Do are for each element : Considering the medium value of ν (Be)in the bulk as a first approximation, that is 3.4 . 10 +13 Hz, the ratio ν (Be) / ν (Al), or the reverse ratio ν (Al) / ν (Be), is finally near the value : 1, value which is very lower than the all other results for the cases studied previously in § 3 (page 4). This means, when ∆S E = 0, that the vibration frequency of the two elements is probably the same near the interfaces