## 1 Introduction  
Evaluation of paintings' authenticity has always been under great attention due to the importance of protecting intellectual property in art. Significant value of the \"name\" of the artists behind the artworks encourages art forgers to mimic the artworks of famous artists [1]. Addressing the subjective nature of authenticity and the interdisciplinary demands of the detection process complexities requires a harmonious blend of traditional art expertise, cutting-edge technology, and rigorous historical research to preserve the integrity of cultural heritage. Computer vision (CV) models are one of the approaches that have demonstrated promising results in addressing the issue of forged painting detection. In this respect, the dependence of the supervised trained models on extensive large amounts of data annotated by the experts has been a crucial challenge for solving this problem using AI models [2]. In addition, extracting features of the artworks in a different stage makes the previous research less automatic to classify or identify the artist [3]. Based on expert analysis orientation, distribution and shape of brushstrokes are recognized as distinctive brushstroke signatures or brushstroke style of the artist [4]. In addition, to highlight the significance of brushstroke styles, a cross-cultural study compared Eastern and Western brushstroke styles, highlighted philosophical differences in art, with Chinese strokes emphasizing flow and spirituality versus Western emphasis on form and texture [5]. The artist's brushstroke representation was used as one of the main sources of information for reflecting the artist's unique style [6] and for training the Convolutional Neural Network (CNN) models [7; 8]. In addition, generator models such as Stable Diffusion and StyleGAN show promise in enhancing forged painting detection by generating synthetic images for training datasets [9]. Reflectance Transformation Imaging (RTI) is one of the methods for representing 3D information in 2D images that makes it possible to capture multiple high-resolution in-depth images. The RTI technique improves the features of artwork's surface shapes and colors using mathematical functions by providing the interactive lighting direction of the artwork [10; 11]. This makes the RTI method a suitable candidate for acquiring sufficient and informative datasets for training the CNNs [12] (the details of capturing RTI images are described in Section 4.1). Here, we proposed a painting's forgery detection method that learned the features of depth brushstroke representation from the original artist's style based on conditional Generative Adversarial Networks (cGANs) and \"pix2 pix\" framework [13]. We trained a model of cGAN to generate the depth visualization of the artist's unique brushstroke style images that were indistinguishable from the original brushstroke RTI image patches. In addition, in this study, both the main artist and the forged artist had no restriction in choosing the density of the brushes for this collection and forgeries. In this research, we made a contribution by adapting the cGAN model to learn the depth characteristics of an artist's brushstroke style, by mapping natural-light painting to RTI painting image patches (see Section 3.1). The total number of paintings used in the training and validation phases was 6, with 3 or 4 images extracted from each painting. In total, 46 images, each at a scale of 7952 \(\times\) 5304, were captured, including 23 natural-light images and 23 RTI images. For details on the quantity of image patches, their scales, and the processing method, see Section 4.2. Next, to assess the authenticity of unseen paintings, we developed two novel approaches (see Sections 3.2 and 3.3). The first method involved calculating patch-level forgery scores for each painting, based on frequency analysis, where the data were converted to grayscale images to minimize the impact of color in the results.