## 1 Introduction
In our case study, starting from the image of a render representing a building in ruins, we intend to obtain the image of the restored building. As we do not have missing pixels but missing architectonical elements, we have defined our work as virtual restoration inpainting, a method to synthesize objects from pixels so that these objects are semantically coherent with the context represented in the rest of the image. The motivation for this work arises because when it comes to virtual restoration. In this way, the appearance that the original construction must have had is based on assumptions and, therefore, on an uncertain solution. However, in some cases, references to determine the original state may be evident. For example, using historical photographs, in most cases, there is no reliable information available on how the missing elements could have been organized. The thesis we put forward is that the architectural language, based on a repetition of constructive, compositional, and structural patterns, can be decisive in intuitive effective solutions for virtual reconstruction. The study of the architectural language of a period or style from the analysis of these patterns can help to consolidate a new and more efficient reconstruction methodology by benefiting from deep learning models. The problem is that we need evaluations adapted to the problem of reconstructing the missing architectural elements of a building in such a way that they make sense from an architectural point of view. The work presented in this paper is based on [3], where different methods were used to restore images of renders representing Greek temples in ruins. In that previous paper, one of the methods was based on the use of a segmented image in which the different architectonical elements were marked with different colors. Although this method obtains really good results, using this segmented image supposes a high expenditure in computational and human resources and time. Our research now explores approachesbased on direct training of GAN (Generative Adversarial Network) models, which means that from only the image of the render of the ruined Greek temple can we obtain its restored version. To this end, we have improved our dataset and fine-tuned the neural models by using different sets of hyperparameters and testing different activation functions among the most up-to-date options currently used in other DL fields. Although this is an improvement from the previous work, the main innovation lies in the process used to evaluate the results of the task of reconstructing Greek temples from images of 3D renders. As the main objective is to reconstruct the architectonical elements, we provide a method to evaluate this task, avoiding problems that arise from the generation of artifacts, image quality, and other issues. These results are assessed through objective (using mathematical metrics) and subjective (asking an expert in the field) evaluations to measure the strengths of direct training that does not have intermediate steps as using segmented images. As mentioned above, this work consists of a method that receives an image of a render representing a Greek temple in ruins and can directly detect which are the missing architectonical elements, returning the same image with the restored temple. For this purpose, we have used generative adversarial networks (GANs) that have been trained with only pairs of an image of the ruined temple and its corresponding image with the complete temple. Following, we list some works related to the actual research. As this work can be framed in the field of data-driven image analysis, we can highlight the following works. In [4], a survey of data drive image methods using Machine Learning or Deep Learning methods applied to digital restoration in the field of cultural heritage is presented. A data-driven methodology for managing and conserving archaeological heritage sites using digital surveying tools and Heritage/Historic Information Modeling (HBIM) within a BIM environment is introduced by [5].