# A New Approach to Image-Based Estimation of Food Volume
## 3 System Evaluation  
We have already evaluated the segmentation algorithm as well as the checkerboard detection method that we use to set a size reference separately in our previous works, where we introduced such approaches [11; 12]. In this work, we completed the system and could finally evaluate the accuracy of our solution for estimating an object's volume. The main objective of the study was to establish a robust and consistent method to estimate food volume. This means that, first, the method should estimate the same volume for the same amount of food in different dishes. Then, the method should present a steady correlation between food amount and estimated volume when one changes the amount of food. If the algorithm is able to produce a result correlated with the actual food amount, it could later be translated into a good estimation of the actual nutrition facts of the food. We evaluated the method using two common types of food items: food items with a solid shape and food with non-solid shapes. In both procedures, we assumed that the shapes were more or less convex, in order to keep the volume estimation simple. Thus, it was possible to estimate the volume of the models that we generated using the Qhull tools [35]. Furthermore, for each test case, we ran the whole procedure twice to have more reliable results. All of the tests were performed on a PC equipped with an Intel(r) CoreTM\(i\)7 2.8 GHz CPU and running the 64-bit version of Windows 7 Professional (Microsoft Corporation Redmond, WA, USA). For the first group, six types of bread were chosen as the test cases. Since we took convex objects into consideration, in this case, our goal was to evaluate the accuracy of the reconstructed shape. In order to establish a precise ground truth, we used an industrial 3D laser scanner _Sick LMS400_ (SICK AG, Waldkirch, Germany) to acquire as accurate a 3D model of the test objects as possible. The device has a spatial resolution of 1 mm and the scanned model was manually segmented to acquire a more accurate ground truth. Table 1 shows the results obtained on the first group of food items (different sorts of bread). The average error rate of the whole process (including acquisition, view selection, segmentation, size reference detection, and 3D model reconstruction) over all cases was 8.27%. As shown in Table 1, the error rate for item number 5 is larger than for the other items due to its poor visual context. In fact, it has a smoother surface showing small variations of shade and color, which allows one to extract only few relevant features. The error on item number 6 is also higher than expected, despite its rich visual context. This appears to be a consequence of its small size, which increases the relative weight of noise. The average processing time on this first test set, including the whole process from segmentation to volume estimation, was around 21 s.  
In the second part, we made tests with pasta and rice as examples of food with non-solid shapes. Two types of evaluations were made on this test set. First, in order to assess the stability of the method, we made several independent tests with the same amount of the same kind of food. For example, for each type of pasta, the same amount of raw pasta was cooked and tested on two different dishes. In addition, for each dish, the test was repeated with a different layout as well (in total, four times for the same amount of pasta). As a second evaluation, we tested the correlation between the actual food weight and the estimated volume. To do so, we cooked twice the weight of the same kind of pasta in the previous dish and checked the correlation between its estimated volume and the estimate of the volume of the previous dish. Moreover, since cooking time can affect the results, all of the test cases were cooked in the same pot at the same time (the same happened with rice).