Matthieu Zins
email: matthieu.zins@inria.frgilles.simon@loria.frmarie-odile.berger@inria.fr

Gilles Simon

Marie-Odile Berger

3D-Aware Ellipse Prediction for Object-Based Camera Pose Estimation

In this paper, we propose a method for coarse camera pose computation which is robust to viewing conditions and does not require a detailed model of the scene. This method meets the growing need of easy deployment of robotics or augmented reality applications in any environments, especially those for which no accurate 3D model nor huge amount of ground truth data are available. It exploits the ability of deep learning techniques to reliably detect objects regardless of viewing conditions. Previous works have also shown that abstracting the geometry of a scene of objects by an ellipsoid cloud allows to compute the camera pose accurately enough for various application needs. Though promising, these approaches use the ellipses fitted to the detection bounding boxes as an approximation of the imaged objects. In this paper, we go one step further and propose a learning-based method which detects improved elliptic approximations of objects which are coherent with the 3D ellipsoid in terms of perspective projection. Experiments prove that the accuracy of the computed pose significantly increases thanks to our method and is more robust to the variability of the boundaries of the detection boxes. This is achieved with very little effort in terms of training data acquisition -a few hundred calibrated images of which only three need manual object annotation. Code and models are released at https://github.com/zinsmatt/ 3D-Aware-Ellipses-for-Visual-Localization.

Introduction

In the last few years, deep learning has invested all the fields of computer vision. That of visual localization has not escaped this wave, but the specific nature of this problem has led to it being approached from a wide variety of angles. On one side, convolutional neural networks (CNNs) have been trained to detect visual beacons independently of the camera viewpoint and environmental conditions [START_REF] Crivellaro | A Novel Representation of Parts for Accurate 3D Object Detection and Tracking in Monocular Images[END_REF][START_REF] Oberweger | Making Deep Heatmaps Robust to Partial Occlusions for 3D Object Pose Estimation[END_REF][START_REF] Tekin | Real-Time Seamless Single Shot 6D Object Pose Prediction[END_REF]. These methods require an accurate geometric model of the scene for both training and actual pose computation, e.g. by PnP [START_REF] Lepetit | EPnP: An Accurate O(n) Solution to the PnP Problem[END_REF]. At the opposite side of the spectrum, the six pose parameters are directly obtained from end-to-end CNN regression, thanks to prior training on data associating images with ground truth poses [START_REF] Kendall | Posenet: A convolutional network for real-time 6-dof camera relocalization[END_REF][START_REF] Kendall | Modelling uncertainty in deep learning for camera relocalization[END_REF][START_REF] Melekhov | Imagebased localization using hourglass networks[END_REF]. Intermediate or alternative approaches have also emerged, making more or less intensive use of geometric models [START_REF] Kendall | Geometric loss functions for camera pose regression with deep learning[END_REF][START_REF] Sundermeyer | Implicit 3D Orientation Learning for 6D Object Detection from RGB Images[END_REF][START_REF] Xiang | PoseCNN: A Convolutional Neural Network for 6D Object Pose Estimation in Cluttered Scenes[END_REF].

While model-free methods perform poorly when computing the pose for images distant from the training data [START_REF] Sattler | Understanding the limitations of cnn-based absolute camera pose regression[END_REF], obtaining an accurate geometric model of a multiobject scene can be challenging especially when specular or textured-less objects are considered.

In this paper, we propose a method for coarse pose computation which is robust to large changes in motion and environmental conditions and does not require a detailed model of the scene. This method meets the growing need of easy deployment of robotics or augmented reality applications in any environments, especially those for which no accurate model nor huge amount of ground truth data are available. Our method builds on [START_REF] Gaudillière | Camera Relocalization with Ellipsoidal Abstraction of Objects[END_REF][START_REF] Gaudillière | Perspective-2-Ellipsoid: Bridging the Gap Between Object Detections and 6-DoF Camera Pose[END_REF] where a model-based method which operates at the level of objects is proposed. Considering objects as features for pose computation allows us to take advantage of the performance of recognition systems, especially their good invariance to pose and environmental condition changes, while not necessitating systematic retraining of the system when a new scene is considered. In [START_REF] Gaudillière | Camera Relocalization with Ellipsoidal Abstraction of Objects[END_REF][START_REF] Gaudillière | Perspective-2-Ellipsoid: Bridging the Gap Between Object Detections and 6-DoF Camera Pose[END_REF], pose is computed from 2D/3D object correspondences with 2D objects detected by any object detection algorithm such as YOLO [START_REF] Redmon | YOLO9000: better, faster, stronger[END_REF]. Approximating 2D objects with ellipses and 3D objects with ellipsoids allowed the authors to obtain direct solutions for pose computation without initial guess (Fig. 1).

Though the method is very promising, the main source of inaccuracy originates from a poor approximation of objects with an ellipse aligned with the image axes and inscribed in the detection bounding box (BB). In this paper, we go one step further and propose a learning-based method which detects improved elliptic approximations of objects which are coherent with the 3D ellipsoid i.e. that are likely to be the projection of the ellipsoid. This way of detecting elliptic abstractions of objects significantly improves the accuracy of the recovered pose. Our main contributions are as follows:

• A network for predicting ellipses around objects that are coherent with their 3D ellipsoidal abstractions. Its goal is to overcome the weaknesses of directly fitting the ellipses to the axis-aligned BBs. We propose a data augmentation procedure that allows for robustness to box boundaries variability. We also show that, even if the box boundaries contain a part of background that might be learnt by the network, our method is almost unaffected in typical scenarios, where the scene does not change between training and testing.

• We show how the concept of ellipsoidal abstractions of objects and 3D-coherent ellipse predictions can be used for robust pose computation when only a small amount of data is available on the scene. We show that the pose accuracy little depends on the choice of this ellipsoidal abstraction, which makes the method flexible and easy to use in practice. Only three calibrated images need to be annotated by hand to build the ellipsoid cloud. Annotations of the object are then obtained by projection in the training images.

Experiments prove that the accuracy of the computed pose dramatically increases thanks to our 3D-aware ellipse detection procedure and is close to the accuracy obtained with learning-based methods that require an accurate 3D model for training.

Background and related works

Pose computation from monocular RGB images is an important problem in computer vision which witnessed a complete renaissance with the emergence of deep learning. Thanks to the ability of such methods to detect features across a wide range of viewpoints, largely independently from environmental conditions, this opens the way towards more robust localization and matching methods, especially able to handle few-textured scenes.

One of the pioneering method in the use of deep learning for pose computation is poseNet [START_REF] Kendall | Posenet: A convolutional network for real-time 6-dof camera relocalization[END_REF] where absolute camera pose is regressed. Besides the difficulty of balancing rotation and translation errors in the cost function, a major default of such approaches, pointed out by Sattler [START_REF] Sattler | Understanding the limitations of cnn-based absolute camera pose regression[END_REF], is that direct pose regression is more closely related to pose approximation via image retrieval than to accurate pose estimation via 3D structure. As a result, such methods generalize poorly to trajectories far from the training sequences. Other methods propose to regress dense 3D scene coordinates [START_REF] Brachmann | Learning less is more -6d camera localization via 3d surface regression[END_REF][START_REF] Bui | Scene coordinate and correspondence learning for image-based localization[END_REF] and estimate the camera pose by solving a PnP problem. These methods were coupled with advanced versions of RANSAC [START_REF] Brachmann | DSAC -differentiable RANSAC for camera localization[END_REF] and obtain very good performance, but only on small-scale scenes.

In order to scale to large environments, [START_REF] Weinzaepfel | Visual localization by learning objects-of-interest dense match regression[END_REF] propose a method that relies on the detection on a set of objects of interest and exploits dense 2D/3D correspondences between them and reference images to estimate the pose. However, their method is limited to planar objects.

Finding the pose of the camera from general shape objects can also be viewed as estimating the objects pose in the camera frame. Many works exist on this subjects [START_REF] Kehl | SSD-6D: making rgb-based 3d detection and 6d pose estimation great again[END_REF][START_REF] Li | CDPN: coordinates-based disentangled pose network for real-time rgb-based 6-dof object pose estimation[END_REF][START_REF] Peng | Pvnet: Pixel-wise voting network for 6dof pose estimation[END_REF][START_REF] Rad | BB8: A scalable, accurate, robust to partial occlusion method for predicting the 3d poses of challenging objects without using depth[END_REF][START_REF] Sundermeyer | Implicit 3D Orientation Learning for 6D Object Detection from RGB Images[END_REF][START_REF] Tekin | Real-Time Seamless Single Shot 6D Object Pose Prediction[END_REF][START_REF] Zakharov | DPOD: 6d pose object detector and refiner[END_REF]. They usually assume to have access to a detailed model of the object in order to generate synthetic training data and, thereby enlarge the 6D pose space where pose can be correctly recovered. SSD-6D [START_REF] Kehl | SSD-6D: making rgb-based 3d detection and 6d pose estimation great again[END_REF] extends the idea of 2D object detection and infers 6D pose based on a discrete viewpoint classification while an autoencoder is used in [START_REF] Sundermeyer | Implicit 3D Orientation Learning for 6D Object Detection from RGB Images[END_REF] to recover the object orientation. Another way to infer object pose is by predicting the 2D projections of the corners of the bounding box of the 3D object with a CNN. This avoids the need for a meta-parameter to balance the position and orientation error since the 6D pose can be estimated with PnP from 2D/3D correspondences. In BB8 [START_REF] Rad | BB8: A scalable, accurate, robust to partial occlusion method for predicting the 3d poses of challenging objects without using depth[END_REF], segmentation is first performed to detect the objects and a CNN then infers the projection of the BBs. Data augmentation with a random background is performed during training to reduce the influence of the scene context. Building on YOLO and BB8, Tekin et al. [START_REF] Tekin | Real-Time Seamless Single Shot 6D Object Pose Prediction[END_REF] proposed a single-shot deep CNN architecture which directly predicts the 2D projections of the 3D BB vertices in the image.

The BB of detected objects can be also used for localization issues with the idea of decoupling the rotation and the translation. In PoseRBPF [START_REF] Deng | Poserbpf: A rao-blackwellized particle filter for6d object pose estimation[END_REF], and PoseCNN [START_REF] Xiang | PoseCNN: A Convolutional Neural Network for 6D Object Pose Estimation in Cluttered Scenes[END_REF] the translation is constrained to be along the vector from the camera center to the center of the BB. T z is then approximately determined from the ratio between 3D ROI and 2D BB sizes. An auto-encoder trained on the synthetic rendering of the 3D object is used for rotation estimation in PoseRBF, while PoseCNN regresses a quaternion for rotation and a mask, both with the need of an accurate model of the object. Without accurate knowledge of the objects, but under some assumptions on the scene, e.g. objects lying on a flat scene, Li et al. [START_REF] Li | Context-coherent scenes of objects for camera pose estimation[END_REF] used object detections to estimate relative camera poses for viewpoints changes. Wang et al. [START_REF] Wang | Normalized object coordinate space for categorylevel 6d object pose and size estimation[END_REF] proposed a category-level approach to predict normalized objects coor-dinates without the need of detailed 3D models. However, the method is not straightforward for new objects from unseen categories and depth information is needed to compute the pose. In the context of autonomous driving, [START_REF] Mousavian | 3d bounding box estimation using deep learning and geometry[END_REF] estimates the pose and the dimensions of an object's 3D BB from a 2D BB and the surrounding image pixels under additional constraints on the box orientation. However, modelling objects as 3D cuboids and the 2D detections by rectangles does not allow to derive closed-form solutions to projection equations and leads to solutions with a high combinatorics.

Modeling 2D/3D objects correspondences based on ellipses/ellipsoids was already used by [START_REF] Rubino | 3d object localisation from multi-view image detections[END_REF] in the context of multiview reconstruction and by Nicholson et al. in [START_REF] Nicholson | Quadricslam: Dual quadrics from object detections as landmarks in objectoriented slam[END_REF] in the context of SLAM. Resolution was based on the minimization of a geometric cost function over the six camera parameters, using odometry sensors for initial position and orientation. Recent works have proposed direct solutions without the need of initial prior for pose computation from ellipse-ellipsoid matches: [START_REF] Gaudillière | Camera Relocalization with Ellipsoidal Abstraction of Objects[END_REF] show that the problem of estimating the camera pose from ellipse-ellipsoid correspondences has at most 3 degrees of freedom, since the position can be obtained from its orientation. Direct closed form solution can thus be estimated once the orientation is known. In [START_REF] Gaudillière | Perspective-2-Ellipsoid: Bridging the Gap Between Object Detections and 6-DoF Camera Pose[END_REF], a direct method for full recovery of the pose from more than 2 ellipse-ellipsoid correspondences was proposed under assumptions satisfied by many robotics applications. In practical experiments, axis-aligned ellipses are inferred from the BBs detected by YOLO. The authors however note that such an elliptic 2D approximation is not always sufficiently accurate and may lead to a significant error on the estimated pose.

Instead of just detecting a rectangular BB of 2D objects, it is also possible to detect elliptic objects. An immediate idea is to perform instance segmentation, as in Mask R-CNN [START_REF] He | Mask R-CNN[END_REF] and directly fit an ellipse to the output mask. A recent work [START_REF] Dong | Ellipse r-cnn: Learning to infer elliptical object from clustering and occlusion[END_REF] shows that such a strategy fails to capture the ellipse orientation and proposes a CNN for ellipse regression. Such a work is typically dedicated to the detection of objects with elliptic shapes. Besides the fact that the detection is not aware of a particular 3D model, another difference with our work is that we are interested in detecting ellipsoids which approximate an object, whose shape may be quite different from a perfect ellipsoid.

System overview

Our method uses an ellipsoid cloud as a light scene model, where each ellipsoid approximates an object. The pose computation system consists of three main components (Fig. 2, bottom part). The first component is a CNN designed to detect objects as BBs. The second component is another CNN aimed at predicting, for each BB, the ellipse corresponding to the projection of the object's ellipsoid ac- cording to the camera pose. Unlike global approaches, such as PoseNet, which apply to the whole image, our prediction network uses local patches around each detected object. This has the advantage of restricting a lot the change of appearance and should enable our prediction network to better interpolate new views. Finally, the last component aims at calculating the pose from the ellipses thus obtained, the ellipsoid cloud and the labels associated with these features.

The object detection network takes as input an image and returns the BBs of the detected objects, with their class. Many networks have already been proposed to solve this task very efficiently [START_REF] Redmon | YOLO9000: better, faster, stronger[END_REF][START_REF] Ren | Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks[END_REF] and many types of objects are already recognized by these networks. It is, moreover, easy to fine-tune a pre-trained network in order to make it recognize new objects, as only a few images are required for that purpose. In order to preserve the aspect ratio of the detected object, the crop box is completed with the content of the image to meet the ellipse prediction network's input requirement. From these cropped images, the network predicts the ellipse parameters expressed in the BB frame. All the ellipses are then transferred to the initial image frame according to the coordinates of the BBs. The transferred ellipses, associated with the detection labels, are then used along with the ellipsoid cloud to compute the pose.

Pose computation from one or more ellipse-ellipsoid pairs is based on the work described in [START_REF] Gaudillière | Camera Relocalization with Ellipsoidal Abstraction of Objects[END_REF][START_REF] Gaudillière | Perspective-2-Ellipsoid: Bridging the Gap Between Object Detections and 6-DoF Camera Pose[END_REF]. The method used depends on whether or not external orientation data are available. Measuring camera orientation from image content or sensor acquisitions is generally easier to do than estimating the position. Indeed, position sensors are often inaccurate (GPS) or have a limited range and are sensitive to environmental disturbances (magnetic, acoustic sensors, etc.). By contrast, automatic vanishing point detection may lead to accurate orientation measures as long as the scene satisfies the Manhattan world assumption [START_REF] Gaudillière | Camera Relocalization with Ellipsoidal Abstraction of Objects[END_REF]. On the other hand, IMU sensors can be used, limiting drift and expressing orientations in an absolute reference frame by taking into account the Earth's magnetic field and gravity. A very interesting result from a practical point of view is that knowing the orientation of the camera, a closed form solution makes it possible to deduce its position from a single ellipse-ellipsoid pair [START_REF] Gaudillière | Camera Relocalization with Ellipsoidal Abstraction of Objects[END_REF]. If the orientation is available, we therefore use a RANSAC procedure with minimal sets of one ellipse-ellipsoid pair [START_REF] Gaudillière | Camera Relocalization with Ellipsoidal Abstraction of Objects[END_REF]. Multiple association hypotheses may occur in case objects of the same class appear in the image, but this only adds as many correspondences to be included in the RANSAC draws, preserving a linear algorithmic complexity. If orientation data is not available, two ellipse-ellipsoid pairs are at least required to compute the pose. We then use RANSAC with minimal sets of two correspondences [START_REF] Gaudillière | Perspective-2-Ellipsoid: Bridging the Gap Between Object Detections and 6-DoF Camera Pose[END_REF].

Ellipse prediction 4.1. Motivation for 3D supervision

We give here an intuition of why a 2D-only supervision is not sufficient for detecting good ellipses. Pose estimation from ellipse-ellipsoid pairs comes down to aligning cones, which means that the accuracy is heavily influenced by how much the ellipse detection satisfies the real projection of the ellipsoid. In Fig. 3, we simulated a "perfect" 2D detector by finding the minimum-area ellipse containing the object and reconstructed an ellipsoid from three views. We can observe that the 2D detections in other views are not fully coherent with the projection of this ellipsoid. In fact, the deformations caused by perspective, the viewpoints used for reconstruction and the shape of the object have a significant impact. This is why our method relies on 3D supervision and manages to be almost unaffected by these factors.

Ellipse parameterization

Different parameterizations of an ellipse can be used, among which the following were considered: (i) three points (center and two points corresponding to the axes ends), (ii) five parameters of the quadratic form matrix, (iii) center, axes lengths and orientation angle.

Using the five parameters of the quadratic form gives a minimal representation, because an ellipse has five degrees of freedom. However, these parameters have no physical interpretation which makes the associated L2 distance loss hard to optimize. Parameterizing an ellipse by three points has the advantage of having a real physical sense. The first point is chosen at the center of the ellipse and the other two points at the end of each axis. An inconvenient of this representation is that there is no implicit constraint to force orthogonality. Instead, we could choose to represent the ellipse with its center, axes lengths and orientation angle. Both parameterizations have ambiguities due to the ellipse symmetries. A canonical form can be obtained by enforcing the first axis to be the largest one, its endpoint to be in the right half-circle and the second axis endpoint to be in the bottom half-circle. Also, the angle is measured between the horizontal axis and the largest axis. This parameterization, however, implies discontinuities in the orientation angle when the ellipse is almost vertical. Moreover, L2 loss functions with non-normalized heterogeneous quantities are hard to optimize (e.g. the camera position and orientation parameters in PoseNet [START_REF] Kendall | Posenet: A convolutional network for real-time 6-dof camera relocalization[END_REF]) are hard to optimize.

To tackle these issues, we use the center, axes and orientation parameterization but with a classified, rather than regressed, orientation angle [START_REF] Mousavian | 3d bounding box estimation using deep learning and geometry[END_REF]. More specifically, this angle is discretized into n overlapping bins distributed between -π 2 and π 2 . Our network predicts the corresponding bin but also regresses a correction angle as a value added to the mid-angle of the predicted bin.

MultiBin Loss

The center and dimensions of the ellipse are both optimized using a L2 loss, respectively

L center = 1 N c gt -c pred 2 (1)
L dim = 1 N d gt -d pred 2 (2)
where c gt and c pred are the ground truth and predicted centers, d gt and d pred are the ground truth and predicted dimensions, and N is the number of images in the batch.

As proposed in [START_REF] Mousavian | 3d bounding box estimation using deep learning and geometry[END_REF], the angular part has been split into both classification and regression. We use a standard crossentropy loss for the classification part (L bin ) and a correction loss is added to reduce the difference between the predicted angle and the ground truth angle in each of the bins that overlaps with this angle (one or two bins).

L correction = - 1 n θ * n i o i • cos(θ * -σ i -∆θ i ) (3)
where θ * is the ground truth angle, n θ * is the number of bins that overlap the ground truth angle (1 or 2), o i is either 0 or 1 and indicates if bin i overlaps the ground truth angle, σ i is the mid-angle of the i-th bin and ∆θ i is the predicted correction angle that is applied to the mid-angle of the bin. This loss has effects only on the correction angles of the bins that actually overlap with the ground truth angle.

The final loss of our network is a weighted combination of each individual loss.

L = α(L center + L dim ) + (L bin + βL correction ) (4)
The parameters α and β are used to balance the loss intensities and were determined empirically. We used the same values for all experiments (respectively 0.01 and 1.0).

Network architecture

Our architecture (Fig. 4) includes a base convolutional network used for features extraction, followed by four parallel branches. We used a pre-trained VGG-19 network as base and just cut off the final softmax part, which is traditionnally used for classification. Then, the parallel branches take these features as input and consist of three-layers fully connected networks with ReLU as non-linear activations.

The center branch predicts two values corresponding to the center coordinates. The dimensions branch regresses the width and height of the ellipse. The bin branch predicts n values, where n is the number of bins. These values correspond to scores or confidences of belonging to a specific bin and are then passed to a softmax layer. Finally, the correction branch regresses 2n values, cos(∆θ i ) and sin(∆θ i ) for each bin. To get valid cosine and sine values, a normalization step was added at the end of this branch.

Network architecture validation

We validated our network architecture and loss function on synthetic data, consisting of multiple views of an object with the camera placed on a semi-sphere around it and random background from COCO dataset [START_REF] Lin | Microsoft COCO: common objects in context[END_REF]. We sampled 100 values of azimuth and 20 of elevation for training and test data were generated at intermediate positions. For evaluation, we computed the IoU between the predicted ellipse and the ground truth one. We obtained very high IoUs (more than 0.95) on the test images, keeping in mind that the viewpoints coverage of the training was quite large. Figure 5 also shows the advantage of the multibin strategy over the direct regression.

Data acquisition and augmentation

The only prerequisite for our system is that images of the scene have been acquired and calibrated from various viewpoints, i.e. we know for each training image the intrinsic parameters of the camera as well as its position and orientation in a global frame. This is the minimum prerequisite of any visual pose computation methods using deep learning. In practice, relatively few images are needed (around 200) both to fine-tune the detection network (if required) and to train the prediction network. Obtaining these data can be done in several ways, e.g. by using a differential GPS coupled with orientation sensors, a Structure-from-Motion (SFM) technique, or a marker [START_REF] Yang | WatchPose: A View-Aware Approach for Camera Pose Data Collection in Industrial Environments[END_REF].

3D model and training data generation

Once the calibrated images have been obtained, we propose a practical method to get both the ellipsoid cloud and the ground truth boxes and ellipses in all training images by just labeling a few boxes in a small number of them. It consists of the following steps (Fig. 2, top): (i) choose a minimum of three images of the scene showing the object(s) from various viewing angles, (ii) define boxes around the objects visible in these images (blue boxes Fig. 2, top) and associate a label to each box, (iii) fit ellipses to these boxes, with axes parallel to those of the boxes, (iv) build the ellipsoid cloud from the 2D ellipses and projection matrices; an analytic solution was obtained by Rubino et al. to solve this problem from only three calibrated views [START_REF] Rubino | 3d object localisation from multi-view image detections[END_REF], (v) reproject the ellipsoid cloud in all training images by using the ground truth projection matrices. The obtained ellipses (in red in Fig. 2) will be used as ground truth data for training the ellipse prediction CNN. (vi) If needed, the BBs of the projected ellipses (red boxes in Fig. 2) will be used as ground truth BBs to fine-tune the object detection CNN.

The ellipsoids obviously depend on the images chosen for reconstruction. Fortunately, we show in Section 6 that their size and orientation may vary significantly without degrading the method performance. This is due to the fact that the ellipsoids are only intermediate data used to calculate the pose from the detected ellipses, themselves predicted to match the perspective projection of the ellipsoids. The only critical point is that the ellipsoids used to generate the training data must be those used at runtime to compute the pose. Also, the internal calibration of the camera does not change between training and testing.

Data augmentation

Data augmentation plays an important role in the training of our prediction network and its generalization with a relatively limited number of annotated images. Several strategies were performed online (during training): (i) Color jittering randomly changes the brightness, contrast and saturation of an image in order to simulate illumination changes. (ii) Blurring filters the images with a randomly-sized Gaussian kernel in order to accommodate different resolutions caused by the object distance. (iii) Shifting randomly translates the images so that the object is not always perfectly centered, which should accommodate noisy object crops. (iv) In-plane rotations as well as (v) perspective deformations (homographies) were added to generate new views of the object. The last two can, for example, simulate a camera which is not held upright, or not aiming at the object center.

Experiments

Metrics

In our experiments, we used three common metrics: reprojection error (in pixels), ADD (as in [START_REF] Hinterstoisser | Model based training, detection and pose estimation of texture-less 3d objects in heavily cluttered scenes[END_REF][START_REF] Kehl | SSD-6D: making rgb-based 3d detection and 6d pose estimation great again[END_REF][START_REF] Rad | BB8: A scalable, accurate, robust to partial occlusion method for predicting the 3d poses of challenging objects without using depth[END_REF]) and camera pose error (either only the position or the full 6D pose). Unless otherwise specified, the percentages in the tables represent the proportion of test images that satisfy a certain threshold.

Camera position estimation

We evaluated the accuracy of the camera position estimated using our predicted ellipses on the LINEMOD dataset [START_REF] Hinterstoisser | Model based training, detection and pose estimation of texture-less 3d objects in heavily cluttered scenes[END_REF], which provides RGBD images of 15 objects in cluttered environments with ground truth pose. Note that we did not perform specific retraining for object detection in LINEMOD and T-LESS and used the 2D boxes given by the reprojected 3D object.

Using an initial ellipsoid, obtained by reconstruction from a few images, we generated ellipse annotations and trained our prediction network. We limit this experiment to the camera position because only one object can be used per sequence (the rest of the scene changes). Thus, the camera orientation is assumed to be known. To be realistic, we added a random noise uniformly sampled in [-2 • , 2 • ] on each of its Euler angle at test time. Figure 6 and Tables 1 and2 show the results obtained in terms of reprojection error, position error and ADD. The experiments show a significant improvement of the position estimation, compared to Gaudilliere et al. [START_REF] Gaudillière | Camera Relocalization with Ellipsoidal Abstraction of Objects[END_REF] (inscribed ellipse) and the obtained accuracies are comparable with Tekin et al. [START_REF] Tekin | Real-Time Seamless Single Shot 6D Object Pose Prediction[END_REF], a state-ofthe-art method trained using a detailed model of the object.

Full 6D pose estimation

We evaluated the performance of our method for the full 6D pose estimation on T-LESS [START_REF] Hodaň | An RGB-D dataset for 6D pose estimation of texture-less objects[END_REF], another RGBD dataset providing 20 scenes of texture-less objects. In each scene, a few objects are placed on a board and images are acquired with the camera placed on a semi-sphere of radius 75 cm. Compared to LINEMOD, several objects can be used in a scene, allowing us to recover the full 6D pose of the camera. We tested our method on a scene with 6 objects and 500 images, split in two halves for training and tests. We obtained the ellipsoid of each object directly from the CAD model and generated our training images. Table 3 shows the 6D-pose errors obtained with our method and compares Gaudilliere et. al. [START_REF] Gaudillière | Perspective-2-Ellipsoid: Bridging the Gap Between Object Detections and 6-DoF Camera Pose[END_REF] Ours Error in orientation (in degrees) it with Gaudilliere et al. [START_REF] Gaudillière | Perspective-2-Ellipsoid: Bridging the Gap Between Object Detections and 6-DoF Camera Pose[END_REF] (inscribed ellipses). This confirms the improvement made by our predicted ellipses, that was previously demonstrated on the position only.

6.4. Important points analysis

Robustness to detection noise

We show here that a major strength of our learning-based approach is its robustness to noisy object detections. As explained before, we use a two-step approach for detecting an object in the form of an ellipse. First, the object is detected with a 2D box, and then, this box is transformed into an oriented ellipse. The object detections step is not the focus of this work, but is nevertheless crucial. In the previous experiments, this step was completely simulated using a 2D box given by the projection of the 3D model. This is not totally realistic and, thus, we measured the influence of noisy objects detections on the pose estimation. On the one hand, it is easy to see that spatial noise on the BB has a direct impact on its inscribed ellipse. On the other hand, our decoupling between the box and the ellipse provides a much better robustness to variance in the detection (Fig. 7 and8). This is especially true for the objects marked with the arrows in Fig. 7. Even though the crop passed to the prediction network does not contain the whole object, the inferred ellipses are still correct. This robustness is mostly achieved thanks to our data augmentation which randomly shifts the image (equivalent to shifting the BB before cropping).

Influence of the reconstructed ellipsoid

In this experiment, we illustrate the influence of the ellipsoid chosen as approximation of the target object. For that, we used three different ellipsoids (Fig. 9). The first one (green) was obtained by reconstruction from five images, the second one (blue) by directly fitting to the CAD model and the third one (red) was the same ellipsoid manually stretched and rotated. The results, available in Table 4, are very similar, which indicates that the choice of ellipsoid has no real influence and thus, that the network is able to learn the projection of more-or-less any ellipsoid. This is an important point of our method, because this decoupling between the ellipse and the object box detection allows us to use, for example, only a sub-part of the object.

Comparison with instance segmentation

The previous experiments clearly show the superiority of our method compared to the axis-aligned ellipses. To get around this axes alignment problem, an alternative could be to fit an ellipse to a mask predicted by an instancesegmentation network. We chose Mask R-CNN [START_REF] He | Mask R-CNN[END_REF], which obtains state-of-the-art results for this task and fine-tuned it on the driller. Table 5 shows that the ellipses fitted to the predicted masks (Ell. Mask R-CNN) or even to the ground truth masks (Ell. GT masks) do not reach the same level of accuracy as our predicted ellipses. This confirms our intuition presented in section 4.1.

New scene configuration

We explain here how our method may adapt to new scene configurations, where some objects are moved between training and runtime, without the need to retrain the system. The underlying idea is to exploit the capabilities of the initially trained predictor to infer non axis-aligned ellipses which are then used to build the ellipsoid from a few images. By reconstructing the scene from these ellipses we should get ellipsoids close to the initial ones and thus avoid having to train the network again. This strategy has been tested on LINEMOD test images of the same sequence, in which the scene has been changed and the target object rotated. An "easy" (the ape) and a "hard" (the driller) objects were chosen in this experiment, depending on how much background is visible in the object crop and how much the object shape changes with a change of viewpoint. Table 6 shows that our method still outperforms the direct BB fitting for the easy object (ape) and reaches similar results for the hard ones (driller). Even if our approach of cropping the object allows us to be insensitive to most of the background, some of it is still visible in the crop. This shows a limit to our light 3D supervision. Having access to a 3D model (even an approximated one, but not just an ellipsoid) would enable us to be more independent to the background by generating random background during training.

Application on a real scenario

We demonstrate our full system on a real case using the WatchPose dataset [START_REF] Yang | WatchPose: A View-Aware Approach for Camera Pose Data Collection in Industrial Environments[END_REF], which provides pose annotated images of 10 objects in industrial environments. For each object, around 200 images are provided. Half of them were acquired "near" the object (around 60 cm) and the rest farther away (1.4 m). This dataset differs from the previous ones and is more representative of a real application. Indeed, the images were acquired with a hand-held smartphone without specific care about motion noise, reflections and shadows.

We follow the protocol explained in Section 5.1 to build the ellipsoids and generate the ellipse annotations. The BBs of the ellipses were used to fine-tune our object detection network whereas the ellipses were used to train our ellipse prediction network. Finally, the two trained networks are used to relocalize the camera on test images. We tested two scenarios: an easy one, where a subset of near and far images were used for training, and a hard one, where training was done only on near images and testing on far images. Our experiments show that our method is able to estimate the camera position with a median error around 3 cm in the easy case and 6.4 cm for the hard one. We compared our approach to Gaudilliere's method [START_REF] Gaudillière | Camera Relocalization with Ellipsoidal Abstraction of Objects[END_REF]. Our 3D-supervised method shows a significant improvement (see Tables 7,8 and Fig. 10). For comparison with a global method (where the network uses the whole image), we trained PoseNet [START_REF] Kendall | Posenet: A convolutional network for real-time 6-dof camera relocalization[END_REF] during 5000 epochs on the near images. While the mean position error obtained by testing also on near images was quite good (around 3 cm), the generalization to more distant images was not satisfactory at all (a mean position error of 80 cm on far images). This confirms that our learning on local object patches has a better generalization ability to handle new viewpoints.

Conclusion

In this paper, we proposed a method for object-based pose estimation which does not require an accurate model of the scene. Its main component is a new 3D-aware ellipse prediction network. By learning from different viewpoints, the network is able to map the object appearance to ellipse parameters which are coherent with the projection of the object ellipsoidal abstraction, and thus, improves the computed pose a lot. Three key aspects of the method are its robustness to variance in the box detection boundaries, its good invariance to the chosen ellipsoidal abstraction and its minimal amount of manual annotations required, making the method of large practical interest.

Figure 1 .

 1 Figure 1. Camera pose estimation from objects.

Figure 2 .

 2 Figure 2. Overview of our full system. The new ellipse prediction block is the key part of our work.

Figure 3 .

 3 Figure 3. Bottom: Images and detections used for reconstruction. Middle: Reconstructed ellipsoid. Top: Projection in new views.

Figure 4 .

 4 Figure 4. Ellipse prediction network.

Figure 5 .

 5 Figure 5. Left: Mean IoUs obtained on test images for an increasing number of training epochs. Right: Example of predicted ellipse (green). The ground truth ellipse is in red.

Figure 6 .

 6 Figure 6. Proportion of positions correctly estimated wrt. the error threshold (in cm) on the horizontal axis. Left: using the inscribed ellipse. Right: using the predicted ellipse.

Figure 7 .

 7 Figure 7. Inscribed ellipses (left) vs Predicted ellipses (right).Noisy BBs used for cropping and extracting the ellipses used for pose computation are in green. Ground truth projection of the ellipsoids are in red and ground truth objects BBs are in blue. Note that, despite noisy crops, the predicted ellipses fit much better to the ground truth projections.

Figure 8 .

 8 Figure 8. Influence of noisy BB detections. Left: Orientation error (in degrees). Right: Position error (in cm). Both horizontal axes represent the half-range of the noisy horiz. and vert. shifts applied on the 2 corners defining the BB.

Figure 9 .

 9 Figure 9. The three different ellipsoids used in our experiment.

Figure 10 .

 10 Figure 10. Predicted ellipses and ground truth projections of the ellipsoid in WatchPose.

Table 1 .

 1 Reprojection error.

		Tekin		Gaudilliere
	Method	et al.		et. al.	Ours
		[31]		[7]
	Thresh.	5 px	5 px 10 px 15 px 20 px	5 px 10 px 15 px
	ape	92.10	95.39 100.0 100.0 100.0	100.0 100.0 100.0
	cam	93.24	49.77 94.47 100.0 100.0	94.47 100.0 100.0
	can	97.44	57.60 79.26 98.62 100.0	99.54 100.0 100.0
	cat	97.41	68.20 98.62 100.0 100.0	90.32 100.0 100.0
	driller	79.41	16.13 61.75 90.32 98.62	96.77 100.0 100.0
	duck	94.65	89.40 100.0 100.0 100.0	100.0 100.0 100.0
	eggbox	90.33	97.70 100.0 100.0 100.0	100.0 100.0 100.0
	glue	96.53	54.38 88.02 95.85 99.54	94.93 99.08 100.0
	holepunc	92.86	83.41 100.0 100.0 100.0	99.54 100.0 100.0
	iron	82.94	17.05 51.15 78.34 93.09	90.78 99.54 100.0
	lamp	76.87	18.43 60.37 84.79 97.24	92.63 99.54 100.0
	phone	86.07	34.56 70.97 88.48 97.24	90.78 100.0 100.0
			Tekin	Gaudilliere
	Method		et al.	et al.	Ours
			[31]	[7]
	Threshold
	(% of diam.)	10%	10% 15% 25%	10% 15% 25%
	ape		21.62	18.43 35.94 56.68	64.98 80.65 93.09
	cam		36.57	34.10 56.68 84.33	47.47 69.12 87.56
	can		68.80	12.90 18.43 31.34	72.81 87.56 98.16
	cat		41.82	26.27 37.33 55.30	24.42 41.01 61.29
	driller		63.51	42.86 57.14 76.04	88.48 95.85 99.54
	duck		27.23	31.34 47.00 67.28	62.67 78.80 93.09
	eggbox		69.85	16.59 22.58 40.09	78.34 91.71 98.16
	glue		80.02	11.98 23.04 32.72	42.40 57.14 79.72
	holepunc		42.63	12.90 20.74 30.88	76.50 88.94 97.70
	iron		74.97	16.59 25.81 40.55	76.50 91.24 97.70
	lamp		71.11	23.04 35.48 58.99	84.79 94.47 97.24
	phone		74.74	22.12 29.03 42.86	64.98 82.03 96.31

Table 2 .

 2 ADD.

Table 3 .

 3 Median error and standard deviation of the orientation and position estimates.

Table 4 .

 4 Results obtained with different ellipsoids.

	Metric	Reprojection error	Position error	ADD
	Threshold	5 pixels error	5 cm	10% of diameter
	Ellipsoid 1	96.77	94.47	84.79
	Ellipsoid 2	96.77	94.93	84.33
	Ellipsoid 3	96.31	92.17	82.49

Table 5 .

 5 Comparison with an ellipse directly fitted to an object segmentation.

	Metric	Reprojection error 5 pixels	Position error 5cm	ADD 10% of diameter
	Ellipse	inscr.	pred.	inscr. pred.	inscr.	pred.
	ape	94.99	96.74	89.72 93.99	29.07	46.87
	driller	21.17	17.15	47.81 52.19	25.91	24.45

Table 6 .

 6 Comparison between the use of inscribed or predicted ellipses in case of a new scene configuration, without retraining.

Table 7 .

 7 Position error in the easy case.

	Method	Median error (in mm)	5 cm	Threshold 10 cm 15 cm	20 cm
	Gaudilliere et. al. [7]	84.11	27.87	57.38	77.05	83.61
	Ours	30.75	76.27	96.61	98.31	100
	Method	Median error (in mm)	5 cm	Threshold 10 cm 15 cm	20 cm
	Gaudilliere et. al.[7]	120.31	14.61	38.20	66.29	85.39
	Ours	63.90	34.01	75.00	90.91	96.59

Table 8 .

 8 Position error in the hard case.


The example developed throughout this second section builds on the 2000 Input-Output table for The Netherlands, available in the workbooks of Eurostat: http://epp.eurostat.ec.europa.eu/portal/page?_pageid=2474,54156821,2474_54764840&_dad=portal&_schem a=PORTAL 2 Since the columns represent the destination of inputs and the rows sum to total output of a sector, the matrix represents a national/regional approach to double entry bookkeeping; total input and output of a sector are equal to each other.

Note to the reader -How to use this material

This report has been designed as a hyperlinked pdf document.

The main text in the specification sheet synthesises the economic assessment method, its relation to systems approach and the appropriate use of the method. It also gives some hints on how to best present the results of your assessment to stakeholders, along with an example of the use of the method.

In the text and in the "further information" section, you will have access to links to the accompanying material available in the rest of the report (page numbers are also provided along the links in case you would like to print this report). A back button on the bottom of each page of supporting material helps you go back to the main text.

SPECIFICATION SHEET

Input-Output multipliers

Method and assumptions

Input-Output (I/O) multipliers can be used to assess the regional (or national) economic impacts from an activity. Multipliers are derived from an I/O table or matrix (either regional or re-scaled from a national one). Learn more on how multipliers can be derived here (p. 6-17). An I/O matrix is a representation of national or regional economic accounting that records the way industries both trade with one another and produce for consumption and investments. The flows of products and services are registered, simultaneously by origin and by destination. The use of I/O multipliers for economic impact assessment rests on the fact that the direct effects of spending for a service (e.g. tourism expenditure) are followed by indirect and induced effects. These two types of effects are observed respectively because purchasing links with other industries in the region exist and employees who work in the value chain spend their incomes on regional goods and services.

Relation to systems approach

Since it is commonly assumed that the impact estimates derived from I/O analysis represent activity within a single year, economic impact assessment is mostly used as a one shot assessment. Hence, the method is not especially well adapted to systems approach. I/O multipliers can however be assumed stable during a certain period after the initial calculation of the I/O table (typically up to 6 years), unless the region's economy has changed significantly. In a systems approach perspective, one can thus yield interesting results in terms of comparisons of scenario impacts (the different scenarios will make the components of the assessment vary), if one works with re initialization of the impact assessment each year.

When this method is especially to be used

The use of Input-Output multipliers is particularly suitable for the evaluation of regional services industries (e.g. tourism) and the impact assessment of broad policy instruments at the regional level. Economic impact analysis only helps answer the question "What is the contribution of an activity to the economy of the region?" (in terms of changes in income and employment in the region). To get a whole picture of the impacts of an economic activity, an environmental impact assessment, a cost benefit analysis or a multi-criteria analysis should be implemented as well.

How to best present results to stakeholders?

The results of an economic impact assessment should be presented and interpreted carefully. Advice should also be given to stakeholders to be cautious with respect to the use of the results.

While presenting the results to stakeholders, bear thus in mind the limitations of the method:

• Such an economic assessment only pertains to regional economic impacts and not to all the impacts of the studied activity (environmental, social or cultural).

• Income or value added are certainly the best measures of economic impact to report, compared to employment impacts. In the tourism sector, for instance, job impacts might be misleading because jobs in this sector are largely part-time and seasonal. Wages and salary rates vary as well across industries and this can make the multipliers vary accordingly.

• Working with Input-Output multipliers literally multiplies up the uncertainties regarding each step of the method: small errors in terms of estimation of the direct impact (expenses or output), of regionalization of the Input-Output matrix and of multipliers are added up and contribute to the uncertainty in the final results.

Some hints to answer those limitations:

• Even though it cannot be clearly measured, presenting the results in terms of ranges of values (rough confidence intervals) rather than a single figure can help to underline the inherent uncertainty of an economic impact analysis. A sensitivity analysis can also help.

• It might also be interesting to first present the direct effects in terms of spending or change in final demand (supposedly highlighted in the simulation model) and the multipliers; to then show the broader impact (including the indirect and induced effects) while explaining the differences and underlying uncertainties with respect to each step of the method. This will help shed light on the importance of broadening the perspective, away from considering the simple direct impacts of one measure. At the same time, it will provide a good picture of the assessment.

To conclude, bear in mind, at all times, the assumptions and limitations of Input-Output methodology while analyzing and using the results, do not oversimplify or misinterpret the results, use them with caution, since it might leave the stakeholders with a sometimes distorted or incomplete understanding of economic effects.

Example of use of the method

In the Firth of Clyde case study, the local stakeholders were interested in "the implications of increased leisure and tourist use of the Firth of Clyde", from the perspective of combining increased tourism trends with social, economic and environmental stability. The action to be valued was thus the increase in quantity of tourist facilities due to increasing leisure and tourism use (in particular for recreational boating activities but also for mussel farming which is not the focus here).

The change in number of tourists was assessed through several scenarios. Mean spending per boat per stay was estimated along with the average length of stay. The direct effects of the increase in tourism trends were captured by these estimates of visitor spending as they represent the amount of money brought into the region by tourists. In order to get a better estimate of the economic effects of increased recreational boating in the area i.e. evaluate the secondary effects of sailing expenditure in the Firth, output multipliers were used. The multipliers were scaled from Scottish national figures to Firth of Clyde level; however, no data were available to allow the figures to be scaled down further to be appropriate for the specific area. Key economic sectors that are mainly impacted by the recreational boating activities were identified; they represent relevant categories of spending: such as Recreational, cultural and sporting activities or Tourism (hotels, catering and pubs). The direct effects were then multiplied up to derive the total economic effects of spending and thus capture the secondary economic effects of tourism activity.

Further information

• To know more about another type of assessment method using Input-Output methodology (green I/O tables), click here (p. 17).

Most references and further reading below focus on tourism impact assessment.

• More detail on I/O multipliers methodology in tourism impact assessment can be found from the Department of Community, Agriculture, Recreation and Resource Studies at Michigan State University: http://web4.canr.msu.edu/mgm2/econ/index.htm, accessed 01/2011 • A more in depth description of economic impacts (mainly of tourism) and of assessment using I/O multipliers methodology can be found here (p. 18-21).

• Other (tourism) economic impact assessment methodologies are shortly described here (p. 22).

• A document on forecasting tourism demand (i.e. establishing how numbers of tourists will change in the future under different scenarios) can be found here (p. 23-25).

• The method for deriving multipliers from an I/O matrix is explained here (p. 6-17).

Basic principles of Input-Output methodology and calculation of Input-Output multipliers

An Input-output matrix (I-O) is a representation of national or regional economic accounting that records the way industries trade with one another and produce (flows of products and services). Those flows are registered in a matrix, simultaneously by origin and by destination (OECD, 2006). The matrix illustrates the relationship between producers and consumers as well as interdependencies of industries for a given year. It is important to note that I/O tables assume linear relations between inputs and outputs from different sectors as well as linear relations between outputs and final demand. This assumption is not always close to reality: it means that there are no economies or diseconomies of scale in production or factor substitution (double the level of production, you'll need to double all the inputs). Moreover, all firms in a given industry are assumed to employ the same production technology.

Another section called domestic investment matrix (in blue in Table 1), accounts for the supplies of goods that are not consumed by domestic industries. The columns therefore include such categories as final consumption (both by households and general government), gross fixed capital formation (investment) and exports. The initial monetary values in the transactions matrices can be converted into ratios called technical coefficients (Table 2). This is done by dividing each cell of the domestic intermediate matrix by its column total (output at basic prices).

Example, cont.

In the first column-third row, the technical coefficient is equal to 3322/21863 = 0.15. This coefficient shows the rate at which inputs are transformed into outputs. Here, 0.15 Euros manufactured products are purchased by Agriculture in order to produce 1 Euro of agricultural output.

These technical coefficients can be used directly to assess the added value of a given sector, calculate investments in this sector and, if the matrix is "greened"3 , determine the impact of this sector on the level of pollutant emitted. Agriculture, forestry and fishing 0,12 0,00 0,04 0,00 0,00 0,00 0,00 0,00 0,00 0,01 0,03 Mining 0,00 0,02 0,01 0,22 0,00 0,00 0,00 0,00 0,00 0,00 0,02 Manufactures 0,15 0,02 0,19 0,03 0,13 0,04 0,09 0,09 0,03 0,10 0,43 210900 Utilities 0,04 0,00 0,01 0,24 0,00 0,01 0,03 0,03 0,00 0,00 0,00 Construction 0,01 0,01 0,00 0,01 0,23 0,02 0,00 0,00 0,01 0,38 0,00 Services 0,13 0,09 0,13 0,08 0,16 0,25 0,64 0,63 0,96 0,19 0,21 435953 Imports 0,08 0,08 0,34 0,10 0,13 0,08 0,12 0,12 0,01 0,20 0,31 Net taxes on products 0,01 0,01 0,00 0,04 0,00 0,02 0,12 0,12 0,00 0,12 0,00 Total Use at purchaser's prices 0,55 0,23 0,73 0,71 0,66 0,41 1,00 1,00 1,00 1,00 1,00 Compensation of employees 0,11 0,04 0,17 0,09 0,24 0,35 Value Added at basic prices 0,45 0,77 0,27 0,29 0,34 0,59 Industry Output at basic prices 1,00 1,00 1,00 1,00 1,00 1,00

In order to finally calculate the output multipliers, one needs to derive Leontief inverse matrices.

The type I inverse matrix shows how much of each industry's output is needed, in terms of direct and indirect requirements to produce one unit of a given industry's output.

It is calculated using the formula:

L = (I-A) -1
Where L is the Leontief Inverse matrix I is the Identity matrix A is the Direct Requirements matrix (each cell of the domestic intermediate demand quadrant divided by its column total i.e. square matrix of technical coefficients)

Example, cont.

When the technical coefficients have been calculated (shaded area in Table 2), an identity matrix of the same dimensions as the so called direct requirements matrix needs to be constructed (in this case the dimension is 6*6, see Table 3). The A matrix then needs to be subtracted from identity matrix to produce the "I-A" matrix (Table 4). This "I-A" matrix must be inverted to construct the type I Leontief inverse matrix (Table 5). All these basic matrix calculations can easily be performed in spreadsheets (for instance in Excel 4 ) or in other programs.

Table 3. Identity matrix 6*6

1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1
Table 4. "I-A" matrix 0,875 0,000 -0,039 -0,002 -0,001 -0,001 0,000 0,977 -0,010 -0,218 -0,003 0,000 -0,152 -0,024 0,809 -0,026 -0,133 -0,039 -0,045 -0,004 -0,011 0,759 -0,001 -0,008 -0,006 -0,006 -0,003 -0,007 0,766 -0,022 -0,132 -0,088 -0,135 -0,077 -0,155 0,755 4 At least for a matrix of dimensions 52*52 in Excel. Agriculture, forestry and fishing 1,154 0,002 0,057 0,006 0,012 0,006 Mining 0,019 1,026 0,018 0,296 0,009 0,005 Manufactures 0,235 0,039 1,261 0,065 0,234 0,073 Utilities 0,075 0,008 0,025 1,322 0,010 0,016 Construction 0,017 0,012 0,012 0,021 1,316 0,039 Services 0,257 0,130 0,242 0,186 0,316 1,349

The type II inverse matrix also shows the induced requirements (in terms of industry's output) of a production of one unit of a given industry's output. Its purpose is to take into account, besides the direct and indirect requirements included in the type I inverse matrix, the flows of money in and out of households and the effect of these flows on industries.

The type II inverse matrix is derived in the same way as the type I inverse matrix. But since it is necessary to include households in the analysis we treat them as an additional industry by adding an extra row and column into the Direct Requirements matrix for "compensation of employees" and "final consumption expenditure by households" coefficients respectively.

The formal notation for this Direct Requirements matrix is:

A = A A A A II IH ⎡ ⎢ ⎤ ⎥ HI HH

⎣ ⎦

Where (A II ) ij is the Direct Requirements matrix A, or the amount of industry i required per unit of industry j (considered above in the type I inverse matrix).

(A IH ) i is the amount of industry i required per unit of total household income from all sources (see note below).

(A HI ) j is the income paid to households per unit of output of industry i (compensation of employees divided by the total output of the industry).

(A HH ) is the household expenditure per unit of exogenous household income. (This cell is set to zero).

Total household income from all sources is used as the denominator when calculating household expenditure coefficients (A IH ) even though it may at first seem odd not to use the total household expenditure figure from the I-O tables (in the example below called Total use at purchasers' prices). However, the total figure of household expenditure from the I-O tables includes household purchases that are bought with unearned income (pensions, dividends, etc).

In other words, not all household expenditure results from 'Income from employment' paid to households. If the Total use at purchasers' prices figure were used as the denominator, the sum of A IH would equal 1 and the resulting type II Leontief would tend to overestimate the induced effects of changes in the economy by artificially inflating the effect of earned income in generating further rounds of household spending.

Example, cont.

Centraal Bureau voor de Statistiek ( 2001) gives a figure of total household income for The Nederlands from all sources of 210485 million Euros 2000; we use this figure as the denominator when calculating household expenditure coefficients (AIH). Coefficients for the household sector can now be included in the Direct Requirements matrix (Table 6).

Following the same procedure as described above: subtracting matrix A from an identity matrix of the same dimensions (7*7) and calculating the inverse of the result (L=(I-A)-1) yields the type II Leontief inverse (Table 7).

Services

Final consumption expenditure by households Agriculture, forestry and fishing 0,12 0,00 0,04 0,00 0,00 0,00 0,00 Mining 0,00 0,02 0,01 0,22 0,00 0,00 0,00 Manufactures 0,15 0,02 0,19 0,03 0,13 0,04 0,08 Utilities 0,04 0,00 0,01 0,24 0,00 0,01 0,03 Construction 0,01 0,01 0,00 0,01 0,23 0,02 0,00 Services 0,13 0,09 0,13 0,08 0,16 0,25 0,59

Compensation of employees 0,11 0,04 0,17 0,09 0,24 0,35 0,00 Once the type I (or type II) inverse matrices have been derived, the calculation of multiplier and effects is quite basic.

The multipliers allow users to make estimates of the effects of changes in the economy.

For instance, if there is an increase in final demand (defined as a change in sales to the final consumers of goods and services for a particular good), we can assume that there will be an increase in the output of that commodity, as producers react to meet the increased demand; this is the direct impact. As these producers increase their output, there will also be an increase in demand on their suppliers and so on down the supply chain; this is the indirect impact. Those two cumulated types of impacts can be calculated using the type I inverse matrix.

As a result of the direct and indirect impacts, the level of household income throughout the economy will increase as a result of increased employment; a proportion of this increased income will be re-spent on final goods and services: this is called the induced effect. This effect, along with the direct and indirect impact, is taken into account when the type II inverse matrix is used for the calculation of the multipliers.

Five different types of aggregate multipliers for both type I and type II effects can be calculated. (Those multipliers are derived for our example and available in table 8 and table 9).

Green Input-Output tables to assess environmental management policy options

By converting the initial monetary values in the Input-Output (I/O) transactions matrices into ratios or technical coefficients, one is able to study the underlying system of interactions and interdependencies. These coefficients can be modeled to examine which industries are important to others. Since Leontief Input-Output tables represent a complete system of interactions for a given year, such modeling can take account of both direct and indirect flows.

For studies on environmental management, I/O tables need to be "greened" by adding a line on pollutant production by each sector and a column on the production of goods and services resulting from the implementation of environmental measures for pollution abatement (reduction of pollutants from agriculture, industry or households).

Using green I/O tables allows us to take into account the impact of environmental policy options (in terms of technical changes or changes in final demand) on the total production of each sector and on employment. Only measures with significant economic impacts (on GDP, on production, on employment… at a national or regional level) can be assessed within an I/O frame: data are too aggregated.

One can thus use I/O methodology to assess the impacts of a broad policy option for marine pollution management targeting a whole sector like, for instance, the introduction of a tax on the plastic 6 industry resulting in higher plastic prices or of subsidies for the production of substitutes for plastics. In that case, I/O analysis can help approach the following (based on and adapted from Leontief, 1974, Essais d'économiques. Ed. Calman Lévy, pp 193-209):

• the impacts of these policy options on the total level of pollution from plastic microparticles in the sea; • the level of pollution abatement for a particular sector, resulting from the implementation of these policy options; • the total pollution resulting from the final demand for products of each sector. I.e.

taking into account the pollution from other sectors intervening in the production (agriculture for instance also needs industrial products and services to generate its production); • the impact of policy options on production levels, total employment and prices, even in sectors not directly impacted by the policy changes. PCBs, DDT, and nonylphenols are very efficiently concentrated in the plastic material. This could harm the Antarctic krill and other zooplankton species by ingestion of small toxic plastic microparticles and cause bioaccumulation through the food chain.

Further reading

OECD (Organisation for

Economic impact assessment of the tourism industry

When tourists visit an area the activities they undertake directly or indirectly generate an increase in economic activity within that area; mostly because they increase demand for goods and services. Economic impact studies attempt to measure the economic benefits arising from tourist activity, i.e. the net increase in the wealth of residents (of a country, region, or more specific locality) which is over the levels that would have been achieved without the tourist activity. In layman's terms this means trying to evaluate the changes in sales, income, tax revenues and jobs that come about because of tourism activities.

Note that an economic impact analysis differs from a cost-benefit analysis in that the former deals solely with actual flows of money which arise from market transactions whilst the latter includes market and non-market values and tries to assess net social benefit from the perspective of economic efficiency. It is therefore important to understand that any economic impact analysis is a partial analysis, in the sense that it does not incorporate all economic impacts, and also since it will be area specific7 . Note also that tourism can have negative effects which may be environmental, cultural, social, or economic. These will not be taken into account as part of this kind of analysis.

Economic impacts of tourism

Generally economic impacts are categorised into three types of effects: direct, indirect and induced (see example below).

• Direct effects only include the immediate effects of additional demand created by tourism. So, for example, this will include tourism spending on accommodation, meals, recreational activities, and so on.

• Indirect effects relate to the increased demand for goods and services by the industries which are serving tourists (that have purchasing links to other firms in the region. This would include, for example, the extra food that restaurants need to purchase; the additional inputs of supplies and labour that hotels need in order to cater for tourists, etc. These effects could also include investment in enhanced public transport infrastructure and sewerage facilities, amongst others.

• Induced effects arise when demand for goods and services from households in the region increases as a result of the direct and indirect effects of tourist activity: those employees whose jobs are supported in the value chain spend their incomes on regional goods and services thereby supporting other economic activity.

Example: Stynes (1997, p 4-5) "Let's say a region attracts an additional 100 tourists, each spending $100 per day. That's $10,000 in new spending per day in the area. If sustained over a 100 day season, the region would accumulate a million dollars in new sales. The million dollars in spending would be distributed to lodging, restaurant, amusement and retail trade sectors in proportion to how the visitor spends the $100. Perhaps 30% of the million dollars would leak out of the region immediately to cover the costs of goods purchased by tourists that are not made in the local area (only the retail margins for such items should normally be included as direct sales effects). The remaining $700,000 in direct sales might yield $350,000 in income within tourism industries and support 20 direct tourism jobs. Tourism industries are labor and income intensive, translating a high proportion of sales into income and corresponding jobs.

The tourism industry, in turn, buys goods and services from other businesses in the area, and pays out most of the $350,000 in income as wages and salaries to its employees. This creates secondary economic effects in the region. The study might use a sales multiplier of 2.0 to indicate that each dollar of direct sales generates another dollar in secondary sales in this region. Through multiplier effects, the $700,000 in direct sales produces $1.4 million in total sales. These secondary sales create additional income and employment, resulting in a total impact on the region of $1.4 million in sales, $650,000 in income and 35 jobs. While hypothetical, the numbers used here are fairly typical of what one might find in a tourism economic impact study."

To sum up, this means that initial rounds of tourism expenditure will have a series of direct, indirect and induced economic effects and that the total economic impact is the sum of these effects within a region. Put another way, the direct effects are multiplied up to derive the total economic effects of spending because of value chain (indirect) and induced income effects. This can be taken into account while using the Input-Output (I/O) framework and I/O multipliers that capture the secondary economic effects of tourism activity.

Measuring the economic impacts of tourism 8

Basically, the economic impacts of tourism are estimated using the simple formula:

Economic impact of tourism = Number of tourists * Average spending by visitor * Multiplier

This formula suggests 3 steps for estimation:

Estimation of the change in the number (and perhaps type) of tourists to the region

Estimates or projections for the number of tourists in an area are not always available. Some local reports on the levels of tourism activity might solve this data need (this corresponds to primary data).

Demand models might also be used, provided they are enough disaggregated (this might be considered as secondary data in a more or less disaggregated form). Good judgment can also help. In the absence of any real data, you would have to rely on subjective estimates.

Within the SAF methodology, scenarios on the increase of the number of local tourists can be explored and different trends of tourist flows assessed, relative to their economic as well as to their environmental impact. However, the "baseline trend" with respect to the number tourists would also be useful to consider and estimate, in order to be used as comparison.

Estimation of the average levels of spending of tourists in the area

The I/O approach enables the assessment of the effects of individual developments, provided that they can be linked with a change in tourism consumption spending. The final demand change (change in sales to the final consumers of goods and services) needs to be estimated.

One thus needs to estimate the mean expenditure of a tourist at local businesses.

When no visitor spending survey exists for the area you are studying, such a survey might need to be implemented (this means acquiring primary data). Those estimates should be based on a representative sample, taking into account variations across seasons, types of tourists and locations within the studied area.

Spending averages might also be borrowed or adapted from other studies: it is possible to rely on secondary data, adjusting it over time using consumer price indices.

As for the estimation of the number of tourists, expert judgment or guesstimates might also be used.

Segments of the total tourism industry can also be explored and assessed. However, estimation of the average level of spending should, as much as possible, take into account the differences existing within the tourist segment studied: i.e., local residents vs. tourists, day users vs. overnight visitors, etc. and consider different spending patterns.

When the number of tourists is multiplied by the average spend per visitor, one gets an estimate of the total tourism spending in the area or direct effect, which represents the amount of money brought into the region by tourists.

Estimation of the local I/O multipliers to determine secondary effects of tourism

To estimate the secondary effects of tourism spending, the I/O multipliers can be used. Multipliers can come from a regional I/O table or be re-scaled from a national I/O table (this can be considered as secondary data). It might be more effective if sector-specific multipliers are used, rather than aggregate tourism spending multipliers.

Care should be taken if you wish to transfer multipliers from existing studies (secondary data), in other contexts: one should not take a multiplier adjusted for one region and apply it in a region of quite a different economic structure.

Stynes (1997, p. 7) notes that" to properly apply tourist purchases of goods to an I/O model (or corresponding multipliers) various margins (retail, wholesale and transportation) must be deducted from the "purchaser price" of the good to separate out the "producer price". Indeed, in an I/O framework, retail margins accrue to the retail trade sector, wholesale margins to wholesale trade, transportation margins to transportation sectors (trucking, rail, air etc.) and the producer prices of goods are assigned to the sector that produces the good". Moreover, he states (p. 7) that "in most cases the factory that produces the good bought by a tourist lies outside of the local region, creating an immediate "leakage" in the first round of spending and therefore no local impact from production of the good. Before applying a multiplier to tourist spending, one must first deduct the producer prices of all imported goods that tourists buy (i.e. only include the local retail margins and possibly wholesale and transportation margins if these firms lie within the region). Generally, only 60 to 70% of tourist spending appears as final demand in a local region".

If uncorrected or rough tourism spending is used, the calculations are thus bound to generate an inflated estimate of tourism impacts. However, such a corrected value for tourism spending is difficult to properly estimate.

Forecasting tourism demand

There is a large and growing literature on forecasting tourism demand. Increasingly sophisticated time-series and other econometric models are being employed by researchers, predominately to forecast international tourism demand, i.e. tourist arrivals/departures at/from a particular region or country.

The typical form of model that is estimated is10 :

DT ij = f(Y j , TC ij , RP ij , ER ij , QF i )
Where Economists have certain expectations of how some of these variables might be related to demand for travel to a particular destination. For example, a positive relation is expected between demand and income in the origin country and a negative relationship is expected between relative tourism prices and transportation costs.

DT ij = demand
There are two ultimate aims of these models:

1. to estimate trends in demand and extrapolate these into the future; 2. to estimate parameters for each of the variables included the model which will allow calculation of elasticities.

An elasticity is economic jargon for a simple concept. For our example the income elasticity of tourism demand for travel to destination i refers to the ratio of the percentage change in tourism demand for travel to destination i to the percentage change in income in origin j. So if demand changes at the same rate as does income then the elasticity estimate will have a value of 1 (unitary elasticity). Different types of goods have different elasticities. Demand for necessities, such as staple food items (e.g. bread, rice), are usually inelastic with respect to their own price (e.g. a 1% rise in price will cause a less than 1% fall in demand). Luxury goods, such as tourism, are generally elastic with respect to their own price (e.g. a 1% rise in the price of travel to destination i will cause a greater than 1% fall in demand). Although a simple concept, these elasticity estimates can provide very useful information to policymakers and researchers who are interested in how tourism demand changes in response to income or prices or other variables.

Practical implementation of tourism forecasting methods

As previously mentioned these kinds of models are estimated using a variety of timesseries and econometric techniques of varying degrees of sophistication. Since all estimations are made using statistical techniques, the statistical significance of the estimates obtained from the model increases as the number of observations increases. Hence most research in this area has used data sets based on national data which has been collected according to consistent data definitions and which is (generally) available over a number of years. For this reason it is unlikely that demand for tourism in a localized area can be estimated since there might not be enough good quality data available that is specific to the geographical area the SAF implementation is dealing with. The most practical course of action open to the researchers will be to use estimates of overall trends or elasticities for specific variables from existing studies.

Tourism demand forecasting studies

There are a large number of studies that have been done related to estimation of tourist demand to or from certain areas. The majority of these use data on movements of tourists between countries and there are few that model demand for domestic tourists.

The listing of publications that follows only includes general papers which are either meta-analyses or reviews of tourism demand studies. These papers give further details of the approaches used. It is recommended to carry out a country specific literature search in order to find literature that would be relevant before using parameters estimated from such models. The World Tourism Organization (UNWTO) has also published more general forecasts for tourism demand for Europe in its 2001 publication Tourism 2020 Vision Vol. 4 Europe, although the accuracy of these forecasts is likely to have been adversely affected by the recent economic downturn. The UNWTO website also has a variety of other information and publications available that may be of some use: http://www.e-unwto.org.

Tourism demand and climate change

Climate change is very likely to have a significant impact on patterns of tourism demand in Europe over the long-term and this should be acknowledged in all coastal areas where tourism is of importance. Possible effects of climate on tourism have been explored in the following recent journal articles:

  Crouch, G. I. (1995) A meta-analysis of tourism demand. Annals of Tourism Research 22, 103-118 Eilat, Y. and Einav, L. (2004) Determinants of international tourism: a three-dimensional panel data analysis. Applied Economics 36, 1315 -1327 Lim, C. (1997) Review of international tourism demand models. Annals of Tourism Research 24, 835-849 Smeral, E. and Weber, A. (2000) Forecasting international tourism trends to 2010. Annals of Tourism Research 27, 982-1006 Song, H. and Li, G. (2008) Tourism demand modelling and forecasting -A review of Recent research. Tourism Management 29, 203-220 Witt, S. F. and Witt, C. A. (1995) Forecasting tourism demand: A review of empirical research. International Journal of Forecasting 11, 447-475

Table 1

 1

	shows the basic structure of the I-O table (also called transaction matrix).
	Basically, the rows represent the outputs (suppliers) and the columns the destination of
	inputs (users).
	Example 1 .
	If we look at the section called the domestic intermediate matrix (in red in Table 1), 6
	sectors are represented: Agriculture with an annual production (or output) of 21863,
	Mining producing 12292, Manufactures with a total output of 210900 and Utilities;
	Construction and Services producing respectively 18249, 60244 and 435953. All those
	outputs are read on the row/column "industry inputs at basic prices" (sum of inputs and
	outputs are typically equal 2 ) and are in million Euros 2000.
	All the cells of the domestic intermediate matrix show the flows between sectors.
	Example, cont.
	If we take the rows, for Agriculture: of the 21863 million Euros produced, 2731 have
	been used inside the sector itself, whereas respectively 3, 8260, 36, 59 and 615 million
	Euros have been used in, Mining, Manufactures, Utilities, Construction and Services.
	The columns describe the structure of the input of the corresponding sector. For
	instance, to produce 21863 million Euros, Agriculture needed 2731 of its own
	production, and, respectively, 4, 3322, 983, 121 and 2884 of the production in Mining,
	Manufactures, Utilities, Construction and Services.

Table 5 .

 5 Type I Leontief Inverse Matrix

	Agriculture, forestry and fishing	Mining	Manufactures	Utilities	Construction	Services

Table 6 .

 6 Direct Requirements matrix

	Agriculture, forestry and fishing	Mining	Manufactures	Utilities	Construction

Table 7 .

 7 Type II Leontief Inverse Matrix

		Agriculture, forestry and fishing	Mining	Manufactures	Utilities	Construction	Services	Final consumption expenditure by households
	Agriculture, forestry and fishing	1,159 0,004 0,063 0,010 0,022	0,015	0,020
	Mining	0,024 1,028 0,024 0,300 0,018	0,014	0,019
	Manufactures	0,292 0,060 1,328 0,111 0,335	0,180	0,218
	Utilities	0,094 0,015 0,048 1,338 0,045	0,052	0,074
	Construction	0,028 0,015 0,024 0,029 1,334	0,059	0,040
	Services	0,575 0,249 0,611 0,442 0,877	1,945	1,206
	Compensation of employees	0,389 0,146 0,452 0,312 0,686	0,728	1,475

Table 8 .

 8 Type I, output and income multipliers

	Output multiplier	Income multiplier	Income effects

Table 9 .

 9 Type II, output and income multipliers

	Output multiplier	Income multiplier	Income effects

Back to the main text, p. 3

A line on pollutant production by each sector and a column on the production of goods and services resulting from the implementation of environmental measures is added to the classical I-O table.Back to the main text, p. 3

Which is unfortunately not the case in our example.Back to the main text, p. 3

This is important to remember as an increase in economic activity in one area due to tourist activity will be accompanied by a decrease in economic activity in the areas from which the tourists originate. This is worth bearing in mind for case studies where tourists are mostly domestic in origin.

The structure and contents of this section mainly builds onStynes (1997).Back to the main text, p. 3

Lim, C. (2006): A survey of tourism demand modelling practice: issues and implications, in, Larry Dwyer and Peter Forsyth (Eds.) International Handbook on The Economics of Tourism, Edward Elgar, Cheltenham)

Output multiplier (O MULT ) j = Σ i L ij

The Type I output multiplier for a particular industry is defined as the total of all outputs from each domestic industry required in order to produce one additional unit of output: that is, the column sums (Σ i ) from the Type I Leontief inverse matrix (L ij ). Similarly, the Type II output multiplier is given from the column sums of Industry rows (i.e. exclude compensation of employees) from the Type II Leontief. Multiplying a change in final demand (direct impact) for an individual industry's output by that industry's type I (respectively type II) output multiplier will generate an estimate of direct + indirect (respectively direct + indirect + induced) impacts on output throughout the economy.

Income multiplier (I

The income multipliers show the increase in income from employment (IfE) -or compensation of employees-that result from a change of €1 of income from employment in each industry. In the formula above, 'v' refers to the ratio of IfE/total output for each industry (last row in the augmented Direct Requirements matrix).

The multipliers show the ratio of direct plus indirect (plus induced if type II multipliers are used) income changes to the direct income change.

Income effects (I

This statistic shows the impact upon income from employment (IfE) -or compensation of employees-throughout the studied economy arising from a unit increase in final demand for industry j's output.

While direct and indirect impacts are calculated using type I multipliers, type II multipliers also include induced effects in the economy.

If data on the level of employment (in FTE, full-time equivalent) is available for each of the industry sectors 5 , employment effects and multipliers can be calculated as well.

Employment multiplier (E MULT ) j = Σ i w i L ij / w j

The employment multipliers show the total increases in employment throughout the economy resulting from an increase in final demand which is enough to create one additional FTE employment in that industry. In the formula above, 'w' is equal to FTE per € of total output for each industry.

The multiplier is the ratio of direct plus indirect (plus induced if Type II multipliers are used) employment changes to the direct employment change.

Employment effects (E eff ) j = Σ i w i L ij

The employment effects statistic calculates the impact upon employment throughout the economy (direct and indirect effect if type I inverse matrix is used, augmented by the induced effect if type II inverse is used) arising from a change in final demand for industry j's output of 1 unit.

Data availability: Input-Output tables

Input-Output tables are available for most of the European countries (except Romania and Cyprus) and for Norway and Turkey.

To access the workbooks by country you can go to. http://epp.eurostat.ec.europa.eu/portal/page/portal/esa95_supply_use_input_tables/dat a/workbooks 9 . It might also be useful to investigate if regional authorities provide regional tables, more suited to the studied area.

When you have the data, the I/O multipliers can be calculated. Note that for the calculation of the I/O multipliers, all the information available (all the industries covered in the table) will be needed. However, if relevant for the issue you wish to study, some categories of expenditure might be aggregated by sectors.

Disaggregation and rescaling of the multipliers

To use the multipliers to assess the economic impact of the chosen tourism issue, you will first need to identify the most relevant categories for the studied issue (select the categories of expenditure in the I/O tables). This part of the assessment can be problematic since tourism employment and activities are difficult to precisely define: visitors often use other services than restaurants and hotels such as postal or health services and tourism is rarely a homogeneous activity (Jones and Munday, 2004).

In order to disaggregate the multipliers to refine the analysis, the national or regional multipliers often need to be re-scaled to a local level.

It would be an error to apply a statewide multiplier to a local region, since multipliers tend to be higher for larger regions with more diversified economies and hence their use would yield estimates of local multipliers effects which would be biased upwards.

The use of an I/O framework to assess tourism activity is not always clear-cut. Data on the tourism industry at a regional level is often scarce. You can rely on rough estimates of the scale of tourism to disaggregate the multipliers. However, if you wish to refine the regional Input-Output table, it might be necessary to collect statistical information on the size and transactions of industries with a significant degree of tourism dependence. A regional survey on tourism activities (business activities, employment, purchasing, etc.) is thus sometimes needed (Jones and Munday, 2004). _______________________________________________________________ 9 If you want some precise data on a particular industry or product, click on "Database functions" and Select in the folders "Economy and finance", "National accounts (including GDP)", "Supply, use and Input-Output tables", "Tables at current prices", "Input-output table-current prices". The table can then be downloaded once you have made your selection regarding the sector, country and year you want to study.

Tourism economic impact methodologies

Most commonly three methods are used to evaluate the economic impact of tourism (or other economic sectors): computable general equilibrium models, Input-Output (I/O) analysis and tourism satellite accounts.

Computable general equilibrium analysis

Computable general equilibrium models are complex, data intensive models of national or regional economies. They consist of equations describing model variables and a database consistent with the model equations. They can be used to explore the impacts upon an economy of changes in policy, technology or other external factors (e.g. tourism demand). Their complexity and data requirements mean that their use is not appropriate within the SAF.

I/O Analysis

I/O models describe the flows of money that occur between the different sectors of a region's economy. From these models multipliers can be estimated which measure how much of direct spending is recirculated within the regional economy in terms of indirect and induced effects, thus allowing the overall economic impact of tourist activity to be evaluated. Many countries produce I/O tables at a national (and some at a regional) level and multipliers derived from these can be adapted for a more local use. Much more detail can be found on this methodology (and other tourism economic impact methodologies) from the Department of Community, Agriculture, Recreation and Resource Studies at Michigan State University which has a website devoted to the economic impacts of recreation and tourism: http://web4.canr.msu.edu/mgm2/econ/index.htm, accessed 01/2011 Tourism Satellite Accounts Some organisations and countries have developed national and/or regional sets of tourism satellite accounts. These accounts extract information from national economic accounts to try and identify the extent to which tourism contributes to these. They are generally only calculated at a national scale (if they are calculated at all) and it seems difficult to scale them down to more localised areas. Furthermore, tourism satellite accounts only account for the direct economic impacts of tourism and do not include indirect or induced effects. Further information on tourism satellite accounts can be found on the World Travel & Tourism Council's website at: http://www.wttc.org/eng/Tourism_Research/Tourism_Satellite_Accounting/ where there are also a number of downloadable tourism satellite accounts country reports.

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