MD Measures in .NET

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4.3 MD Measures
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If the object is metallic, the size and shape detected by an MD should ideally correspond to those found by GPR and IR. If it has a low metal content, the shape and size of the metal cannot be linked with the detections of the other two sensors. The same distinction appears in the terminology of humanitarian demining, where mines are classified, on the basis of their metal content, into three types: metallic, low-metal content (so-called minimum metal content [34]) and nonmetallic. In this classification, a metallic mine is one made almost completely of metal, except e.g. handles, while a mine with low metal content has metal only in small parts, e.g. in the fuse. In addition, depth extracted from deconvolution of the MD image could be used in a similar way as the depth information extracted from GPR. [35]. However, in reality, the scanning resolution in one dimension is set to be around the expected size of AP mines, as a compromise between the necessity not to miss any mine, on the one hand, and on the other, the speed of the data acquisition and the field area to be analyzed. For such a resolution, which is around the size of an AP mine, there is no use of the area and shape measures. Furthermore, due to the fact that there is no knowledge on the PSF of the applied MD, and besides that the image is saturated and the resolution is poor, depth measure extraction through deconvolution is impossible. From each of the regions selected by the local maxima analysis method for saturated images, with or without windows (see Section 3), three parameters can be extracted: number of pixels, Np ; the value of its local maximum, Vmax ; the width of the region in the y-direction, wy .
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5. Modeling of Measures in Terms of Belief Functions and Their Discounting
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In real mine detection situations, the acquired data are far from numerous enough for reliable statistical learning. Besides, they are highly variable depending on the context and conditions [36]. Furthermore, not every possible object, neither mines nor objects that can be confused with them, can be modeled. On the other hand, some general knowledge exists regarding AP mines, their sizes, shapes, burial depths, etc., as well as regarding detection possibilities of each of the sensors. For these reasons, we decide to model and combine the measures of each of the sensors in terms of belief functions within the DS theory, since in this framework, ignorance, partial knowledge, uncertainty and ambiguity can be appropriately modeled [4,5]. Note that all three sensors give images, around 90 % of the mines have an elliptical (regular) top surface seen under some angle, and the major goal of our humanitarian demining efforts is to distinguish between a mine and a non-dangerous (friendly) object (stones, cans, etc.). Therefore, we define the frame of discernment as: = MR, MI, FR, FI . Here, MR is a mine of regular shape, MI a mine of irregular shape, FR a friendly object of regular shape and FI a friendly object of irregular shape. The modeling step aims to define a mass function for each measure expressing the information provided by this measure on the presence of a mine. Note that the mass function is the distribution of an initial unitary amount of belief among the subsets of [6]. In the following, we present a model for each of the measures, based on a bibliographic survey, as well as on the single sensor trials
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Improving Mine Recognition
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within the Belgian HUDEM (HUmanitarian DEMining) project [3]. The proposed equations for mass assignments are only examples illustrating the required tendencies. The numbers and parameters in these mass functions are not really important. Only the general shape of these functions matters, and the method is robust with respect to the choice of parameters. Usually, one of the difficulties when using belief functions is the definition of focal elements, and in particular of disjunctions. The approach we propose here relies on the specificities of the proposed measures. For example, a shape measure is not able to separate MR and FR, and their disjunction will therefore be considered for mass assignment. This approach is detailed for each sensor and each measure below.
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