Abdelhak Loukkal

Yves Grandvalet

Tom Drummond

You Li

Driving among Flatmobiles: Bird-Eye-View occupancy grids from a monocular camera for holistic trajectory planning

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Introduction

Autonomous driving systems are usually composed of carefully engineered modular building blocks. Each building block being developed separately, this makes the whole system more interpretable but can also lead to an accumulation of errors along the pipeline. End-to-end driving CNNs [START_REF] Pomerleau | Alvinn: An autonomous land vehicle in a neural network[END_REF][START_REF] Bojarski | End to end learning for self-driving cars[END_REF][START_REF] Codevilla | End-to-end driving via conditional imitation learning[END_REF][START_REF] Xiao | Multimodal end-to-end autonomous driving[END_REF] consist in neural networks that take raw sensor data as input, or other modalities such as the depth or the optical flow, and output control commands, for example steer-Figure 1: Applying a planar homography to a full segmentation mask causes the pixels located above the ground plane to be stretched in BEV. Our footprint segmentation respects the flat world hypothesis implied by the homography hence avoiding the deformation caused by above the ground pixels.

ing wheel angles. This kind of approach is promising but lacks interpretability because it skips all the building blocks of the autonomous driving pipeline [START_REF] Zeng | End-to-end interpretable neural motion planner[END_REF]. Mid-to-mid driving [START_REF] Bansal | Chauffeurnet: Learning to drive by imitating the best and synthesizing the worst[END_REF] is a more recent approach to this problem that instead of taking images as input takes intermediate representations of the driving scene provided by the perception building block. In the middle ground of these two approaches lie mediated perception approaches [START_REF] Chen | Deepdriving: Learning affordance for direct perception in autonomous driving[END_REF][START_REF] Sauer | Conditional affordance learning for driving in urban environments[END_REF][START_REF] Kim | Interpretable learning for self-driving cars by visualizing causal attention[END_REF][START_REF] Mueller | Driving policy transfer via modularity and abstraction[END_REF][START_REF] Li | Rethinking self-driving: Multitask knowledge for better generalization and accident explanation ability[END_REF] that take raw sensor data as input, have an explicit intermediate representation of the observed scene and then forecast motion based on this representation. However, none of the existing monocular camera based end-to-end approaches leverage a Bird-Eye-View (BEV) intermediate representation when it seems to be the best candidate for motion forecasting as the scale in this plane is homogeneous and the size of the observed objects is invariant to their distance to the sensor.

In this paper, we introduce a novel holistic end-to-end trajectory planning network that takes a sequence of monocular images as input, leverages a BEV mediated perception strategy and plans the trajectory of the ego vehicle knowing 1 its destination position at a 3s horizon. The intermediate representation of our network comes in the form of two binary Occupancy Grid Maps (OGMs) in BEV, one giving the drivable area and the other one the occupancy of the vehicles in the scene. As it is not straightforward to directly obtain BEV outputs from a camera plane input while preserving the receptive field, the first stage of our network first outputs these OGMs in camera view then warps them in BEV using the planar homography between the camera plane and the BEV plane. However, a planar homography relates a transformation between two planes, so we introduce the Flatmobile representation to warp the vehicles from camera view to BEV without the "stretching" effect observed in Fig. 1. This simple yet very effective representation consists in segmenting the footprint of the vehicles, i.e., the "ground" face of their 3D bounding boxes in camera view, so that the flat world assumption is respected when warping these masks in BEV. In an end-to-end fashion, an encoder-decoder LSTM is fed with these OGMs, the past trajectory and the destination position of the ego vehicle to produce the future trajectory.

In summary, the contributions of this work are two-fold:

• The main contribution is to propose a novel learning protocol to learn BEV Occupancy Grids from a monocular camera;

• The relevance of this protocol is shown by its integration into a holistic end-to-end trajectory planning pipeline that takes advantage of these occupancy grid maps as an intermediate representation.

The gain in performance on both tasks is demonstrated on the nuScenes dataset [START_REF] Caesar | nuscenes: A multimodal dataset for autonomous driving[END_REF].

Related work

Occupancy grid maps: Occupancy grid maps [START_REF] Elfes | Occupancy grids: A stochastic spatial representation for active robot perception[END_REF] represent the spatial environment of a robot and reflect its occupancy as a fine-grained metric grid. These grid maps have been widely used to model the environment of indoor and outdoor mobile robots as well as automotive systems. Once acquired, they can be used for various tasks such as path planning. OGMs can be acquired with range sensors like LiDAR or RADAR, but also from RGB-D cameras [START_REF] Himstedt | Online semantic mapping of logistic environments using rgb-d cameras[END_REF], stereo cameras [START_REF] Li | Occupancy grid mapping in urban environments from a moving on-board stereo-vision system[END_REF], or from the fusion of multiple sensors [START_REF] Oh | Fast occupancy grid filtering using grid cell clusters from lidar and stereo vision sensor data[END_REF]. For example, semantic OGMs are predicted from a Li-DAR and a monocular camera thanks to deep learning and Bayesian filtering in [START_REF] Erkent | Semantic grid estimation with a hybrid bayesian and deep neural network approach[END_REF]. Taking only monocular camera images as input, a Variational Encoder-Decoder (VED) can predict semantic OGMs [START_REF] Lu | Monocular semantic occupancy grid mapping with convolutional variational encoderdecoder networks[END_REF]. However, this approach leverages poor ground-truth OGMs obtained by warping semantic segmentation masks using the associated disparity maps. The Orthographic Feature Transform (OFT) network [START_REF] Roddick | Orthographic feature transform for monocular 3d object detection[END_REF], whose original purpose is to output 3D bounding boxes, consists in projecting the features extracted in camera view to an orthographic space. To do so, voxel-based features are generated by accumulating camera-view features; then these features are collapsed along the vertical dimension to obtain features in an orthographic plane. In addition to bounding boxes coordinates and dimensions, this network also outputs a confidence map in BEV which can be assimilated to an occupancy grid map. To the best of our knowledge, OFT and VED are the only comparable approaches to take monocular camera images as input and output a dense OGM-like grid.

Behavior cloning based ego-motion forecasting: Imitation learning consists in reproducing a desired behavior based on expert demonstrations. Behavior cloning consists in learning a policy that reproduces the desired behavior by learning a direct mapping from states to actions. Autonomous Land Vehicle In a Neural Network (ALVINN) [START_REF] Pomerleau | Alvinn: An autonomous land vehicle in a neural network[END_REF] was a pioneering work on ego-motion forecasting that used behavior cloning and a neural network to accomplish lane following. More recently, [START_REF] Bojarski | End to end learning for self-driving cars[END_REF] introduced an end-toend driving network that maps camera images to steering commands. A similar approach was adopted in [START_REF] Codevilla | End-to-end driving via conditional imitation learning[END_REF] with the difference that the steering commands are conditioned with high-level commands, e.g., turn left. Also adopting conditional imitation learning, [START_REF] Xiao | Multimodal end-to-end autonomous driving[END_REF] uses multi-modal inputs and explores different fusion schemes. In our holistic end-toend network, we condition our output with the destination position which makes it a trajectory planning set-up.

Another body of work incorporates an intermediate representation in the form of affordances [START_REF] Chen | Deepdriving: Learning affordance for direct perception in autonomous driving[END_REF][START_REF] Sauer | Conditional affordance learning for driving in urban environments[END_REF], attention maps [START_REF] Kim | Interpretable learning for self-driving cars by visualizing causal attention[END_REF] or semantic segmentation masks [START_REF] Mueller | Driving policy transfer via modularity and abstraction[END_REF][START_REF] Li | Rethinking self-driving: Multitask knowledge for better generalization and accident explanation ability[END_REF]. These approaches address the main flaw of the end-to-end approach by making the results interpretable by a human examinator. Instead of learning an intermediate representation and learning motion from this representation, [START_REF] Xu | Endto-end learning of driving models from large-scale video datasets[END_REF] learned to forecast motion from a sequence of input images and learned the semantic segmentation of these input images as a side task invoking privileged learning. However, all these camera-based solutions reason in camera view whereas it seems to be more suitable to forecast motion in BEV where the size of objects does not depend on their position in the image. The network developed in this paper takes only monocular images as input but has a BEV intermediate representation that is used for motion forecasting.

ChauffeurNet [START_REF] Bansal | Chauffeurnet: Learning to drive by imitating the best and synthesizing the worst[END_REF] adopts a mid-to-mid driving model that uses the BEV output of a perception module as input to predict a trajectory. Using a mid-level representation as input allows to augment the training data with synthetic worst case scenarios hence improving the performance of the network in a real-world scenario. Mid-to-mid driving is also adopted by the privileged learner of [START_REF] Chen | Learning by cheating[END_REF]. Alleviating the burden of manually designed planning cost functions [START_REF] Paden | A survey of motion planning and control techniques for self-driving urban vehicles[END_REF], Figure 2: For each camera frame (a), a BEV map of size 100 × 55 (in meters) is extracted as a binary semantic mask. A vehicle binary mask with the same scale and size is generated from the ground-truth 3D bounding boxes (c), where the red dot indicates the ego vehicle. These two masks are projected in camera view (b) using the homography between the two planes. Better viewed in color.

[31] introduces an end-to-end motion planner that takes a 3D point cloud and an HD map as input and has an intermediate interpretable representation in the form of 3D detections and their predicted trajectories.

End-to-end planning with BEV mediated perception

Since our method requires certain annotations in the nuScenes dataset [START_REF] Caesar | nuscenes: A multimodal dataset for autonomous driving[END_REF], we start by describing them. They will be used directly or indirectly as targets in the learning process of our holistic end-to-end network.

Data

Experiments are conducted on the nuScenes dataset [START_REF] Caesar | nuscenes: A multimodal dataset for autonomous driving[END_REF], which records the measurements of a complete suite of sensors: 6 cameras, 32-channels LIDAR, long-range radars. The whole dataset comprises 40 000 annotated frames but for intellectual property reasons we are currently limited to the preview version, with 3 340 annotated frames from five driving sequences in Boston and 81 sequences in Singapore. Each driving sequence lasts around 20s and images are acquired at a framerate of 2Hz. The two most important features of nuScenes for this paper are the availability (i) of 3D bounding boxes, (ii) of layers of the drivable area are also provided as binary semantic masks, where each pixel corresponds to 0.1 × 0.1 square meters.

Ground-truth OGMs: For each of the considered frames, a map portion of size 1 000 × 550 (that is, 100m×55m) is extracted with the ego vehicle positioned at (1000, 300) from the origin at the top left corner of the map portion. This map portion is rotated according to the ego vehicle heading angle such that it always faces forward. Given the 3D position of each vehicle in the scene, it is possible to draw its ground-truth bounding boxes on a blank canvas aligned with the map portion, with the correct size and position. These two binary semantic masks, depicted in the right-hand side of Fig. 2, can also be viewed as OGMs with grid cells of size 0.1m × 0.1m.

Ground-truth trajectories:

In addition to the semantic masks, the past and future trajectories are also preprocessed. The past and future positions are measured relatively to the current position of the ego vehicle. The past trajectory is defined as the 6 previous positions, with a 0.5s time-step. The future trajectory is defined in the same way, with the sixth point defined as the destination and the 5 intermediate points as ground truth for motion planning. After removing the frames that do not have 6 previous and future positions, the dataset is split in 1917 training samples and 415 testing samples from held-out sequences.

Homography estimation:

A key input of our holistic end-to-end network is the homography matrix between the camera plane and the OGM plane. The homography between the two planes maps a point in the camera plane (u, v, 1) T to a point in the BEV plane (x, y, 1) T such that:

  x y 1   =   h 11 h 12 h 13 h 21 h 22 h 23 h 31 h 32 h 33     u v 1   . (1)
Our framework relies on the availability of the homography matrix at each frame. For doing so, we build a training set with ground-truth homographies to predict homographies from camera frames. We take advantage of the annotated 3D bounding boxes to get corresponding points in the BEV and the camera planes. The pixel positions of the 3D bounding boxes "ground" face corners in the camera image are matched with their 3D position in the BEV plane (see Fig. 2), and the homography matrix is obtained using the getPerspectiveTransform() function of OpenCV that applies the Direct Linear Transformation (DLT) algorithm [START_REF] Hartley | Multiple View Geometry in Computer Vision[END_REF]. Not all training samples contain enough matching points, so only a subset of the original training set is Figure 3: For training images with enough matching points, the homography is computed with the matching method. These samples become training data for a neural network that learns to estimate the homography from RGB input images. This trained network is then used to pre-compute the homographies of all the samples in the dataset. Better viewed in color.

available for fitting a network predicting homographies (see Fig. 3). The homography network is composed of a ResNet-18 encoder and 4 fully connected layers with the fourth layer outputting 9 values corresponding to the elements of the homography matrix. The homography matrix contains 4 rotational terms and 2 translation terms. The difference in magnitude between these terms must be taken into account during training. The authors of [START_REF] Daniel Detone | Deep image homography estimation[END_REF] circumvent this issue by predicting 4 matching points instead of the homography matrix elements as there is a one-to-one correspondence between the two representations; we simply rescale the rotational and translation terms with a constant factor such that all the elements of the homography have the same magnitude. The L2 loss function is then used as the training criterion.

For each frame in the dataset, the predicted homography is used to warp the drivable area and vehicle OGMs in the camera plane (cf. Fig. 2). These warped masks are used as ground truths in the network described in Fig. 4. Each sample has a sequence of 6 input camera images separated by 0.5s, the camera view semantic masks for every image in the sequence, the homography matrices for every mask in the sequence, the past and future trajectories.

Footprint segmentation: OGMs from a monocular camera

Model formulation: The overall approach consists of two stages, as depicted in Fig. 4. The first stage generates OGMs from the input sequence of monocular images. These OGMs' cells can take two states, occupied or free. Two OGMs are considered: one that gives an information about the drivable area, and the other one about the position of the vehicles in the observed scene. The considered OGMs being homologous to binary semantic masks, their estimation is formulated as the semantic segmentation of the drivable area and the vehicles in the scene. State of the art semantic segmentation CNNs come in an encoderdecoder configuration where the input and the output of the network have the same aspect ratio and are in the same geometric plane. The ultimate goal of this stage is to output BEV semantic masks for each image of the input sequence. However, it is not straightforward to directly output BEV masks from a camera plane input as the receptive field of a pixel in the BEV output would not match the region of the image that is responsible for its processing. Hence, the semantic masks are first outputted in the camera plane.

ResNet-101 [START_REF] He | Deep residual learning for image recognition[END_REF] is used as the encoder and Deeplab v3+ [START_REF] Chen | Encoder-decoder with atrous separable convolution for semantic image segmentation[END_REF] as the decoder. Deeplab v3+ combines A trou Spatial Pyramid Pooling (ASPP) [START_REF] He | Spatial pyramid pooling in deep convolutional networks for visual recognition[END_REF] and a convolutional decoder module to benefit from rich contextual information and better object boundaries delineation. Two decoding heads output the drivable area and vehicle semantic masks in camera view. The encoder-decoder network is applied t times where t is the number of images in the input sequence. The final step of this stage of the network is to warp the output masks in BEV using a perspective warping layer [START_REF] Riba | torchgeometry: when pytorch meets geometry[END_REF] with the homography matrix between the camera plane and the BEV plane. However, vehicles are 3D objects and projecting regular semantic masks in BEV leads to the "stretching" effect observed in Fig. 1. To cope with this deformation, we introduce the Flatmobile representation to warp the vehicles from camera view to BEV. This simple yet very effective representation consists in segmenting the footprint of the vehicles, i.e., the "ground" face of their 3D bounding boxes in camera view. By doing so, only pixels located on the ground surface (assumed to be locally flat) are segmented and warped in BEV which respects the planar world hypothesis required by the homography. The homography for each sample is obtained with a homography estimation network trained separately from the end-to-end network but on samples from the same training set, see Fig. 3. The output size of the decoding heads is s times smaller than the original camera image so the homography needs to be re-scaled as following:

H s = S • H • S -1 , with S =   s 0 0 0 s 0 0 1 0   , (2)
where H s is the re-scaled homography, H the original homography and s is the (fixed) scaling factor accounting for the ratio of image to decoder output size.

Cost function and learning:

We initially tried to make the most of ground-truth signals by computing two losses, one in the camera plane and the other one in the bird-eye view plane. However, we eventually train from the camera plane only, since the bird-eye view loss diverged. This is due to the fact that errors in the camera plane are amplified in the BEV plane. We chose to predict separately a binary OGM for the vehicles and another one for the drivable area, since our problem is best formalized as a multi-label classification problem rather than a multiclass classification problem. Indeed, each cell can belong to one of the four classes: {vehicle, drivable, vehicle and drivable, none}. The overall loss of this stage of the network, denoted L perception , is defined as the sum of two binary cross-entropy losses: one for the drivable area, and the other one for the vehicle occupancy.

Encoder-decoder LSTM for trajectory planning

Model formulation: The second stage of the network implements mid-to-end trajectory planning. The two sequences of drivable area and vehicle BEV masks are concatenated along the channel dimension at each time step and flattened to obtain a sequence of feature vectors f -τ , ..., f 0 . These feature vectors become input to an encoder-decoder LSTM [START_REF] Cho | Learning phrase representations using RNN encoder-decoder for statistical machine translation[END_REF]. The encoder embeds the sequence of feature vectors of length τ + 1 and processes it introducing the following recurrence:

e t = φ e (f t ; W e )
a t = φ a ((x t , y t ); W a )

h t = LST M (h t-1 , concat(e t , a t ); W l ) , (3)
where (x t , y t ) is the position of the ego vehicle at time t, φ e and φ a are the embedding functions, W e and W a are the embedding weights, h t and W l are respectively the hidden state and the weights of the encoder LSTM. The final cell state c 0 and hidden state h 0 of the encoder that summarizes the input OGM sequence are fed to the decoder as its initial cell and hidden states. The decoder then recursively outputs the sequence of future positions:

a t = φ a (s t-1 ; W a ) h t = LST M (h t-1 , a t ; W l ) s t = φ s (concat(h t , (r, α)); W s ) , (4)
where φ a and φ s are the embedding functions, W a and W s are the embedding weights, (c t , h t ) and W l are respectively the cell/hidden states and the weights of the decoder LSTM, s t the estimated future position at time t and (r, α) the polar coordinates of the destination point. The prediction of the future positions s 1:T is expressed in Cartesian coordinates, whereas the destination point is expressed in polar coordinates, for encouraging solutions that depart from a simple direct interpolation, thereby enhancing the impact of different design choices.

Cost function and learning: At each time-step during decoding (i.e., planning) time, the LSTM predicts the distribution of the future position of the ego vehicle as developed in (4). Similar to [START_REF] Alahi | Social lstm: Human trajectory prediction in crowded spaces[END_REF], the output s t of the encoder-decoder LSTM module predicts the parameters of a bi-variate Gaussian distribution characterized by its mean µ t = (µ x t , µ y t ) and its covariance matrix parameterized by the standard deviations σ t = (σ x t , σ y t ) and the correlation ρ t . The predicted position of the ego vehicle at time t is given by (x t , y t ) ∼ N (µ t , σ t , ρ t ). The parameters of the encoder-decoder LSTM module are learned by minimizing the negative log-likelihood of the Gaussian distribution:

L motion = - T t=1 log(P(x t , y t |µ t , σ t , ρ t )) . (5)
For the holistic end-to-end network, the final loss function is a linear combination of the perception loss and the motion loss:

L total = α L perception + L motion , (6)
where α is empirically set to 0.1.

Experimental evaluation 4.1. Evaluation metrics

The Average Displacement Error (ADE) corresponds to the average Euclidean distance between the predicted trajectory and the ground-truth one:

ADE = 1 N T N i=1 T t=1 Z t i -Z t i 2 ,
where N is the number of samples, T is the number of prediction timesteps, Z t i are the ith ground-truth coordinates at time step t and Z t i are their predictions. As the OGM prediction amounts to semantic segmentation, the classical Intersection over Union (IoU ) metric is also adopted.

Occupancy grid maps

Evaluation baselines The performance of the first stage, OGMs from a monocular camera, is evaluated against the following baselines:

• VED [START_REF] Lu | Monocular semantic occupancy grid mapping with convolutional variational encoderdecoder networks[END_REF]: Multi-task training led to poor results so this model was trained to output the vehicles and drivable area OGMs separately.

• OFT [START_REF] Roddick | Orthographic feature transform for monocular 3d object detection[END_REF]: this model was trained with a binary crossentropy loss to solely output the occupancy grid maps.

• BEV-LiDAR: The available LiDAR point clouds were processed to obtain BEV 3-channels images that encode the distance to the LiDAR, the height and the intensity. A Deeplab v3+ was then trained to take these images as input and output the vehicles and drivable area OGMs.

Training setup In this evaluation, the models are compared on the whole preview dataset. The dataset is split into 77 training sequences (2982 frames) and 9 held-out testing sequences (358 frames). All networks are trained over 100 epochs with Stochastic Gradient Descent (SGD) and a batch size of 8, with learning rate of 10 -7 for OFT and 10 -3 for our network and VED. The grid in OFT is set to 100 × 55 (in meters) with resolution of 1m per pixel.

Quantitative results Results presented in Table 1 show that our network outperforms OFT net [START_REF] Roddick | Orthographic feature transform for monocular 3d object detection[END_REF] by 5.4% on the vehicle OGM and 2.5% on the drivable area OGM. The gain in performance comes from the better accuracy in close range with an increase of more than 50% on the drivable OGM and more than 25% on the vehicle OGM. However, OFT has a better performance in long range: since it predicts directly in BEV, it does not suffer from the increase in error due to the imprecision in warping. Also, compared to OFT, our training criterion gives a higher relative weight to closer objects. Indeed, since our network learns in camera view, where closer objects appear bigger, it has an incentive to being more accurate in close range. The same conclusions can be drawn from the comparison with VED [START_REF] Lu | Monocular semantic occupancy grid mapping with convolutional variational encoderdecoder networks[END_REF].

The BEV LiDAR baseline has a much better performance on the full OGM and in long range due to the 3D nature of the sensor but still falls behind our approach in close range. A better performance in close range seems to be appropriate when planning a short-term trajectory.

Qualitative results

Qualitative results for the first stage of the network are shown in Fig. 6. As our network operates only on planar surfaces, warping the vehicle masks from camera view to BEV does not cause the "stretching" that is observed in Fig. 1 when warping regular semantic masks without the knowledge of depth. Hence, our approach can distinguish two vehicles in front of each other by simply applying the connected components algorithm to the binary masks. Again, we observe that results in BEV are better in the lower part of the OGMs, which corresponds to the first meters in front of the camera.

Trajectory planning

Evaluation baselines The performance of the holistic two-stage end-to-end model with intermediate OGM outputs is compared against the following baseline models:

• LSTM E-D: Same architecture than the LSTM encoder-decoder described in Fig. 5, except that it takes only the past trajectory as input.

• End-to-end: This model takes a sequence of camera images as input, encodes it with a ResNet-101, flattens the feature maps and feeds the obtained sequence of feature vectors to the same encoder-decoder LSTM described in figure 5. This model is comparable to direct perception approaches like [START_REF] Pomerleau | Alvinn: An autonomous land vehicle in a neural network[END_REF][START_REF] Bojarski | End to end learning for self-driving cars[END_REF][START_REF] Codevilla | End-to-end driving via conditional imitation learning[END_REF] with the difference that it takes a sequence of images as input and leverages a LSTM model to process this temporal information.

• Mid-to-end: Similar to the end-to-end model, ex- cept that it takes as input a sequence of concatenated ground-truth drivable area and vehicle semantic masks. This model is comparable to mid-to-mid approaches like [START_REF] Bansal | Chauffeurnet: Learning to drive by imitating the best and synthesizing the worst[END_REF] or the privileged learner of [START_REF] Chen | Learning by cheating[END_REF].

Training setup All networks are trained using SGD with a batch size of 10 for 200 epochs. All results were obtained with a momentum of 0.9 and a learning rate of 10 -3 .

Quantitative results

The results for motion planning are presented in Table 2. The L1 norm of lateral and longitudinal displacements are presented in addition to the Average Displacement error (ADE) metric. The two-stage holistic network shows improvements on the three metrics over its regular end-to-end counterpart, mostly due to an improved accuracy in the longitudinal direction. Overall, the regular end-to-end network has the worst performance among the image-based tested networks, which confirms the intuition that the intermediate BEV representation is an asset for motion forecasting. The mid-to-end network is accurate in the longitudinal direction but falls behind the holistic network in the lateral direction. A possible explanation for this surprising fact is that, our network learning the OGMs from camera images in an end-to-end fashion, it may benefit from pieces of information contained in the natural images which help disambiguate some driving scenarios. In other frameworks, accurate smooth estimates of discrete quantities have already been shown to be more efficiently processed than the ground truths themselves [START_REF] Hinton | Distilling the knowledge in a neural network[END_REF]. Our continuous masks, which are quite accurate in close range and camera view, may thus convey more information for fitting the second stage of the network in critical areas. The importance of having access to a scene context is highlighted by the inferior results obtained by the LSTM E-D model.

Ablation study

We show the importance of some components of the approach introduced here with the degraded results that are presented in Table 2. Removing the past trajectory input is an important ablation to investigate the usefulness of the BEV when there is no prior about the past motion. An important gap in performance is observed between the holistic network that leverages BEV information to forecast motion and the end-to-end network with up to 17cm difference in short term longitudinal forecast, 7cm in long-term longitudinal forecast and 11 cm in long-term lateral forecast. The importance of the BEV is also highlighted by removing the perspective warping layer from the holistic network architecture and feeding the Camera-View (CV) features as input to the second stage. The BEV version of the holistic network achieves a much better longitudinal performance than its CV counterpart with an average gain of 18cm at a horizon of 0.5s and 13cm at a horizon of 2.5s. However it is surprising to observe that the regular end-toend network achieves a better performance than the holistic CV network. A possible explanation is that even if the RGB camera images are not optimal for motion forecasting, they still convey a better depth and perspective information than the camera-view semantic masks.

Conclusion

In this paper, a novel method to output bird-eye-view occupancy grid maps from a monocular camera is introduced, by leveraging 3D bounding boxes and a HD-map raster. This method is used to build a new monocular camera-based holistic end-to-end motion planning network. It takes as input a sequence of camera images and leverages the aforementioned bird-eye-view occupancy grid maps as an intermediate output. Compared to its regular end-to-end counterpart, our method is better at imitation driving and provides interpretable intermediate results. The benefit of embedding computer vision tools for the transformation from the camera view to the bird-eye-view intermediate representation is also highlighted in our ablation study. Though end-to-end driving may not be reliable enough to be used as a primary solution in autonomous vehicles, having such a cheap camera based processing could be useful as an extra component for redundancy into a more complex system.

Figure 4 :

 4 Figure 4: Two-stage network for end-to-end trajectory planning from a monocular camera with intermediate BEV OGM outputs. Better viewed in color.

Figure 5 :

 5 Figure 5: Encoder-decoder LSTM for trajectory planning. Better viewed in color.

Figure 6 :

 6 Figure 6: Bird-eye-view qualitative results for the first stage of the network. The blue part of the predicted masks corresponds to the limits of the camera's field of view. GT stands for Ground Truth. Better viewed in color.

Table 1 :

 1 OGMs evaluation by IoU (in %). Full refers to the whole OGMs, close focuses on a region of 50m ahead of the ego vehicle and 10m on each side, far on the region farther than 50m ahead of the ego vehicle.

			IoU drivable		IoU vehicles
		Camera	Bird-Eye	Camera	Bird-Eye
	Range	Full	Full Close Far	Full	Full Close Far
	VED [21]	NA	60.1 48.6 70.3	NA	48.9 47.1 50.0
	OFT [27]	NA	58.6 41.2 71.4	NA	60.0 54.6 55.9
	Ours	94.5	61.1 92.4 40.5	79.3	65.4 80.0 49.7
	BEV LiDAR	NA	86.5 68.5 90.9	NA	69.7 69.9 49.8

Table 2 :

 2 Average displacement errors and L1 norm (in meters) for lateral and longitudinal displacements. NP (No Past) refers to models that do not take the past trajectory as input; CV (Camera view) refers to a model where the predicted OGMs are not warped in BEV. Best results are shown in bold.

		ADE	L1 longitudinal	L1 lateral
		0.5s 1.5s 2.5s	0.5s 1.5s 2.5s	0.5s 1.5s 2.5s
	LSTM E-D	0.63 0.91 1.32	0.38 0.33 0.31	0.37 0.70 1.15
	End-to-end	0.54 0.84 1.21	0.32 0.34 0.28	0.34 0.61 1.04
	Mid-to-end	0.51 0.81 1.17	0.27 0.26 0.19	0.32 0.63 1.04
	Holistic end-to-end CV	0.65 0.95 1.26	0.45 0.45 0.33	0.31 0.64 1.05
	Holistic end-to-end (ours) 0.48 0.78 1.16	0.27 0.26 0.20	0.29 0.60 1.02
	End-to-end NP	0.78 1.04 1.40	0.64 0.52 0.42	0.30 0.68 1.14
	Mid-to-end NP	0.65 0.94 1.25	0.44 0.44 0.32	0.31 0.62 1.03
	Holistic end-to-end NP	0.66 0.94 1.26	0.47 0.46 0.35	0.30 0.61 1.03


Vladan Kuzmanović
email: vladankuzmanovic@yahoo.com

Conceptual Marketing In the Age of Interactive Consumer

Keywords: Paramarketing, Referral Marketing, Complex Product, Relationship Marketing, Conceptual Marketing, Industrial Marketing, Contextual Markets, Partnership Model

Marketing is a system, a value, a complex. Marketing is a behavioral, interpersonal, and cultural concept. The value of total marketing is the value of the exchange of signs, labels, recognition, identity, trends, time and comfort. Contextual markets are complexes that are remarketed or resold in different iterative contexts, and under different circumstances. Marketing brings to the market a holistic system, the whole complex not just a part or a process. Conceptual marketing deals with holistic entities. A context product is a marketing entity. The buyer also has the need for market reminiscences. The product complex includes the basic, extended, and external product. The second part of paper debate my new Partnership model. The project is an intermediation because it is the relationship between the equilibrated actors who are in the process of optimizing their positions. However, individuals are actors of a whole personality, one partner has a privileged position but in the long term the equilibrium is sustainable.

Introduction

Marketing is all in relation with marketing. Marketing are ancillary activities and para-activities. Cultural marketing, market art, concepts of markets, market habits market ambiences and market acts. [START_REF] Janssen | habits and changing preferences: Simulation of psychological factors affecting market dynamics[END_REF] At the beginning of the century, an interesting approach to freakonomics emerged [2] from all that it produced as a by-product of economics. Economics is the whole complex not only the focus, economics is at the very least a civilizational culture (economic behavioral culture), not just a social phenomenon, a set of social activities. [3][4][5] Furthermore, with the development of marketing, a whole series of marginal disciplines and marginal concepts emerged. Instead of a multidisciplinary managerial approach, transdisciplinary phenomena come forth, exempli gratia between market art and marketing art, or marketing concept and market concept, etc. Conceptual marketing in this case refers to much more than a marketing conceptit is a concept of marketing and namely conceptual marketing. By ''conceptual marketing'' we mean a conceptual act, or conceptual activity as a border category.

Once the price as a market activity is formed or tendered as a conceptual act it is by all mean market price. Price is a marketing concept not a factor. The price act refers to price as a conceptual, experimental value. Price is not a variable but a concept or attitude. An actor is a bidder or price creator, as a product. Price is a product. Price is a product on offer, price is a concept. In a series of non-artistic topics, an economic objects occur: brands, logos, labels, articles, commodities. [START_REF] Tian-Si | An Investigation into the Marketing Civilization[END_REF] The basis of pop art is the one of economic phenomenon -consumerism. Artecon is everything from mass design to high art. Forth on art becomes a design concept instead of expendable design.

Total marketing and complex product

Design and price are concepts of new border disciplinemarginal or boarder marketing. Non-market act, non-price mass distribution, mass distribution from nonmarketing to paramarketing activities, etc. Marketing is everything except what is not marketing. Non-marketing is marketing, where marketing is used as a relational phenomenon. As Baudrillard suggests [START_REF] Firat | Marketing in a postmodern world[END_REF], consumption is increasingly becoming a productive process, goal-oriented, and purposeful; furthermore, it requires that individuals be educated to carry out this process. In customizing oneself to (re)present marketable (self-)images, the consumer is interacting with other objects in the market to produce oneself, to purposefully position oneself. In this production process of the self-image(s) `the consumer also acts as the marketer of self, selecting to use and interact with different other products that fit and enhance the image to be cultivated in each situation. Paramarketing encompasses a whole range of para-marketing activities which do not constitute mainstream marketing yet are closely related to the marketing culture. [START_REF] Firat | Marketing in a postmodern world[END_REF] Paramarketing is a consumer-mediated activity and refers to the immediate experience of (co) lateral market experiences. Paramarketing is a set of para-activities. Para-marketing is a consumer-mediated activity, marketing itself is seen from the consumer's point of view as an object of offer. [START_REF] Firat | Marketing in a postmodern world[END_REF] Marketing's role in contemporary culture can best be understood by placing it into the system of exo/esomodernities. The market, and marketing as its institutionalized set of practices, has become a key institution of modern culture. Marketing does not create a concept / consumption, but a concept that is also an object of consumption.

Marketing is a system, a value, a complex. Marketing is a behavioral, interpersonal, and cultural concept. [START_REF] Tian-Si | An Investigation into the Marketing Civilization[END_REF] The value of total marketing is the value of the exchange of signs, labels, recognition, identity, trends, time and comfort. [START_REF] Baudrillard | Selected Writings[END_REF][8] Marketing consists of a set of brands, labels, logos, cultural patterns, communicative processes and interpersonal relationships. The complex product represents the overall marketing effect, not just the economic, segmental, targeted or lateral effects of marketing.

Total marketing is a set of activities related to a complex product and involves planning, creating, concepting, registering and reusing of product complex. Total marketing involves revaluation, interaction, enhancement of utility as a transfer in progressive marketing model.

Conceptual Marketing

Marketing itself can be a need, in addition to dealing with needs. Imediation of marketing for marketing as a subject of marketing, remarketing of market and wider, overall, social effect of marketing.

In addition to the basic goal -finding the need, marketing also generates other goals, which generally oriented to increasing customer convenience through a marketing environment and a set of referral values.

Total marketing includes basic, extended and referral marketing, which recalibrates conventional marketing by resetting the entire process as a new process offering. Classical marketing referral is about activity correction. The use of marketing as a form is represented through conceptual marketing: once realized, the marketing process becomes a form that can be sold, changed and offered. Contextual markets are complexes that are remarketed in different iterative contexts, and under different circumstances. Seller brings to the market a holistic system, the whole complex not just a part or process. Conceptual marketing deals with holistic entities. A context product is a marketing entity. Customer perception is a metanarrative. The buyer also has the need for market reminiscences. The product complex includes the basic, extended, and external product (Figure 1).

It seems that postmodernism is no longer a theory or a philosophical stance but a reality which impacts upon many facets of life in, specifically, Western societies. It is represented in world views which are increasingly becoming prominent, and also in the conditions, such as, hyperreality, fragmentation, decentring of the subject, reversal of production and consumption, paradoxical juxtaposition of opposites, and noncommitment to meta-narratives. [START_REF] Fırat | Marketing: culture institutionalized[END_REF] An external product is reffered to the position and interaction of the product in a marketing environment. The marketing environment is the practice of the customer to value non-economic phenomena / variables as economic, according to their market experience, habits, profile attitude or feelings.

The external product primarily involves a large number of paramarketing activities as consumer habits and behavioral processes.

Just few examples of hobby marketing activities, and the hippie marketing subculture. The phenomenon of fanacons began in the early 1970s in America. Antimarketing, anti-shopping, and a whole host of deviant three-way behaviors, originated in response to consumerist culture. [START_REF] Barksdale | Consumer attitudes toward marketing and consumerism[END_REF][11] [START_REF] Firat | Postmodernism and the marketing organization[END_REF] In some Western countries, buying is seen as a ritual, and more, as a cult, and the buying process itself is implemented as a performance, subversion, or sentimental act. The buyer is proactive or deactive, the buyer is not only delaying specific marketing messages or incentives. [START_REF]Consumerism[END_REF][14] Purpose-innovative consumers are an important market segment. [15][16] Para-shopping is activity of buying irrelevant, unnecessary and unwanted things, buying out of the mainstream, deliberately buying non-advertised goods, including superficial and collateral shopping, with a selection of less desirable and less important items as an act.

The concept of recreational shopper identity, a dimension of the consumer's selfconcept, is contrasted with simple shopping enjoyment, which has characterized most past research on recreational shopping. Recreational shopping enthusiasts are found to engage more extensively in a range of retail shopping behaviors, to spend more money shopping (i.e., they are not just browsers), and are more "multi-channel" than other shoppers. [START_REF] Bellenger | Profiling the recreational shopper[END_REF] A collected object becomes a reminder of the story of its acquisition. The object is, thus, a cue for recalling and retelling this story. The images that a collection conjures up may therefore be a part of the collector's personal history of times and places. Stewart calls these associations "souvenirs" (because of their metonymic authentication of the past) and distinguishes them from collections (which she contends involve only a metaphoric derivation of authenticity from the past). However, we consider personal history to be an inescapable part of collections. "it is as if the experience of possession could be transformed into the possession of experience". [START_REF] Reynolds | Traditional malls vs. factory outlets: comparing shopper typologies and implications for retail strategy[END_REF] Affiliate marketing takes place between the buyer and the seller, the result is a surefire effect, greater than expected, in deact or proact, irrational rationality, dynamic marketing relationship, a recognizable affect versus effect. The customer subjectively responds to objective influences. [START_REF] Guiry | Defining and measuring recreational shopper identity[END_REF] The buyer is creative, which means that he does not only respond formally to marketing stimuli. Objective influences always expect objective reactions, however reactions are subjective, behavioral. The solution to this is in subjective stimuli, in a one-to-one project marketing relationship.

Fanecon

Fanecon is a person who lives on very margings of marketing culture, collect labels, promos, business leaflets, brands and other marketing staff, and is passionate collector of market brands, pamphlets and generic products. He is multi obsessionist even an art lover, expert in brand history, unusual economic facts, rare currencies, company logos, economic eccentricities collector, marketing culture enthusiast who enjoys the abundance of propaganda material, or just is rapt with objects.

Fanecons have in some sense made a mark in marketing culture with the advent of hippie culture and consumerism branding and marketing expansion in the 70's. Fanecon binds to specific brand products or is experimenting with brands. Fanecon is a sub-cultural consumer. Fanecon is a consumer of the time market. And, why not, fanekon is a proactive consumer. [START_REF] Belk | Collecting in a consumer culture[END_REF] [START_REF] Kotler | From sales obsession to marketing effectiveness[END_REF] Brand culture refers to the cultural influences and implications of brands in two ways. First, we live in a branded world: brands infuse culture with meaning, and brand management exerts a profound influence on contemporary society. Brand culture represents one interdisciplinary framework for understanding how brands create value and meaning. Second, brand culture provides a third leg for brand theory in conjunction with brand identity and brand image, brand culture provides the necessary cultural, historical and political grounding to understand brands in context. Future consumer research on visual issues must acknowledge images' representational and rhetorical power both as cultural artefacts and as engaging and deceptive bearers of meaning, reflecting broad societal, cultural, and ideological codes. [START_REF] Beatty | Impulse buying: Modeling its precursors[END_REF][22] A brand community is a specialized bound community based on a structured set of social relations among admirers of a brand. Muniz [START_REF] Muniz | Brand community[END_REF] uses ethnographic and computer mediated environment data to explore the characteristics, processes, and particularities of three brand communities (those centered on Ford Bronco, Macintosh, and Saab). These brand communities exhibit three traditional markers of community: shared consciousness, rituals and traditions, and a sense of moral responsibility.

Economics is not a disciplinary approach, but a disciplinary fundability instead. Discipline is in this new order of things, a concept, not projection but output, effectuation. Instead of bijection, there is an inversion of concepts, instead of a variable concept -a concept variable. Price concept -concept price, design conceptconcept design, market concept -concept market, marketing conceptconceptual marketing, active concept -concept activity. Conceptual marketing consists of concepts that are not aspects but economic projects; each discipline is a concept or project -behavioral, psychological, cultural, communicative, etc. [START_REF] Schroeder | Brand Culture: Trade marks, marketing and consumption[END_REF]

Project as an exchange process

The activities of the individuals should be summarized as a project. Marketing is an active project. Marketing is ultimately conceived as an economic project toward everything. Marketing is an economic project. The firm is understood as a set of individual activities. After all, is marketing an individual activity? If it wants to determine responsibility, if it wants to accomplish a task, set goals that an actor of a certain system should accomplish. The set goals are not projections (as in the classical scheme) but projects. This means that activities are viewed by individuals as their own capabilities, they do not mediate them but rather recognize them.

Activities are an internal set of goals and activities effectuate individuals. In a firm, activity is understood as a project, and the individual is motivated to accomplish the task. If he accomplishes the task, he is realized not only as an employee, but also as a personality. Personality has far greater potential than non-personality, employee. The projection does not go from operator to operator (or function holder to function holder) in delegating responsibilities, but from individual to individual and from project to project (as in a dynamic set). The organization consists not of a set of projections but a set of bijections, the company is based on the integrity of mutual projects. Project of one individual is project of another individual. Thus relationships are structured, but there are no basic problems in project marketing: detraction, demotivation, abuse, isolation, formalism, pressure, deception. The problem of efficiency arises as a result of psychological factors. The individual does not subsequently activate for the benefit of the company because the firm does not see them as an individual but as a operator. Individuals are driven by economic motives. The problem is that motives are in conflict with organizational goals; individual motives are in discrepancy with economic principles; employee perceives principles as something that in opposition to his own motives and wants. In empirics, there is a tacit collision of individual motives and economic goals.

In the firm, there is a diseconomy between individual and general goals. The overall goals are latent projections. The economy is plagued by the problem of economic communication. Therefore it proved necessary to grasp form as content, there is a formal tension that leads to a further decline in efficiency. Economic individuals are frustrated and just formally functional.

Psychological marketing is a powerful tool in the cases of formal tension. Organizational output is a synergy of individual activities. First of all, consumers are seen as internal customers. In the concept of individual marketing, employees are seen as internal customers and external customers as customers. The relationship of the project organization is externalized, the relationship is purely individual, direct communication between individuals as system actors. Economic interaction is individual. The project that engages the employee also realizes the customer. As postpurchase activity, satisfaction is a firm-employee-customer relationship. The firm is formed from a triple customer-employee-firm relationship, and effectiveness is understood as a fine outcome. In marketing, goals are aligned, safisfaction is interactive and mutual. If there is no win-win option in the long term, a weakening, dissatisfaction with relationships, loss of loyalty, and a decline in efficiency. Relationships are a win-win economic option. An actor relationship of actors is a partner relationship. So a project is a relationship between two or more economic partners, as economic agents of a particular activity; there must be fine-tuning between economic partners, finally the relationship is an exchange. [START_REF] Cox | Consumerism and Marketing Management: How do consumers perceive consumerism… and what are the implications of these perceptions for marketing managers?[END_REF] Staff unit managers in a range of disciplines who want to better serve internal publics can effectively market their services internally by understanding and responding to internal decision processes and expectations.

The terms ''internal relationship marketing'', ''internal relationship management'', or ''internal social process management'' are proposed as a development of other terms used by the writers discussed. These new terms recognise the applicability of the marketing concept through the identification of (intra-organisational) exchanges in working relationships and between the organisation and its customers, since ''all employees are customers of managers who wish to carry out the firm's objectives''. [START_REF] Cox | Consumerism and Marketing Management: How do consumers perceive consumerism… and what are the implications of these perceptions for marketing managers?[END_REF] Internal marketing is . . . an important activity in developing a customer-focused organisation . . . Fundamental aims of internal marketing are to develop internal and external customer awareness and remove functional barriers to organisational effectiveness.

From this conceptual review, a number of themes have been identified as offering a contribution to the development of a more sophisticated and valuable conception of internal marketing. These themes are:

. marketing-oriented service employee management;

. marketing as exchange;

. organisation as a ''domesticated'' (internal) market;

. internal marketing as a social process;

. a relational perspective on communication;

. internal marketing as a new form of industrial relations. [START_REF] Muniz | Brand community[END_REF] The consumer is part of the company, the customer is on both sides. The goal is not one-sided customer satisfaction, but mutual satisfaction. Marketer dissatisfaction may reflect on customer satisfaction in subsequent iterations of purchase, in the long run. The marketer, on the other hand, can pass the dissatisfaction on to the buyer. This broadened theory of internal marketing may be further elaborated on as a goaloriented social process, and a conceptual system for continually creating rapid strategic organisational change in response to the macro-environment (society) and the micro-environment. [START_REF] Muniz | Brand community[END_REF] All employees are sellers of satisfaction services. [START_REF] Harrell | Internal marketing of a service[END_REF] The relationship that is valid in the company is also the relationship outside the firm, towards third parties. [START_REF] Varey | A broadened conception of internal marketing[END_REF] Relationship in the company and the relationship outside the company is an exchange, a project, a customer is a part of the company in the long run. [START_REF] Harrell | Internal marketing of a service[END_REF] Each customer is an investor in the company. The relationship is immediate and psychologically profiled. The relationship between buyer and seller is first and foremost an intermediation. In the mediation, the customer expresses his needs directly. Due to the fact that the needs are irregular, the relationship is immediate. Immediate relationship arises from the immediation of needs (Figure 2). Furthermore, economic relationship is an exchange, this can only be answered by an immediate response, immediate satisfaction as a service, at the customer's request. Immediate service is an answer to an immediate need. The relationship consists of at least two requests and two answers. In the model outlined here, the economic relationship is the exchange of requests and answers (satisfaction).

Relationship-project is an exchange of immediate requirements and immediate safisfaction. A project is an economic transaction, a relationship is an economic, interactive dynamic transfer between partners as actors. The project is an intermediation because it is the relationship between the equilibrated actors who are in the process of optimizing their positions. The economic act is not isolated outside the project and is understood as a process. Sales are a set of acts that are not isolated but create a system of immediate consumption. In terms of satisfaction both actors have identical starting positions. However, individuals are actors of a whole personality, one partner has a privileged position but in the long term the equilibrium is sustainable.

Optimization is achieved in a series of individual equilibriums, transfers of fair satisfaction. The economic effect of partner transfer is greater because of synergy, greater mutual benefit, and intersatisfaction (in addition to intrasatisfaction of classical exchange). Positions are promoted and aligned with iterative acts with the need for an optimal position. Optimization is achieved only when both actors maximize their satisfaction. Satisfaction is an exchange of economic type. Thus, it is only at the optimal equilibrium, that satisfaction is maximized. The actors are looking through a set of harmonized experiences for the most favorable mutual position, as a project. With the partnership being actively mildly asymmetrical. One partner has bigger requirements, while the other one meets the requirements. However, both are aware of long-term mutual satisfaction in terms of positive addiction. A partnership is not a monopoly but a loyalty. Conditionality and dependence are not possible in a substantive and decisive way in a project. Conditionalities are dynamic incentives and mutual partner dependency is a flexible mechanism. [START_REF]Inside marketing: Practices, ideologies, devices[END_REF] [START_REF] Sweeney | Marketing: management technology or social process[END_REF] Long-run equilibrium curve, and the individual satisfaction curve oscillates around the long-run economic equilibrium curve. One partner has a privileged position (slightly greater satisfaction than the other partner's safisfaction; more satisfaction with it). In the next iteration, the satisfaction is equalized, equilibrated, a new disquilibrium in a more favorable position brings the partner who satisfied the other partner in the previous transfer. [START_REF] Campbell | Do customer partnerships improve new product success rates?[END_REF] [START_REF] George | Internal marketing and organizational behavior: A partnership in developing customer-conscious employees at every level[END_REF] An economic equilibrium, a transfer relationship, makes a set of mutual concessions and benefits. The long-term satisfaction curve tilts slightly in favor of one of the partners, in an asymmetric equilibrium situation characterized by iterative transfers. Aggregately, a set of win-win situations is made up of sub-sets of frequent win-win, win-lose and lose-win market affiliate transfers. The relationship is a tuning set. Transfer is a process of matching needs. The project is interaction. With both parties actively engaged. Customers actively participate in the satisfaction process, they are being progressively complied with. The satisfaction process is dynamic. Satisfactions are short-term, benefits are long-term. Satisfactions are short-term and renewable, thus their equilibrium is long-term. i) satisfaction is exchange, that is, transfer. In order to achieve a transfer between actors, ii) safisfaction is an active interaction because it pleads for a long-term effect. The project involves the active interaction of partners, the classic consumption of actors involves only one actor who is: passive, privileged, non-engaged, non-interactive and unproductive; however, transfer is a production, versus a projection of short-term transfer (satisfaction), the long-term benefit of transfer is valid.

Current competitive pressures require organizations to adopt a higher degree of market orientation for their projects and to build and maintain strong relationships with their stakeholders, customers, financial and political backers, and the general public. [START_REF] Martin | The Planetree model hospital project: An example of the patient as partner[END_REF][33] [START_REF] Kotler | Broadening the concept of marketing[END_REF] Project participants need to identify, anticipate, and satisfy customer requirements and to satisfy customers' needs through a process of exchange. [START_REF] Odekerken-Schröder | Strengthening outcomes of retailer-consumer relationships: The dual impact of relationship marketing tactics and consumer personality[END_REF][36]

The partnership model

Participants in the process do not act as actors but as partners, aiming to secure the partner's win position not only their own win, in the long term. In the relationship model, satisfation is derived and reciprocal. The transfer model explicates about immediate and altruistic, mutual benefit. Both partners will achieve the long-term goal only after two iterations have been completed. After the buyer's safisfaction has been achieved, which has resulted in the seller's safisfaction. Repeated purchase and repeated satisfaction, repeated purchase is the result of a project relationship, that is, customer satisfaction that has led to seller satisfaction.

The thing about interactive consumption is that the saturation is not repeated but increased. The thing about satisfaction is that once achieved satisfaction wants to be repeated, however, repeated satisfaction does not contain the same level of satisfaction as the previous one, but diminished. Repeated consumption is effected at a lower level of satisfaction due to the effects of the principle of saturation. Expected satisfaction is not a real satisfaction either, due to the fact that satisfaction is relative rather than absolute. Satisfaction is the degressing absolute satisfaction of the consumption process. However, real satisfaction is a progressive relative contentvariable of the interactive process (Figure 3).

Expected satisfaction is a progressive variable of the interactive process. Economic transfer is a relationship in which the exchange of satisfaction takes place between the two actors involved in the process. Process is a relationship of mutual satisfaction. Increasing satisfaction is positively correlated with increasing utility.

An interactive relationship is a transfer of progressive satisfaction. The involvement of both partners ensures a positive long-term relationship. The relationship on its part is a progressive, reciprocal relationship. The project relationship is about: customer benefit, customer-customer relationship, communicative transfer, expected real satisfaction, interactive benefit, partners as economic actors, fine tuning, maximizing individual satisfaction, (slightly) asymmetric partnership, coming through a series of iterative transfers to the long-term equilibrium of optimal individual preferences (See Figure 4). [START_REF] Odekerken-Schröder | Strengthening outcomes of retailer-consumer relationships: The dual impact of relationship marketing tactics and consumer personality[END_REF] Preferences are exchanges between satisfaction, pursuit of privileged positions, increased positive economic effects, in this case two-sided benefits as a long-term relationship, privileged benefits, exchange of privileged positions, if the parities are asymmetrical they are iteratively exchanged through a set of iterative pursuits, to optimal position-long-term equilibria. Profitably targeted as a long-term variable, the long-term benefit derives from the relationship of maximizing the individual satisfaction of actors in the process. The project is not a classic buyer-seller relationship. The projecter is an active stakeholder relationship in the exchange process. [START_REF] George | Internal marketing and organizational behavior: A partnership in developing customer-conscious employees at every level[END_REF][36] [START_REF] Lecoeuvre | Project Marketing By Three Organizations: Marketing By, For, And Of The Project[END_REF] Employees are actors, as well as customers. A firm is a structure consisting of a group of economic actors in the transfer process. Interactive transfer is a positive effect, which means that it provides progressive benefit / satisfaction. Economic transfer (firm) is characterized by communication and participation. The firm is the relationship of all partners in the process. [START_REF] Franco | Customer satisfaction: the partnership imperative[END_REF][40]

Conclusion

Expected satisfaction is a progressive variable of the interactive process. Economic transfer is a relationship in which the exchange of satisfaction takes place between the two actors involved in the process. Process is a relationship of mutual satisfaction. Thus, it is only at the optimal equilibrium, that satisfaction is maximized. The actors are looking through a set of harmonized experiences for the most favorable mutual position, as a project.

With the partnership being actively mildly asymmetrical, one partner has bigger requirements, while the other one meets the requirements. However, both are aware of long-term mutual satisfaction in terms of positive addiction. A partnership is not a monopoly but a loyalty. Conditionality and dependence are not possible in a substantive and decisive way in a project.

Conditionalities are dynamic incentives and mutual partner dependency is a flexible mechanism.

Figure 1 .

 1 Figure 1. Product Complex consisting of basic, extended and external product.

Figure 2 .

 2 Figure 2. Internal Marketing mindset.

Figure 3 .

 3 Figure 3. General Partnership Model

Figure 4 .

 4 Figure 4. Partnership model with optimal traits and motivational forces.

Submitted to Management, page 21-33 www.itspoa.com/journal/mana

Acknowledgments

The Author wish to thanks the Editor of the Journal and Colleagues for Helpful comments.

Conflicts of Interest Copyright

The author declare that there is no conflict of interest regarding the publication of this article.