# FCN-Based 3D Reconstruction with Multi-Source Photometric Stereo
## 1 Introduction  
Vision-based 3D reconstruction technology can obtain 3D information on the target object from a 2D image in a non-contact manner, which has the advantages of being less affected by the shape of the actual object and giving a more real and robust reconstruction effect. Vision-based reconstruction methods can be roughly divided into active vision methods and passive vision methods. The reconstruction accuracy of active 3D reconstruction methods is relatively high, such as laser scanning and structured light methods, but their cost and complexity are also higher and their reconstruction speed is slow. The passive vision method can make up for the above shortcomings of the active vision method, but still faces challenges in terms of reconstruction accuracy. As a 3D reconstruction method based on passive vision, the shape from shading (SFS) [1] can analyze the lightness and darkness information in the image and use the reflected illumination model to recover the normal information of the object from a single image. However, a single image contains less information, so the actual reconstruction effect of this method is average. Therefore, in order to improve the shortcomings of the SFS, [PERSON] [2] first proposed the Photometric Stereo, using data redundancy to solve the problem of single image reconstruction in SFS due to factors such as shadows and specular reflections, improving the effect and robustness of the reconstruction. On this basis, someresearchers have found that increasing the number of light sources can provide more equations to the solution of unknown parameter parameters [3], thereby compensating for the surface microscopic information missed by the three-dimensional measurement method with three light sources and improving the accuracy of the dimensional measurement, i.e., multi-source Photometric Stereo. Currently, the research and improvement of Photometric Stereo 3D reconstruction mainly focuses on light source calibration, non-Lambertian reconstruction [4], gradient reconstruction depth [5] and so on. The classic Photometric Stereo method usually assumes that the light intensity on the observation images taken under different illuminations is the same, and the sensor exposure is constant, but these assumptions are difficult to achieve in practical applications. In response to this, [PERSON] et al. [6] developed a method for accurately determining the surface normal direction that is not affected by these factors for situations where the light direction is known but the light intensity is unknown, which improves the accuracy of the Photometric Stereo method in practical applications. [PERSON] et al. [7] proposed a method for calculating the geometry of objects with general reflection characteristics from the image to solve the complex calibration problem of photometric three-dimensional reconstruction, which can be applied to any remote and unknown lighting with almost no calibration operation surroundings. With the extensive study of deep learning in various fields, neural network frameworks have also been gradually applied to the field of 3D graphics [8; 9]. As we all know, the convolutional neural network (CNN) performs well in tasks such as classification and regression. At present, some studies have used CNN to complete three-dimensional tasks. [PERSON] et al. [10] use the CNN to mix three different three-dimensional shape expressions together, which can bring a better performance to many three-dimensional tasks compared with a single expression. The 3D ShapeNet established by [PERSON] et al. [11] is an earlier proposed 3D reconstruction model of a single image based on voxel representation, using a convolutional depth confidence network to represent geometric 3D graphics as a probability distribution of binary variables on the 3D voxel grid. Its 3D reconstruction was realized by continuously predicting shape types and filling unknown voxels. In a related work, [PERSON] et al.