Aseem Behl

C V Jawahar

M Pawan Kumar

Optimizing Average Precision using Weakly Supervised Data

The performance of binary classification tasks, such as action classification and object detection, is often measured in terms of the average precision (AP). Yet it is common practice in computer vision to employ the support vector machine (SVM) classifier, which optimizes a surrogate 0-1 loss. The popularity of SVM can be attributed to its empirical performance. Specifically, in fully supervised settings, SVM tends to provide similar accuracy to the AP-SVM classifier, which directly optimizes an AP-based loss. However, we hypothesize that in the significantly more challenging and practically useful setting of weakly supervised learning, it becomes crucial to optimize the right accuracy measure. In order to test this hypothesis, we propose a novel latent AP-SVM that minimizes a carefully designed upper bound on the AP-based loss function over weakly supervised samples. Using publicly available datasets, we demonstrate the advantage of our approach over standard loss-based binary classifiers on two challenging problems: action classification and character recognition.

Introduction

Several problems in computer vision can be formulated as binary classification tasks, that is, determining whether a given input belongs to the positive or the negative class. As a running example throughout this paper, we will consider the task of action classification, that is, automatically figuring out whether an image contains a person performing an action of interest (such as 'jumping' or 'walking'). The importance of binary classification has contributed to the development of several supervised learning approaches, where a binary classifier is estimated using datasets that consist of training samples along with their class information. One such binary classifier that is widely employed in computer vision is the support vector machine (SVM) [START_REF] Vapnik | Statistical learning theory[END_REF]. Given a fully supervised dataset, an SVM is learned by minimizing a convex regularized upper bound on the 0-1 loss (that is, the loss is 0 for a correct classification and 1 for an incorrect classification).

As the most commonly used accuracy measure for binary classification in computer vision is the average precision (AP) [START_REF] Everingham | The pascal visual object classes (voc) challenge[END_REF], the choice of SVM may appear surprising. Specifically, while AP depends on the ranking of the samples, the 0-1 loss optimized by SVM is only concerned with the number of incorrectly classified samples. The case for its use appears even weaker when we consider that there already exists a related classifier (henceforth referred to as AP-SVM) that optimizes an AP-based loss function (henceforth referred to as the AP loss) [START_REF] Yue | A support vector method for optimizing average precision[END_REF]. However, a closer look at the empirical evidence reveals the reasoning behind this choice: SVM can be trained more efficiently, and provides comparable accuracy to AP-SVM.

The above observation suggests that we should continue to collect fully supervised datasets and use simple loss functions. If the supervision entails labeling each sample with its class, then this task does not appear to be daunting. However, recent research has shown that the key to achieving high classification accuracy is to provide additional annotations for each sample that can guide the classifier towards the correct output [START_REF] Delaitre | Recognizing human actions in still images: a study of bag-of-features and partbased representations[END_REF][START_REF] Felzenszwalb | Object detection with discriminatively trained partbased models[END_REF][START_REF] Maji | Action recognition from a distributed representation of pose and appearance[END_REF][START_REF] Yang | Unifying discriminative visual codebook generation with classifier training for object category recognition[END_REF][START_REF] Yao | Human action recognition by learning bases of action attributes and parts[END_REF]. Going back to the example of action classification, it would be helpful to not only know the class information of each image but the exact location of the person in the image.

The need for complex additional annotations makes supervised learning impractical. To overcome this deficiency, researchers have started exploring weakly supervised learning [START_REF] Blaschko | Simultaneous object detection and ranking with weak supervision[END_REF][START_REF] Deselaers | Localizing objects while learning their appearance[END_REF][START_REF] Felzenszwalb | Object detection with discriminatively trained partbased models[END_REF][START_REF] Kumar | Modeling latent variable uncertainty for loss-based learning[END_REF][START_REF] Kumar | Learning specific-class segmentation from diverse data[END_REF][START_REF] Miller | Max-margin min-entropy models[END_REF][START_REF] Prest | Weakly supervised learning of interactions between humans and objects[END_REF]17,[START_REF] Russakovsky | Objectcentric spatial pooling for image classification[END_REF][START_REF] Vezhnevets | Weakly supervised structured output learning for semantic segmentation[END_REF][START_REF] Wang | Discriminative learning with latent variables for cluttered indoor scene understanding[END_REF], where the annotations of some or all the samples contain missing information. Not surprisingly, the convenience of using partial annotations comes at the cost of a significantly more challenging machine learning problem. Specifically, weakly supervised learning typically requires us to solve a non-convex optimization problem, which makes it prone to converge to a bad local minimum. Given the inherent difficulty of the problem, we hypothesize that the choice of the loss function becomes crucial in such settings. In order to provide empirical evidence for our hypothesis, we propose a novel latent AP-SVM framework that models the missing additional annotations using latent variables.

Our formulation differs from the standard latent structured SVM (latent SSVM) [START_REF] Yu | Learning structural svms with latent variables[END_REF] for general loss functions in three significant aspects. First, it uses a more intuitive two-step prediction criterion, where the first step consists of choosing the best latent variable for each sample and the second step consists of ranking the samples. This is in contrast to the latent SSVM formulation, which requires the joint optimization of the latent variables and the ranking. For example, in 'jumping' action classification, our latent AP-SVM formulation would first pick out the bounding box that is most likely to contain a 'jumping' person in each image, and then rank them. In contrast, the latent SSVM formulation would require us to simultaneously classify the samples as positive or negative, while picking out the best bounding box for the positive images (bounding box that is most likely to contain a 'jumping' person) and the worst bounding box for the negative images (bounding box that is least likely to contain a 'jumping' person). Second, using the above prediction criterion, the parameters of latent AP-SVM are learned by minimizing a tighter upper bound on the AP loss compared to latent SSVM. Third, unlike latent SSVM, latent AP-SVM lends itself to efficient optimization during learning that is guaranteed to provide a local minimum or saddle point solution. While the first of the aforementioned differences makes our approach more intuitive, the latter two differences provide a sound theoretical justification for its superiority to latent SSVM. In order to demonstrate that the theoretical superiority also translates to better empirical results, we provide a thorough comparison of latent AP-SVM with the baseline methods for two challenging problems: action classification and character recognition. For the sake of clarity, we defer the details that are not essential for the understanding of the paper to the appendices provided in the supplementary material. To facilitate the use of latent AP-SVM, we have made our code and data available online at http://cvit.iiit.ac.in/projects/lapsvm/.

Related Work

The popularity of support vector machine (SVM) [START_REF] Vapnik | Statistical learning theory[END_REF] can be gauged by its numerous applications in computer vision including, image classification [START_REF] Lin | Large-scale image classification: Fast feature extraction and svm training[END_REF][START_REF] Yang | Linear spatial pyramid matching using sparse coding for image classification[END_REF], action classification [START_REF] Delaitre | Recognizing human actions in still images: a study of bag-of-features and partbased representations[END_REF][START_REF] Maji | Action recognition from a distributed representation of pose and appearance[END_REF][START_REF] Yao | Human action recognition by learning bases of action attributes and parts[END_REF] and object detection [START_REF] Dalal | Histograms of oriented gradients for human detection[END_REF][START_REF] Vedaldi | Multiple kernels for object detection[END_REF]. The main advantages of SVM are its well-understood connections to statistical learning theory [START_REF] Vapnik | Statistical learning theory[END_REF] and the availability of efficient algorithms to learn its parameters [START_REF] Joachims | Making large-scale SVM learning practical[END_REF]9,[START_REF] Shalev-Shwartz | Pegasos: Primal estimated sub-gradient solver for SVM[END_REF].

One of the disadvantages of SVM is that it optimizes the 0-1 loss instead of the average precision (AP) over the training dataset. This disadvantage can be addressed by using the AP-SVM [START_REF] Yue | A support vector method for optimizing average precision[END_REF] to optimize an upper bound on the AP loss over the training samples. However, empirically, the performance of SVM is comparable to AP-SVM. Furthermore, SVM requires less training time compared to AP-SVM.

Another important disadvantage of SVM is its inability to handle missing information in the annotations. This problem is alleviated by latent SVM [START_REF] Felzenszwalb | Object detection with discriminatively trained partbased models[END_REF], which models missing annotations as latent variables. The 0-1 loss based latent SVM can be thought of as a special case of latent structured SVM (latent SSVM) [21,[START_REF] Yu | Learning structural svms with latent variables[END_REF], which optimizes a general loss function. Latent SSVM has received considerable attention in the computer vision community [START_REF] Felzenszwalb | Object detection with discriminatively trained partbased models[END_REF][START_REF] Kumar | Learning specific-class segmentation from diverse data[END_REF][START_REF] Lan | Discriminative latent models for recognizing contextual group activities[END_REF][START_REF] Vezhnevets | Weakly supervised structured output learning for semantic segmentation[END_REF][START_REF] Wang | Discriminative learning with latent variables for cluttered indoor scene understanding[END_REF][START_REF] Wang | A discriminative latent model of object classes and attributes[END_REF]29], on tasks ranging from binary classification (such as object detection) to structured output prediction (such as semantic segmentation and indoor scene understanding). While it can be employed to optimize the AP loss, we will provide both theoretical and empirical arguments for the superiority of our novel latent AP-SVM formulation.

Preliminaries

Notation. We use a similar notation to [START_REF] Yue | A support vector method for optimizing average precision[END_REF]. The training dataset consists of n samples X = {x i , i = 1, • • • , n} together with their class information. The indices for the positive and negative samples are denoted by P and N respectively. In other words, if i ∈ P and j ∈ N then x i belongs to the positive class and x j belongs to the negative class. Furthermore, for each sample x, the dataset can also provide additional annotations, which we denote by h. For example, in action classification each sample represents an image and the additional annotation h can represent the bounding box of the person in the image. To simplify the discussion in this section, we will assume that the additional annotations h are known for all samples. In the next section, we will describe the setting where the additional annotations are latent. We denote the set of all additional annotations for the positive and negative samples by H P = {h i , i ∈ P} and H N = {h j , j ∈ N } respectively.

The desired output is a ranking matrix

Y of size n × n, such that (i) Y ij = 1 if x i is ranked higher than x j ; (ii) Y ij = -1 if x i
is ranked lower than x j ; and (iii) Y ij = 0 if x i and x j are assigned the same rank. The ground-truth ranking matrix Y * is defined as: (i) Y * ij = 1 and Y * ji = -1 for all i ∈ P and j ∈ N ; (ii) Y * ii ′ = 0 and Y * jj ′ = 0 for all i, i ′ ∈ P and j, j ′ ∈ N . AP Loss. Given a training dataset, our aim is to learn a classifier that provides a high AP measure. Let AP(Y, Y * ) denote the AP of the ranking matrix Y with respect to the true ranking Y * . The value of the AP(•, •) lies between 0 and 1, where 0 corresponds to a completely incorrect ranking -Y * and 1 corresponds to the correct ranking Y * . In order to maximize the AP, we will minimize a loss function defined as ∆(Y, Y * ) = 1 -AP(Y, Y * ). Joint Feature Vector. For positive samples, the feature vector of the input x i and additional annotation h i is denoted by Φ i (h i ). Similarly, for negative samples, the feature vector of the input x j and additional annotation h j is denoted by Φ j (h j ). For example, in action classification, Φ i (h i ) can represent poselet [START_REF] Maji | Action recognition from a distributed representation of pose and appearance[END_REF] or bag-of-visualwords [START_REF] Delaitre | Recognizing human actions in still images: a study of bag-of-features and partbased representations[END_REF] features extracted from an image x i using the pixels specified by the bounding box h i . Similar to [START_REF] Yue | A support vector method for optimizing average precision[END_REF], we specify a joint feature vector of the input X, output Y, and additional annotations {H P , H N } as

Ψ(X, Y, {H P , H N }) = 1 |P||N | i∈P j∈N Y ij (Φ i (h i ) -Φ j (h j )). (1)
In other words, the joint feature vector is the scaled sum of the difference between the features of all pairs of samples, where one sample is positive and the other is negative.

Parameters. The parameter vector of the classifier is denoted by w, and is of the same size as the joint feature vector. Given the parameters w, the ranking of an input X is defined as the one that maximizes the score, that is,

Y opt = argmax Y w ⊤ Ψ(X, Y, H), (2)
where H is the set of all the given additional annotations. Yue et al. [START_REF] Yue | A support vector method for optimizing average precision[END_REF] showed that the above optimization can be performed efficiently by sorting the samples (x k , h k ) in descending order of the score w ⊤ Φ k (h k ). Supervised AP-SVM. Given the input X, ranking matrix Y, and additional annotations H P and H N , we would like to learn the parameters of the classifier such that the AP loss over the training dataset is minimized. However, the AP loss is highly non-convex in w, and minimizing it directly can result in a bad local minimum solution. To avoid this undesirable outcome, Yue et al. [START_REF] Yue | A support vector method for optimizing average precision[END_REF] proposed the AP-SVM formulation, which minimizes a regularized upper bound on the AP loss. Specifically, the model parameters are obtained by solving the following convex optimization problem:

min w 1 2 ||w|| 2 + Cξ, (3) s
.t. ∀Y : {w ⊤ Ψ(X, Y * , {H P , H N }) -w ⊤ Ψ(X, Y, {H P , H N })} ≥ ∆(Y * , Y) -ξ.
Intuitively, the above problem introduces a margin between the score of the correct ranking and all incorrect rankings. The desired margin is proportional to the difference in their AP values. The hyperparameter C controls the trade-off between the training error and the model complexity. Problem (3) is specified over all possible rankings Y, which is exponential in the number of training samples. Nonetheless, it can be solved efficiently using a cuttingplane algorithm [START_REF] Yue | A support vector method for optimizing average precision[END_REF] (described in Appendix A).

Optimizing Average Precision with Weak Supervision

The main deficiency of supervised learning is that it involves the onerous task of collecting detailed annotations for each training sample. Since detailed annotations are also very expensive, such an approach quickly becomes financially infeasible as the size of the datasets grow. In this work, we consider a more pragmatic setting where the additional annotations H P and H N are unknown. For example, consider 'jumping' action classification, where each input represents an image that can belong to the positive class or the negative class. In order to learn a classifier that can distinguish between 'jumping' and 'not jumping' images, we only require image-level annotations instead of the bounding box of the person in each image.

The convenience of not specifying additional annotations comes at the cost of a more complex machine learning problem. Specifically, we need to deal with two confounding factors: (i) since the best value of the additional annotation h i for each positive sample i ∈ P is unknown, it needs to be imputed automatically; (ii) since a negative sample remains negative regardless of the value of the additional annotation h j , we need to consider all possible values of H N during parameter estimation. In the 'jumping' action classification example, this implies that (i) we have to identify the bounding box of the jumping person in all the positive images, and (ii) ensure that the scores of the identified jumping person bounding boxes are higher than the scores of all possible bounding boxes in the negative images. In the following subsection, we describe how the standard latent SSVM attempts to resolve these confounding factors in order to optimize the AP loss. This will allow us to identify its shortcomings and correct them with our novel formulation in subsection 4.2.

Latent SSVM Formulation

Given an input X, the prediction rule of a latent SSVM requires us to maximize the score jointly over the output Y and the additional annotations H, that is,

(Y opt , H opt ) = argmax (Y,H) w ⊤ Ψ(X, Y, H). (4)
The parameters w of a latent SSVM are learned by minimizing a regularized upper bound on the training loss. Specifically, the parameters are obtained by solving the following optimization problem:

min w 1 2 ||w|| 2 + Cξ, (5)
s.t. ∀Y, H : max Ĥ {w ⊤ Ψ(X, Y * , Ĥ)} -w ⊤ Ψ(X, Y, H) ≥ ∆(Y * , Y) -ξ.
Intuitively, the above problem introduces a margin between the maximum score corresponding to the ground-truth output and all other pairs of output and additional annotations. Similar to the supervised setting, the desired margin is proportional to the AP loss.

There are three main drawbacks of the standard latent SSVM formulation in the case of AP loss optimization. The first drawback is the prediction rule. This is specified by problem (4), which requires us to simultaneously label the samples as positive or negative (optimize over Y) and find the highest scoring additional annotations for the positive samples and the lowest scoring additional annotations for the negative samples (optimize over H) in order to maximize the score. This is in stark contrast to the prediction rule of existing weakly supervised binary classifiers, which first obtain the score of each sample by maximizing over the additional annotations (regardless of whether they will be labeled as positive or negative), and then ranking them according to their scores. For example, in action classification, we rank the images according to the highest scoring bounding box of a person in each image. In other words, we never compare the scores of particular choice of additional annotations with a different set of additional annotations. The second drawback is the learning formulation. This is specified by problem [START_REF] Everingham | The pascal visual object classes (voc) challenge[END_REF], which provides a very loose upper bound on the AP loss. The third drawback is the optimization. Specifically, to the best of our knowledge, the local optimum solution of problem (5) cannot be found efficiently due to the lack of an appropriate cutting plane algorithm. For the details on the difficulty of optimization of latent SSVM, as well as an approximate algorithm used in our experiments, we refer the reader to Appendix C.

Latent AP-SVM Formulation

We now describe a novel latent AP-SVM formulation that overcomes the three drawbacks of the standard latent SSVM framework discussed in the previous section. Specifically, latent AP-SVM uses an intuitive prediction rule, provides a tighter upper bound on the AP loss, and lends itself to efficient optimization.

Intuitive Prediction

We use a two-step prediction rule. In the first step, we obtain the value of the additional annotations for each sample by maximizing the score, that is,

h opt = argmax h w ⊤ Φ(h). (6)
Next, we obtain the optimal ranking Y opt for the additional annotations H opt , that is,

Y opt = argmax Y w ⊤ Ψ(X, Y, H opt ), (7)
where H opt is the set of all the additional annotations obtained by solving problem (6) for all samples. Similar to the supervised setting, the optimal ranking is computed by sorting the samples in descending order of their scores. Note that our prediction rule is the same as the ones used in conjunction with the current weakly supervised binary classifiers [START_REF] Blaschko | Simultaneous object detection and ranking with weak supervision[END_REF][START_REF] Felzenszwalb | Object detection with discriminatively trained partbased models[END_REF].

Tighter Bound on the AP Loss

We learn the parameters of latent AP-SVM by solving the following optimization problem:

min w 1 2 ||w|| 2 + Cξ, (8)
s.t. ∀Y, H N : max

H P {w ⊤ Ψ(X, Y * , {H P , H N }) -w ⊤ Ψ(X, Y, {H P , H N })} ≥ ∆(Y * , Y) -ξ.
Intuitively, the above problem finds the best assignment of values for the additional annotations H P of the positive samples such that the score for the correct ranking (which places all the positive samples above the negative samples) is higher than the score for an incorrect ranking, regardless of the choice of the additional annotations H N of the negative samples. It is worth noting the significant difference between the optimization corresponding to latent AP-SVM and the standard latent SSVM. Specifically, in the constraints of problem [START_REF] Everingham | The pascal visual object classes (voc) challenge[END_REF], the values of the additional annotations for a correct and incorrect ranking are independent of each other. In contrast, the constraints of problem (8) are specified using the same values of the additional annotations. The following proposition provides a sound theoretical justification for preferring problem (8) over problem [START_REF] Everingham | The pascal visual object classes (voc) challenge[END_REF].

Proposition 1. The latent AP-SVM formulation provides a tighter upper bound on the AP loss compared to the standard latent SSVM formulation (proof in Appendix D).

Efficient Optimization

The local minimum or saddle point solution of problem ( 8) can be obtained using the CCCP algorithm [START_REF] Yuille | The concave-convex procedure[END_REF], as described in Algorithm 1. The algorithm involves two main steps. In the first step (step 3 of Algorithm 1), it imputes the best additional annotations H P of the positive samples given the current estimate of the parameters. In the second step (step 4 of Algorithm 1), given the imputed values of H P , CCCP updates the parameters by solving the resulting convex optimization problem. We discuss both these steps in detail below.

Algorithm 1

The CCCP algorithm for parameter estimation of latent AP-SVM. Require: X, Y * , w 0 , ǫ 1: t ⇐ 0 2: repeat 3:

For the current set of parameters w t , obtain the value of the latent variables H * P that minimizes the objective function value of problem (8). Imputing the Additional Annotations. For a given parameter w, we need to obtain the values of the additional annotations H P for the positive samples such that it minimizes the objective function of problem [START_REF] Joachims | Making large-scale SVM learning practical[END_REF]. Since w is fixed, the first term of the objective function (that is, the squared ℓ 2 norm of w) cannot be modified. Instead, we need to minimize the slack ξ, which is equivalent to solving the following problem:

min H P max Y,H N {∆(Y * , Y) -w ⊤ Ψ(X, Y * , {H P , H N }) (9) +w ⊤ Ψ(X, Y, {H P , H N })}.
We refer to the above problem as output-consistent inference (since it fills in the missing information under the constraint that it is consistent with the output, that is, the optimal ranking). Although problem (9) contains Y and H N , the following proposition shows that it can be optimized easily with respect to H P .

Proposition 2. Problem ( 9) can be solved efficiently by independently choosing the latent variable for each positive sample using the following criterion:

h * i = argmax hi w ⊤ Φ i (h i ), ∀i ∈ P ( 10
)
(proof in Appendix E).
Updating the Parameters. Given the imputed latent variables H * P , the parameters are updated by solving the following convex problem:

min w 1 2 ||w|| 2 + Cξ, (11)
w ⊤ Ψ(X, Y * , {H * P , H N }) -w ⊤ Ψ(X, Y, {H * P , H N }) ≥ ∆(Y * , Y) -ξ, ∀Y, H N .
Similar to supervised AP-SVM, the above problem can be solved using a cutting plane algorithm. The computational feasibility of the cutting plane algorithm relies on being able to efficiently compute the most violated constraint. In our case, the most violated constraint is found by solving the following problem:

Ŷ, ĤN = argmax Y,H N {w ⊤ Ψ(X, Y, {H * P , H N }) -w ⊤ Ψ(X, Y * , {H * P , H N }) + ∆(Y * , Y)}. ( 12
)
We refer to the above problem as loss-augmented inference (since it augments the score of the ranking with its AP loss). Note that, in contrast to supervised AP-SVM, we not only need to optimize over the ranking Y, but also the variables H N . The following proposition allows us to perform the joint optimization efficiently.

Proposition 3. Problem ( 12) can be solved by first maximizing over H N using the following criterion:

h * j = argmax hj w ⊤ Φ j (h j ), ∀j ∈ N ( 13
)
(proof described in Appendix E). Using Proposition 3, problem (12) can be solved in two steps. In the first step we maximize the loss-augmented score over H N by maximizing the score of each negative sample independently. The second step is to maximize the loss-augmented score over Y, which is achieved using the optimal greedy algorithm of Yue et al. [START_REF] Yue | A support vector method for optimizing average precision[END_REF] (described in Appendix B).

Experiments

The previous section shows the theoretical benefit of latent AP-SVM over the standard latent SSVM formulation, namely that it minimizes a tighter upper bound on the AP loss and allows for efficient inference, while using an intuitive prediction rule. We now show that the theoretical benefits translate to improved empirical performance using two important and challenging problems in computer vision.

Action Classification

Dataset. We use the PASCAL VOC 2011 [START_REF] Everingham | The pascal visual object classes (voc) challenge[END_REF] action classification dataset, which consists of 4846 images depicting 10 action classes. The dataset is divided into two subsets: 2424 'trainval' images for which we are provided the bounding boxes of the persons in the image together with their action class; and 2422 'test' images for which we are only provided with the person bounding boxes.

Recall that our main hypothesis is that the challenging nature of weakly supervised learning makes it essential to use the right loss function during training. In order to test this hypothesis, we use the 'trainval' images to create five types of datasets that vary in their level of supervision. Specifically, each type of dataset provides the ground-truth additional annotations1 for S percent of the positive and the negative samples, where S ∈ {0, 25, 50, 75, 100}. The additional annotations for the remaining 100-S percent of the samples are treated as latent variables. The putative values of each latent variable are restricted to the top T = 20 boxes obtained by a standard person detector [START_REF] Felzenszwalb | Discriminatively trained deformable part models[END_REF]. During testing, we use the learned parameters to classify the given person bounding boxes in the 'test' dataset. The performance is measured by submitting the scores of all the bounding boxes to the PASCAL VOC evaluation server.

Features. Given a bounding box h i of the image x i , we use the standard poselet-based feature vector [START_REF] Maji | Action recognition from a distributed representation of pose and appearance[END_REF] to specify Φ i (h i ). It consists of 2400 activation scores of actionspecific poselets and 4 object activation scores. In addition, we use the score of the person detector [START_REF] Felzenszwalb | Discriminatively trained deformable part models[END_REF], which results in a 2405 dimensional feature vector.

Methods. We compare our latent AP-SVM formulation with the baseline latent SVM that is commonly used in computer vision. Latent SVM consists of two hyperparameters: (i) C, the trade-off between the regularization and the loss; and (ii) J, the relative weight of the positive samples. In order to further strengthen the baseline, we add robustness to outliers using a further hyperparameter c. Specifically, we prevent the classifier from considering the most confusing c% bounding boxes in the negative samples under the constraint that at least one bounding box is used per negative image. We obtain the best settings of the hyperparameters via a 5-fold cross validation, where the 'trainval' set is split into 1940 training images and 484 validation images. We consider the following putative values: C ∈ {10 -3 , 10 -2 , . . . , 10 4 }, J ∈

|P|+|N | |P|

× {10 -4 , 10 -3 , . . . , 10 1 } and c ∈ {0, 0.1, . . . , 0.9} (note that, when c = 0, the resulting baseline is the standard latent SVM without robustness). In addition, we also compare the performance of our latent AP-SVM with latent SSVM. For the latent AP-SVM and latent SSVM, we only need to specify a single hyperparameter C, whose value is also obtained via 5-fold cross-validation. In order to mitigate the effects of initialization, we use 5 random seeds and choose the one that provides the minimum objective value for each method independently. Complexity. The running time for latent AP-SVM and the baseline methods is dominated by computation of the most violated constraint. Empirically, we found that computation of most violated constraint in latent AP-SVM is around 5 times slower and 100 times faster compared to latent SVM and latent SSVM respectively. However, latent AP-SVM does not require any extra hyperparameter to weight the positive samples, therefore does not worsen the overall computational complexity compared to training latent SVM. Results. Figure 1 shows the best mean AP value over all 10 action classes obtained during 5-fold cross validation. Note that as the amount of supervision decreases, the gap between our method and the two baselines steadily increases. In the fully supervised setting, that is, S = 100, latent AP-SVM provides statistically significant improvements over latent SVM for only 4 out of 10 classes (using paired t-test with p-value less than 0.05), with an overall improvement of less than 3%. Note that, for fully supervised datasets, both latent AP-SVM and latent SSVM are equivalent to the AP-SVM, and hence provide the same results. However, in the more interesting weakly supervised setting, that is, S = 0, latent AP-SVM provides statistically significant improvements over latent SVM for 6 out of 10 classes, and an overall improvement of more than 5%. We note that, for standard latent SVM, i.e., when c = 0, the mean AP obtained during cross-validation over all ten classes is 39.5%. Adding robustness and cross-validating c, we get an overall improvement of 2.4%. This illustrates that, by incorporating robustness, we get a stronger baseline than standard latent SVM. Similarly, latent AP-SVM provides statistically significant improvements over latent SSVM for 7 out of 10 classes and an overall improvement of more than 4%.

Table 1 shows the comparison of our latent AP-SVM with latent SVM and latent SSVM on the test set. Note that we use 5 different random seeds for each method. The hyperparameters are set using 5-fold cross-validation. Latent AP-SVM classifier performs better than latent SVM for all 10 classes with significant increase in performance for 4 classes. Overall, we get an improvement of 5.1% on the test performance compared to latent SVM. Similarly, latent AP-SVM classifier performs better than latent SSVM for 8 out of 10 classes. Overall, we get an improvement of 3.7% on the test performance compared to latent SSVM.

Figure 2 exemplifies the significance of using the right accuracy measure. It shows a sub-sequence of images from two rankings predicted for the 'ridingbike' action. The top and bottom rows are from the rankings predicted by latent SVM and latent AP-SVM respectively. Latent SVM predicts 2 incorrect images out of 4 but makes mistakes in the top two images. Whereas, latent AP-SVM makes the same number of mistakes but for images at lower rankings (first and fourth in this example). This may be explained by the fact that, in terms of 0/1 loss both predictions are equivalent. However, the bottom ranking sequence is preferred by a classifier that is attempting to optimize the AP loss. The testing is performed on the 'test' dataset and evaluated on the PASCAL VOC server. The last column ('Overall') shows the mean average precision over all ten action classes.

Character Recognition in Natural Images

Dataset. We use the IIIT 5K-WORD [START_REF] Mishra | Scene text recognition using higher order language priors[END_REF] scene text dataset, which consists of 5000 cropped word images from scene texts and born-digital images, which are divided into 2000 'trainval' images and 3000 'test' images. Each image is annotated with the corresponding word, that is, a string where each character is an upper case letter ('A' to 'Z'), a lower case letter ('a' to 'z'), or a number ('0' to '9'). In addition, the dataset also provides the bounding boxes for each character of the word, which we discard during learning. Instead, we treat the bounding box of the characters as latent variables whose putative values are restricted to T = 20 boxes obtained by a standard character detector [START_REF] Dalal | Histograms of oriented gradients for human detection[END_REF].

Using this dataset, we perform binary classification for the 22 classes that contain at least 150 samples in the 'trainval' dataset.

Features. Given a character bounding box h i of the word image x i , we use the histogram of oriented gradients (HOG) [START_REF] Dalal | Histograms of oriented gradients for human detection[END_REF] features to specify Φ i (h i ). The HOG features are computed by resizing the bounding box to 48 × 48 pixels.

Methods. We compare our latent AP-SVM formulation with the baseline latent SVM. We use the same formulation of the baseline latent SVM as described in the action classification experiments. All the hyper-parameters are once again fixed using 5-fold cross validation over 80%/20% splits of the 'trainval' dataset. Each method is initialized using 3 different random seeds and the solution corresponding to the minimum objective value is chosen.

Results. Figure 3 shows the best AP values for all the 5 classes where the performance of latent AP-SVM is statistically different from that of latent SVM (using paired t-test with p-value less than 0.05). Latent SVM provides statistically significant improvements over latent AP-SVM for only 1 class. In contrast, latent AP-SVM improves the performance for 4 classes. In terms of the mean AP value, latent AP-SVM provides an improvement of 6.3% for the 5 classes shown in figure 3 and3.2% over all 22 classes. Figure 4 shows the AP values for the 5 statistically significant characters on the 'test' set. Similar to the crossvalidation results, latent AP-SVM outperforms latent SVM for 4 out of the 5 classes. In terms of the mean AP value, latent AP-SVM provides an improvement of 3.5% for the

Discussion

We proposed a novel latent AP-SVM formulation that allows us to learn accurate classifier parameters by minimizing a carefully designed difference-of-convex upper bound on the AP loss. We showed the advantage of our approach over latent SVM and the standard latent SSVM for action classification and character recognition using standard, publicly available datasets.

An interesting direction of future research would be to extend the latent AP-SVM formulation to learn from images that have been labeled by noisy tags. This will allow us to exploit the large, freely available datasets provided by photo-sharing websites (for example, Flickr or Picasa). The large size of such datasets would also make it necessary to improve the efficiency of the CCCP.

4 :

 4 Update w t+1 by fixing the latent variables to H * P and solving the resulting convex problem

  .

5 :t ← t + 1 6 :

 56 until Objective function cannot be decreased below tolerance ǫ

Figure 1 .

 1 Figure 1. The best mean average precision over all 10 action classes obtained during 5-fold cross validation. The x-axis corresponds to the amount of supervision provided. The y axis corresponds to the mean average precision. As the amount of supervision decreases, the gap in the performance of latent AP-SVM and the baseline methods increases, thereby illustrating the importance of using the correct loss function and the correct learning formulation for weakly supervised learning.

Figure 2 .

 2 Figure 2. Top and bottom rows show a sub-sequence of images from rankings predicted by latent SVM and latent AP-SVM respectively for 'ridingbike' action class. Both first and second row have two incorrect (highlighted by red border) and correct (highlighted by green border) images each, but latent AP-SVM puts the incorrect images in the lower rank.

5

  classes shown in figure 4 and 2.7% over all 22 classes. Comparison with latent SSVM and detailed results over all 22 classes are provided in the supplementary material.

Figure 3 .

 3 Figure 3. The best average precision values for the 5 statistically significant character classes obtained during 5-fold cross validation on the 'trainval' set of the IIIT 5K-WORD dataset. The x-axis corresponds to the characters. The y axis corresponds to the average precision. Latent AP-SVM provides statistically significant improvements over latent SVM for 4 out of the 5 characters.

Figure 4 .

 4 Figure 4. The average precision values for the 5 statistically significant characters obtained on the 'test' set of the IIIT 5K-WORD dataset. The x-axis corresponds to the character categories. The y axis corresponds to the average precision.

Table 1 .

 1 The average precision of latent AP-SVM and the baseline latent SVM and latent SSVM methods under weak supervision. The training is performed over the entire 'trainval' dataset with S = 0 using the best hyperparameters obtained during 5-fold cross-validation.

	Method	Jump	Use	Play	Read Ride Ride Run Take	Use	Walk Overall
			phone instrument	bike horse	photo computer
	Latent AP-SVM 45.7	30.5	34.0	21.1 75.5	74.9 76.0	15.7	24.6	47.5	44.6
	Latent SSVM	37.6	26.5	33.9	22.5 71.2	66.7 66.8	17.4	21.9	44.8	40.9
	Latent SVM	36.9	28.0	32.2	20.6 65.3	68.2 63.5	13.4	21.6	45.7	39.5

Additional annotation provided is the bounding-box obtained by a standard person detector overlapping most with the ground-truth bounding box in PASCAL VOC.

Acknowledgements

This work is partially funded by the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013)/ERC Grant agreement number 259112, and the INRIA International Internship Programme.


Zewen Liu

Huiliang Liu

Julien Sarrazin

Tunable RF MEMS and Its Applications

With fast development of mobile communication technology, the increasingly complex communicating environment and the crowded spectrum have raised stringent requirements on the RF front-end performance. In this paper, the influence of human body on the communication performance is analyzed. In particular, it is shown that the antenna input impedance faces huge variation in the frame of body-centric devices. Consequently, automatic impedance matching appears to be crucial to improve the performance withstand the inconstant environment. The investigation of key tunable components of RF MEMS is therefore presented. A variable capacitor with symmetric balanced structure is designed to achieve a large capacitance tuning ratio and a remarkable linearity of the C-V response. The proposed RF MEMS variable capacitor was modeled and simulated. The results show a linearity factor of 99.82% in C-V response and a large tuning ratio of 480% in a low actuation voltage range from 0V to 16.3V.

Introduction

With fast development of wireless communication technology, the growth in the number of mobile users has been explosive. Besides the requirement of voice communication, the growth of the usage of mobile internet and multi-media services are still far from saturation [START_REF] Bolton | Mobile Device RF Front-End TAM Analysis and Forecast[END_REF], which also drives the demand for higher data rates. The mobile terminals continue to develop to multi-mode multi-band devices at a rapid pace [START_REF] Sahota | RF front end requirements for 3G and beyond[END_REF]. For example the 3GPP release 11 standard has twenty RF bands (3). The realization of multi-band multi-mode device needs to be supported by reducing form factor, complexity and BOM count of modules [START_REF] Cheng | Compound Semiconductor Integrated Circuit Symposium (CSICS)[END_REF], which cause stringent requirements on design. Tunable RF MEMS supplies possible solution to make the front-end modules reconfigurable for different bands and modes to meet the space limitation with reduction of the component number [START_REF] Walsh | 3G/4G Multimode Cellular FrontEnd Challenges[END_REF][START_REF] Rebeiz | IEEE 13th Topical Meeting on Silicon Monolithic Integrated Circuits in RF Systems (SiRF)[END_REF]. The greater effect of human body on multi-band multi-mode device is another reason to make the front-end tunable. The detail influence of human body on the communication performance is analyzed in next section, by considering the characteristics of propagation in close proximity of the human body. From this study, the need of automatic impedance matching networks is highlighted. To meet the requirement of such applications, tunable RF MEMS components are considered in this paper. With its advantage of low loss, high Q-factor and high linearity, the excellent electrical performance of RF MEMS tunable capacitors determines the good selectivity and linearity. Several typical structures of RF MEMS variable capacitors are investigated. The design of a symmetric balanced structured MEMS varactor, with flexible upper plate of the capacitor moves upwards when the voltage added on the control electrodes increases, presents a highly linear decrease of the capacitance with increasing control voltage.

Effect of human body

In addition to the consideration of integration, the effect of human body on multiband multi-mode device is another reason to make the front-end tunable. The increasingly complex communicating environment with the instantaneous change of human effect has raised more stringent requirements on the RF front-end performance, especially on the antenna behavior. Two main sorts of degradation can be caused by the operator's gesture. One is the increase of absorption, the other is the increase of detuning or impedance mismatching. The increase of user interaction would cause a change in the antenna driving point impedance, as the antenna becoming more resistive and inductive [START_REF] Boyle | [END_REF]. In the frame of Body Area Networks (BAN), where multiple sensors are embedded on the human body or in the clothes, this issue is even more critical. Depending on the human posture or on the space between the cloth and the skin, the environment surrounding the antenna changes drastically. This has an effect on the near-field distribution of the antenna, thereby modifying its input impedance over time. Consequently, in order to increase antenna efficiency in all flexible conditions, an impedance matching network needs to be considered. To get an idea of the range of variation that the input impedance of an antenna can face in close proximity of the human body, a miniaturized loop antenna (so non-resonant) has been simulated over human tissue at 2.45 GHz with CST Microwave Studio. As a first approximation, the tissue is supposed homogeneous and has a relative permittivity of ε r =50 and a conductivity of σ=1.7S/m (8). The radius of the loop is a= 7 mm and the distance between the loop and the human tissue is h. Antenna input impedance results are shown in Figure 1 over the distance h. It can be noticed that the variation cannot be neglected and the real part of the impedance decreases from 165Ω down to 12.2Ω as the distance h between the antenna and the human tissue increases. The imaginary part does not follow a constant increase or decrease and is consequently less predictable. It faces a variation of 14% about its mean value.

These results highlight the need of automatic matching impedance circuits for devices operating in close vicinity of human body. Networks capable of matching a wide range of impedance values use tunable capacitors (9). Furthermore, the power consumption of such matching networks should be kept as low as possible. Consequently, RF MEMS technology appears to be a good candidate as it can provide variable capacitors with lowloss, high linearity and low power consumption.

Tunable RF MEMS Components

The development of RF MEMS switches, capacitors and the integration of these elements into tunable filters, phase shifters and matching networks has been extensively investigated [START_REF] Rebeiz | RF MEMS Theory, Design, and Technology[END_REF]. Both switched and voltage controlled variable capacitors can be used as a tuner in RF front end [START_REF] Rebeiz | [END_REF]. A good example of the switched capacitor has been developed within a mass production capable HV RF CMOS process [START_REF] Natarajan | IEEE 11th Topical Meeting on Silicon Monolithic Integrated Circuits in RF Systems (SiRF)[END_REF]. These RF MEMS capacitors are grouped in flip-chip cells that exhibit a high quality factor of 87 at 2 GHz and operate using a 3.3V supply voltage. The tuning ratio of on-state and off-state is almost 10:1. As it only has two steady state, the switched capacitor can be used in switchable array to form a digital tunable capacitor [START_REF] Morris | [END_REF]. Compared to switched capacitor, MEMS variable can be tuned continuously with precise capacitance control within the tuning range. But one challenge is the nonlinear C-V response of the common parallel-plate MEMS varactor. The capacitance value changes faster near the pull down point [START_REF] Rebeiz | RF MEMS Theory, Design, and Technology[END_REF], which makes the capacitor more sensitive to the little change of control voltage. To avoid the pull-down effect and enhance the capacitance change range with high linear, a Non-Planar Up-plate and Side Leverage Electrode RF MEMS capacitor (NPUSLE capacitor) is proposed in this paper.

Variable Capacitors

The schematic structure of the proposed variable capacitor is shown in Figure 2. The variable capacitor consists of a movable upper plate and a fixed bottom plate. The symmetric balanced leverage structure controls the movement of the upper plate. Two additional non-plane step structures connected to the upper plate result in a decrese of the initial gap of the capacitor to increase the incipient capacitance value and also lead to a reduction of the upper plate deformation to release the stress. Electrostatic force emerges and makes the upper plate of the capacitor moves upward when control voltage is added. The increasing gap between the upper and bottom plates results in the reduction of capacitance value. The change rate of the plate displacement increases as the control voltage increasing while the change rate of the capacitance value decreases. Therefore, the counteraction of these two change rate leads to a high linearity of the C-V response. As the initial capacitance value is optimized by the non-planar step structure, a variable capacitor can be achieved with a large capacitance tuning ratio and linear C-V response. Figure 3 shows the cross-section of half of the symmetric capacitor structure. When V is added to the control electrode, an electrostatic torque M e emerges. Then the deformation of the torsion beams generate the restoring torque M t . An equilibrium will be reached when the two torques are equal as [START_REF] Bolton | Mobile Device RF Front-End TAM Analysis and Forecast[END_REF] where K is the torsional spring constant of the torsion beam and a is the rotation angle of the lever beam. The electrostatic torque M e can be expressed as [START_REF] Sahota | RF front end requirements for 3G and beyond[END_REF] (14) where ε 0 is the permittivity of air, A e is the area of the control electrode and the other geometrical parameters are shown in Figure 3. The torsional spring constant K t can be calculated as [3] (15) Where l t , w t and t t represent the length, width and thickness of the torsion beam, respectively. G is the shear modulus of the torsion beam, which is 27 GPa for gold. The the expression of the control voltage V can be derived from the equation [START_REF] Bolton | Mobile Device RF Front-End TAM Analysis and Forecast[END_REF] as [START_REF] Cheng | Compound Semiconductor Integrated Circuit Symposium (CSICS)[END_REF].

ε    - =- +    -- -    [2]
ε = - -+ -- - [4]
The capacitance value between the upper and bottom plates can be expressed as [START_REF] Walsh | 3G/4G Multimode Cellular FrontEnd Challenges[END_REF] 34

34 0 Si N Si N c A C t g ε ε = + [5]
where A is the area of the capacitor plate, t Si3N4 is the thickness of the Si N 4 isolation layer on the bottom plate and ε Si3N4 is the dielectric constant of Si 3 N 4 . The gap between upper and bottom plates g c could be approximately expressed as [START_REF] Rebeiz | IEEE 13th Topical Meeting on Silicon Monolithic Integrated Circuits in RF Systems (SiRF)[END_REF] due to the lever principle and the neglect of lever deformation.

( )

2 00 1 = cc l gg g g l ×-+ [6]
To design a variable capacitor with large tuning ratio, low control voltage and initial capacitance value C max more than 2.5pF, the capacitor plate area is designed 200 × 200 µm 2 . (The width of the control electrode is also 200µm.) The Thickness of Si 3 N 4 isolation layer, t Si3N4 , is 3000Å. The initial gap between the capacitor's upper plate and lower plate, g 0c , is 0.1µm. To get a stable structure and a reasonable control voltage, the length, width and thickness of the torsion beam, l t , w t and t t , are 50µm, 25µm and 2µm, respectively. Zero-biased beam height of the outer end of the lever, g 0 , is 3µm. Then, the relationship between l 1 , l 2 and l 3 will be analyzed and how they affect the linearity of C-V response will be presented. Finally, the optimized parameters will be given. The linearity factor LF can be calculated as [START_REF] Boyle | [END_REF] 00 0 22 22 00 0 0

nn n ii i i ii i nn n n ii i i ii i i nC V C V LF nC C nV V == = == = = - =      --              ∑∑ ∑ ∑∑ ∑∑ [7]
To analysis how lever ratio l 1 / l 2 affect linearity of C-V response and the capacitance tuning ratio, Figure 4 shows the relationship of gap distance g c versus control voltage and capacitance versus control voltage with different lever ratio l 1 / l 2 . When l 1 / l 2 changes from 1 to 10, the capacitance tuning ratio diminishes as 814%, 671%, 457% and 171%, respectively and the calculated LF values are 98.32%, 98.99%, 99.86% and 96.95%, respectively. The tuning ratio is maximized when l 1 / l 2 =1 due to the larger g c , but the LF value 98.32% does not reach the maximum in this situation. As calculated, the optimized LF value maximizes to be 99.90% when l 1 / l 2 is 1.875 and the capacitance tuning ratio is 470% in this situation. To analysis how relative length of control electrode l 3 /l 1 affect the control voltage and linearity of C-V response, Figure 5 shows the relationship of gap distance versus control voltage and capacitance versus control voltage with different relative length of electrode l 3 /l 1 . When l 3 /l 1 changes from 0.2 to 0.8, the calculated maximum control voltage needs to be 26.0V, 18.8V, 16.8V and 16.1V, respectively, to achieve a fixed tuning ratio. The LF value diminishes as the relative length of control electrode l 3 /l 1 increses, which is 99.94%, 99.91%, 99.86% and 99.80%, respectively. This reveals the smaller relative length of control electrode l 3 /l 1 offers a higher LF value, but also needs a higher control voltage to achieve the same tuning ratio. Considering the design target of low control voltage and the lithography margin in fabrication, the relative length of control electrode l 3 /l 1 was set to 0.75 in this work with a tradeoff with linearity. Considering the balance and stability of the whole structure, the l 1 , l 2 and l 3 were finally set to 150µm, 80µm and 110µm, respectively. The optimized structure parameters are listed in TABLE 1. The simulated control voltage was 16.3V with the 480% capacitance tuning ratio as shown in Figure 6. The calculated LF value was 99.82%. LF = 99.82%

◇ l 1 / l 2 =10 □ l 1 / l 2 =2 ○ l 1 / l 2 =1.25 ※ l 1 / l 2 =1 (a) (b) ◇ l 1 / l 2 =10 □ l 1 / l 2 =2 ○ l 1 / l 2 =1

Conclusion

The influence of human body on the communication performance is analyzed. According to the simulation over human tissue at 2.45 GHz, the input impedance of a miniaturized loop antenna changes tremendously, which includes the decrease of real part from 165Ω to 12.2Ω and 14% variation of imaginary part, with the gap between antenna and human tissue increase from 2mm to 10mm. A variable capacitor with symmetric balanced structure is designed to achieve a large capacitance tuning ratio and an remarkable linearity of the C-V response. The proposed RF MEMS variable capacitor was modeled and simulated. The effect of lever ratio and control electrode size on C-V linearity is analyzed. The results show a high linearity factor (LF) of 99.82% in C-V response and a large tuning ratio of 480% in a low actuation voltage range from 0V to 16.3V.

Figure 1 .

 1 Figure 1. Antenna input impedance variation above human tissue

Figure 2 .

 2 Figure 2. The 3-D structure of the variable capacitor

4 Figure 3 .

 43 Figure 3. Cross-section of half part of the symmetric capacitor

Figure 4 .◇ l 3 / l 1 =0. 2 □ l 3 / l 1 =0. 4 ○ l 3 / l 1 =0. 6 ※ l 3 / l 1 =0. 8 ◇ l 3 / l 1 =0. 2 □ l 3 / l 1 =0. 4 ○ l 3 / l 1 =0. 6 ※ l 3 / l 1 Figure 5 .

 432343638323436315 Figure 4. Calculated results of (a) gap distance versus control voltage (b) capacitance versus control voltage when l 1 / l 2 is 1, 1.25, 2 and 10.

Figure 6 .

 6 Figure 6. Calculated result of C-V response with optimized structure parameters.

TABLE I .

 I Structure Parameters.

	Parameter	Value	Parameter	Value
	Area of the capacitor	200 × 200 μm
	plate (A)

2 Area of control electrode (A e ) 110 × 200 μm 2 Length of the outer end of the lever (l 1 ) 150μm Length of the inner end of the lever (l 2 ) 80μm Thickness of the upper plate (t) 2μm Zero-biased beam height of the outer lever (g 0 ) 3μm


Luca Petrillo
email: lpetrill@ulb.ac.be

Theodoros Mavridis

Julien Sarrazin
email: julien.sarrazin@upmc.fr

Jean-Michel Dricot

Aziz Benlarbi-Delaï

Philippe De Doncker

BAN Working Frequency: a Trade-Off Between Antenna Efficiency and Propagation Losses

Keywords: Millimeter wave propagation, Surface waves, Wireless body sensor networks

This communication addresses power issues at physical layer in Body Area Networks. Friis equation is discussed by taking into account body path loss and antenna efficiency from frequency ranging from 400 MHz to 60 GHz. Then power balance is presented for fixed antenna dimensions and varying frequency in order to establish a balance.

I. INTRODUCTION

Medical sector is facing great challenges nowadays. The capacity of healthcare system has not kept pace with the demand for emergency and trauma care. Emergency Departments today operate at or over capacity. Aging population requires also more health-care. In a period of economical crisis, efficiency of the medical system needs to be increased significantly.

Recent years have witnessed the emergence of wireless Body Area Networks (BANs) for medical applications. BANs are sensor networks that are embedded on the human body and provide useful health-care monitoring such as EEG (Electroencephalography), ECG (Electrocardiography), EMG (Electromyography), blood pressure, glucose... The use of wireless technology to interconnect sensors enables practical and seamless means to monitor patients. It thus can lead to more efficient patient's management in hospital and during mass-casualty disasters by automatically monitoring the vitals signs of many patients simultaneously to shorten patient's wait-times. If BANs are connected to the Internet through a cellular network for example, they can also achieve continuous monitoring. This aspect has great outcomes since it is the key for fighting disease with a preventing approach and detecting at an early stage when a person's health changes to the worse, thereby preventing emergency cases such as heart attacks. Continuous monitoring also represents a comfortable and effective economic way of taking care of age-related illnesses. Furthermore, these capabilities enable large-scale infield medical and behavioral studies.

Consequently, Medical BANs (MBANs) have a huge potential and are expected to become a successful medical system that will help in solving the medical crisis and also in creating a new market in medical ICT (Information and Communication Technologies).

A key success factor of such wireless sensor networks will be their potential to be autonomous in terms of energy. In fact, depending on the applications, sensors have to operate during a few hours up to a few years while relying on batteries or, as considering by on-going research studies, on micro energy harvesters or wireless power transfer. In any case, the amount of available energy is limited. This limitation becomes more crucial as sensors decrease in size, thereby limiting the room for battery. However, for patients to accept wearing such BANs, it is obvious that sensors should be as small as possible.

Consequently, this communication addresses the power issues at the physical layer by considering the propagation channel on the human body surface and the antenna characteristics. In particular, the trade-off between sensor miniaturization and operating frequency will be discussed. Some theoretical bounds will be drawn for the path gain between sensors of a given size and operating at a given frequency.

II. BODY CHANNEL

Body channel for BAN has been widely studied at frequency ranging from 400 MHz to 60 GHz and beyond. Path loss and shadowing have been investigated in different scenarios, for static and dynamic cases, for vertical or horizontal polarization. For our study, we are interested in giving a generalized Friis equation in order to compare the influence of the gain of the antennas and the spatial attenuation on the received power. Analytical expressions can be used for this scope. Friis equation is :

P r = P t + G t + G r + 20 • log 10 λ 4πr (1)
where P t and P r are radiated and received powers in dBm, G t and G r are the gains of the antennas at the transmitting and receiving side in dB, λ is the wavelength in free space at the operating frequency and r is the distance between transmitter and receiver. The term 20 • log 10 λ 4πr is the free-space path loss and it can be modified by taking into account the presence of the human body. For instance, in the case of planar (same side of the torso) on-body propagation, Norton equations can be used [?] [?]. In Fig. ?? we have traced body channel measurement reported in the literature [?], [?] and we have compared them with the modified Friis path-loss term :

20 • log 10 λ 4πL(r) (2)
where L(r) is extracted from Norton formulations for an elementary dipole radiating above a conducting surface [?]. In that can be seen that (??) fits well measurement at 400 MHz, 2.45 GHz and 60 GHz, even at distances d < λ. It is important to note that using Friis equation allows to consider antenna gain as well. For on-body propagation around the torso, experimental results are well predicted by creeping wave formulations [?], [?]. Again, these formulations can be used to extend Friis formula for propagation around the body.

III. ANTENNA GAIN

In BANs, antennas dimensions play a crucial role, since their miniaturization is a key factor for wearability. However, miniaturization can affect gain through efficiency, which, at lower frequencies, can result in a very low gain. Thus, the physical limitations of small antennas is determined using the well known Chu expression [?] in order to obtain the Q-factor of the small antenna as well as its input impedance. Using these characteristics, the appropriate matching network can be designed using a two-element L-section network. Knowing the antenna's Q-factor and its matching circuit, the overall efficiency η s can be then calculated using expressions given in [?]. Fig. 2 shows the efficiency η s of a small antenna of diameter 5 mm with respect to frequency. Results are given for several Q-factor values of the matching circuit components.

IV. CONCLUSION

In this communication the propagation channel and the antenna gain are discussed for BANs ranging from 400 MHz to 60 GHz. A modified Friis equation is proposed for taking into account the body channel and then a on-body path loss term is introduced and compared with measurement results reported in the literature. Antenna efficiency with respect to antenna dimensions and matching circuit Q values is studied. In the conference speech, we will point out conclusions about the trade off between path-loss and efficiency at different frequencies of interest for BANs.

Fig. 1 .

 1 Fig. 1. Modified Friis path-loss term (solid lines) and path-loss model from measurements (dotted lines) for three frequencies in BAN scenario.

Fig. 2 .

 2 Fig. 2. Small antenna (diameter equal to 5 mm) efficiency with respect to the frequency for different Q values of the matching circuit components.


Martin Seidl
email: martin.seidl@leesu.enpc.fr

Claire Bich

Thuy Trinh

Dominique Imbert

Gilles Hubert

Dual water supply system as a way to better resources utilization. The case of Paris

Keywords: water reuse, dual supply systems, urban non potable water uses, Paris, sustainability indicators

The rarefaction of the water resources and the degradation of their quality are a major challenge of the 21st century. France, although it has important water reserves, is not free from these problems. As most industrialized countries, France uses great quantities of water of its rivers and its water ground water for drinkable water supply, but also for industrial processes, of urban cleaning and irrigation which, in theory do not require a high water quality. These processes could be satisfied by non potable water like raw water, the rainwater or recycled water like treated effluents. Like rainwater harvested and used for toilet flushing, alternative resources to drinking water could be used for other urban uses such as green spaces watering or roadways cleaning.

The use of non potable water not only makes it possible to preserve the natural resources, by avoiding in situ extraction, but improves also the sustainability of the urban system by limiting energy consumption necessary for extraction, treatment and transportation. In case of domestic effluent reuse for watering and irrigation also nutrients like phosphorus and nitrogen are saved.

In Europe 1 billion m3 (2.4% of total use) are re-used, mainly in the countries like Spain, Italy and Greece. In France recycling is limited to agriculture (Clermont Ferrand, Achères,…) or to irrigation of golf course. In Europe Spain is one of the rare countries using reclaimed water for urban purposes as street cleaning. Nevertheless in France we can find several cities like Paris, Nice and Lyon using raw water for non potable urban services.

If we consider the usual urban water cycle, we can observe a linear use starting with extraction usually upstreams of the urbanized area, passing by potabilisation in peripheral area, in city use and waste water treatment and discharge downstream of the urban area. The agricultural re-use can be seen as ultimate step of treatment and a point to point application. An urban re-use however, obliges to reconsider the trajectory of water. The return of water downtown or cyclic use, requires a specific delivery system. Some cities like Madrid or Hong Kong with an important hydric stress has implemented such a dual system. Though cities owning already a dual system due to historical practices of different water type use (application of treated raw water for private inside uses and non treated water for collective outside uses), can optimize their dual system according to all available non potable resources.

The recent re-municipalization of water services in 2012 in Paris and the on going rehabilitation of its non-drinkable water supply network give to Paris the possibility to exploit other resources like ground water pumped from metro system and treated domestic waste water. The use of alternatives urban resources incontestably requires an adaptation of the uses and their organization.

The presentation proposes a schematic overview and first analysis of the existing resources in the urbanized perimeter of Paris, the actual and potential uses and a selection of possible modifications of the flows on global and local scale. The data used were collected in 2012 after the re-municipalization in the framework of research programmes PIRVE and OPUR4 within the technical services of the Paris municipality, the new public distribution company Eau de Paris and field surveys. The data are treated with flow chart programs and GIS. Based on preliminary interviews with the principal actors the article will present first insights in organizational and institutional bottlenecks linked to new uses and supply schemes.

  7th biennial IWA Efficient Conference: "Water Efficiency Strategies for Difficult Times." October 22-25, 2013 in Paris.