The construction industry's carbon footprint may be reduced by switching to the usage of natural stones as building materials. Construction of dry-joint stone masonry structures is difficult because of the irregular shapes and the nonuniform sizes of the stones, typically requiring skilled masons who are in massive shortage nowadays. Using stone stacking robots provides an efficient solution to build such structures. Therefore, it is crucial to create effective algorithms for designing the layout of stones while guaranteeing the structural and architectonic standards such that a robot can finish the physical construction successfully. The lateral resistance of masonry walls is seldom taken into account by existing algorithms. In this regard, we propose an image-based solution for automating the stacking of raw stones in the construction of 2D load-resistant stone masonry walls. Image processing techniques are employed to speed up the process of choosing and placing stones, as well as to produce a computation model to evaluate the lateral strength of the wall based on limit analysis. The computation simulation models are based on a variational rigid-block modeling method, using mathematical programming to obtain the load multiplier of the wall directly. The structural performance of walls constructed with the algorithm is compared to that of walls constructed using existing algorithms and by expert masons, and competitive typology measures are established to facilitate this comparison. It is demonstrated that the developed algorithm is comparable with skilled masons, capable of building walls of different sizes using different stone data sets efficiently. Based on the results of the computational performance analysis, the algorithm can design a 32-stone wall in just 10 seconds, having the potential to be used in real-time applications with robots for the construction of masonry walls.