Surface-from-gradients (SfG) aims to recover a three-dimensional (3D) surface from its gradients. Traditional methods encounter significant challenges in achieving high accuracy and handling high-resolution inputs, particularly facing the complex nature of discontinuities and the inefficiencies associated with large-scale linear solvers. Although recent advances in deep learning, such as photometric stereo, have enhanced normal estimation accuracy, they do not fully address the intricacies of gradient-based surface reconstruction. To overcome these limitations, we propose a Fourier neural operator-based Numerical Integration Network (FNIN) within a two-stage optimization framework. In the first stage, our approach employs an iterative architecture for numerical integration, harnessing an advanced Fourier neural operator to approximate the solution operator in Fourier space. Additionally, a self-learning attention mechanism is incorporated to effectively detect and handle discontinuities. In the second stage, we refine the surface reconstruction by formulating a weighted least squares problem, addressing the identified discontinuities rationally. Extensive experiments demonstrate that our method achieves significant improvements in both accuracy and efficiency compared to current state-of-the-art solvers. This is particularly evident in handling high-resolution images with complex data, achieving errors of fewer than 0.1 mm on tested objects.

This paper describes an approach to estimate illumination directions of 3D surface texture based on Active Basis. Instead of applying Gabor wavelet transform to extract texture features, we represent our texture features with a simple Haar feature to improve efficiency. The Active Basis model can be learned from training image patches by the shared pursuit algorithm. The base histogram can then be obtained based on each model. We measure the illumination directions by minimizing the Euclidean distance and the entropy difference of base histograms between the test image and the training sets. Experimental results demonstrate the effectiveness and accuracy of the proposed approach.

We introduce a simple texture synthesis method based on Support Vector Machines (SVM). Although SVM has been effectively used for various pattern recognition tasks, there is no report available on directly applying SVM for texture synthesis. The advantage of using SVM is that the sample can be simply modeled by a linear model and is not required during the synthesis stage. In addition, the method can be further extended to synthesize 3D surface texture or Bidirectional Texture Functions. Our experimental results show that the method can successfully model and synthesize semi or highly structured textures, which can be difficult subjects for previous texture synthesis methods based on parametric models.