## 1 Introduction  
Nowadays, the micro-scale spherical and cylindrical surface modeling plays an important role in inspecting micro-scale sphericity and cylindricity [1, 2]. In the micro-scale manufacturing industry, object machining, surface roughness, drilling, and object measurements are determined via spherical and cylindrical surface models and robotic vision systems [3, 4, 5]. To achieve these manufacturing processes, mathematical models have been implemented to represent micro-scale spherical and cylindrical surfaces. For instance, the spherical surface modeling has been implemented in geomatics to determine rock surface sphericity [6, 7], in optics to estimate lens sphericity [8, 9], in object machining to determine surface sphericity [10, 11], in pharmaceuticals to determine proppants sphericity [12, 13], in object prototyping to determine assemble sphericity [14, 15], and so on. Moreover, the cylindrical surface modeling has been implemented in surface machining to inspect cylindrical surface [16, 17], in surface milling to estimate milling cylindricity [18], and so on. Based on these statements, surface models have been constructed via surface data and mathematical equations for representing micro-scale spherical and cylindrical surfaces [19, 20]. Currently, micro-scale spherical and cylindrical surface models are carried out via surface information, which is retrieved by means of optical microscope imaging systems [21, 22]. These microscope systems construct the surface models by employing surface data obtained via gray-level image processing and the least squares method [23, 24]. In addition, the least squares optimization is employed by the vision systems' models to determine surface data [25]. However, sometimes the least squared method does not provide the most accurate model fitting [26]. Therefore, artificial intelligence algorithms have been implemented to accurately construct surface models. For instance, an algorithm with an adaptive fuzzy logic controller has been implemented to construct spherical surface models [27]. This algorithm minimizes an error function by employing surface data to obtain the spherical surface model parameters. Furthermore, a harmony search algorithm has been implemented to construct cylindrical surface models [28]. This algorithm implements a music process by employing surface data to optimize an error function to obtain the cylindrical surface model parameters. Usually, the spherical and cylindrical surface modeling is carried out by an optical microscope imaging system, which retrieves the surface shape via gray-level image processing. For instance, an optical microscope system based on machine vision determines micro-scale spherical surface via gray-level image processing [29]. In the same way, an optical microscope imaging system computes the micro-scale cylindrical surface by means of a frequency transform via a gray-level image [30]. The above-mentioned optical microscope systems determine the micro-scale surface topography via a gray-level profile. However, the gray-level profile does not depict accurately the surface profile. It is because the gray-level depends on the light source, surface reflectance, and the viewing angle. This means that the gray-level profile does not reproduce the surface topography. Therefore, the spherical and cylindrical surface models do not fit to the surface with great accuracy. This leads to a decrease in the micro-scale surface modeling accuracy. Based on these statements, it is established that the micro-scale surface modeling performed by the optical microscope imaging systems still represents a difficult task. To improve the micro-scale spherical and cylindrical surface modeling accuracy, the surface models should be generated by means of the surface topography. The proposed micro-scale spherical and cylindrical surface modeling is carried out by a metaheuristic genetic algorithm based on micro laser line projection, which depicts accurately the surface topography.