Cross-polarized images are beneficial for skin pigment analysis due to the enhanced visualization of melanin and hemoglobin regions. However, the required imaging equipment can be bulky and optically complex. Additionally, preparing ground truths for training pigment analysis models is labor-intensive. This study aims to introduce an integrated approach for generating cross-polarized images and creating skin melanin and hemoglobin maps without the need for ground truth preparation for pigment distributions. We propose a two-component approach: a cross-polarized image generation module and a skin analysis module. Three generative adversarial networks (CycleGAN, pix2pix, and pix2pixHD) are compared for creating cross-polarized images. The regression analysis network for skin analysis is trained with theoretically reconstructed ground truths based on the optical properties of pigments. The methodology is evaluated using the VISIA VAESTRO clinical system. The cross-polarized image generation module achieved a peak signal-to-noise ratio of 35.514dB. The skin analysis module demonstrated correlation coefficients of 0.942 for hemoglobin and 0.922 for melanin. The integrated approach yielded correlation coefficients of 0.923 for hemoglobin and 0.897 for melanin, respectively. The proposed approach achieved a reasonable correlation with the professional system using actually captured images, offering a promising alternative to existing professional equipment without the need for additional optical instruments or extensive ground truth preparation.