In order to take into account the local direction, we count, for a given pixel f **of the found boundary, how** many pixels from the found boundary are linked by the minimal distance to the same pixel e **of the reference**
boundary. This number is noted nef , e.g. **on figure 3**
we have nef = 3 for three different f**. We redefine the**
well-detection boundary measure by:

$$W D C={\frac{}{(\mathbf{n})}}$$

![0_image_0.png](0_image_0.png)

Pf DCf /nef
(maxf (DCf /nef ).Pe We)
a . (6)
The problem is that the number nef **does not adequately represent a number of pixels on the same**
boundary and take into account only orthogonal direction. However this measure gives a good evaluation of the proportion of the found boundaries.

## 3.2 False Detection Boundary Measure

The false detection boundary measure is based on the same principle as the well-detected boundary measure, but the Gaussian-kind distribution of weights must be inversed. Hence we can defined a false detection criterion by:
F DCf = 1 − DCf /We, (7)
where the pixels f and e **are linked by the minimal**
distance df e**. As a consequence, the false detection**
boundary measure can be defined by the normalized false detection criterion by:

$$FD=1-\exp\left(-\frac{\sum_{f}\left(FDC_{f}.n_{e f}\right)}{\max_{f}(FDC_{f}.n_{e f}).\sum_{e}W_{e}}\right).\tag{8}$$

Here we have described the two measures F D and W DC **that compare two images: one image classified**
by the algorithm and the other one provided by only one expert. In order to evaluate image segmentation algorithms on many images and/or fuse the expert opinions, we can use a weighted sum of these both measures. The weights are given by the image sizes, which can be different for all considered images.

## 4 Fusion Of Classifiers Of Sonar Images

presented in [7]. Indeed, underwater environment is a very uncertain environment and it is particularly important to classify seabed for numerous applications such as Autonomous Underwater Vehicle navigation.

In recent sonar works (e.g. **[10, 11]), the classification**
evaluation is made only by visual comparison of one original image and the classified image. That is not satisfying in order to correctly evaluate image classification and segmentation.

$${\frac{n_{e f}}{\cdot\sum_{e}W_{e})^{a}}}.$$
$$(6)$$

## 4.1 Database

Our database contains 42 sonar images provided by the GESMA (Groupe d'Etudes Sous-Marines de l'Atlantique). These images were obtained with a Klein 5400 lateral sonar with a resolution of 20 to 30 cm in azimuth and 3 cm in range. The sea-bottom depth was between 15 m and 40 m.

Three experts have manually segmented these images giving the kind of sediment (rock, cobble, sand, silt, ripple (horizontal, vertical or at 45 degrees)), shadow or other (typically ships) parts on images, helped by the manual segmentation interface presented in figure 4. All sediments are given with a certainty level (sure, moderately sure or not sure), and the boundary between two sediments is also given with a certainty (sure, moderately sure or not sure). Hence, every pixel of every image is labeled as being either a certain type of sediment or a shadow or other, or a boundary with one of the three certainty levels. We choose the weights: 2/3, 1/2 and 1/3, for respectively the certainty levels: sure, moderately sure and not sure. The proportion of each sediment given by the three experts are given in the table 1. Note that the proportion of the different sediment are very different and that can be a problem for the classification. The proportions are very similar for the three experts. We see that sand and silt are the most present and the shadow and other are very few represented on these images.

![0_image_1.png](0_image_1.png)

## 4.2 Fusion Approaches

We present here our image classification and segmentation evaluation in a fusion of classifiers of sonar images We consider here four methods of features extraction based on four representations of the image: