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There are different applications in Engineering that require to compute improper integrals of the first kind (integrals defined on an unbounded domain) such as: the work required to move an object from the surface of the earth to infinity (Kynetic Energy), the electric potential created by a charged sphere, the probability density function or the cumulative distribution function in Probability Theory, the values of the Gamma (Γ) function (which is useful to compute the Beta (β) function used to compute trigonometric integrals), Laplace and Fourier Transforms (very useful for example in Differential Equations),. .. Therefore, these applications need to deal with the following types of improper integrals:

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There are currently several new technologies being used to generate digital elevation models that do not use photogrammetric techniques. For example, LiDAR (Laser Imaging Detection and Ranging) and RADAR (RAdio Detection And Ranging) can generate 3D points and reflectivity information of the surface without using a photogrammetric approach. In the case of LiDAR, the intensity level indicates the amount of energy that the object reflects after a laser pulse is transmitted. This energy mainly depends on the material and the wavelength used by LiDAR. This intensity level can be used to generate a synthetic image colored by this attribute (intensity level), which can be viewed as a RGB (red, green and blue) picture. This work presents the outline of an innovative method, designed by the authors, to generate synthetic pictures from point clouds to use in classical photogrammetric software (digital restitution or stereoscopic vision). This is conducted using available additional information (for example, the intensity level of LiDAR). This allows mapping operators to view the LiDAR as if it were stereo-imagery, so they can manually digitize points, 3D lines, break lines, polygons and so on.