A ruled surface is a shape swept out by moving a line in 3D space. Due to their simple geometric forms, ruled surfaces have applications in various domains such as architecture and engineering. In the past, various approaches have been proposed to approximate a target shape using developable surfaces, which are special ruled surfaces with zero Gaussian curvature. However, methods for shape approximation using general ruled surfaces remain limited and often require the target shape to be either represented as parametric surfaces or have non-positive Gaussian curvature. In this paper, we propose a method to compute a piecewise ruled surface that approximates an arbitrary freeform mesh surface. We first use a group-sparsity formulation to optimize the given mesh shape into an approximately piecewise ruled form, in conjunction with a tangent vector field that indicates the ruling directions. Afterward, we utilize the optimization result to extract seams that separate smooth families of rulings, and use the seams to construct the initial rulings. Finally, we further optimize the positions and orientations of the rulings to improve the alignment with the input target shape. We apply our method to a variety of freeform shapes with different topologies and complexity, demonstrating its effectiveness in approximating arbitrary shapes.

Recovering the shape and appearance of real-world objects from natural 2D images is a long-standing and challenging inverse rendering problem. In this paper, we introduce a novel hybrid differentiable rendering method to efficiently reconstruct the 3D geometry and reflectance of a scene from multi-view images captured by conventional hand-held cameras. Our method follows an analysis-by-synthesis approach and consists of two phases. In the initialization phase, we use traditional SfM and MVS methods to reconstruct a virtual scene roughly matching the real scene. Then in the optimization phase, we adopt a hybrid approach to refine the geometry and reflectance, where the geometry is first optimized using an approximate differentiable rendering method, and the reflectance is optimized afterward using a physically-based differentiable rendering method. Our hybrid approach combines the efficiency of approximate methods with the high-quality results of physically-based methods. Extensive experiments on synthetic and real data demonstrate that our method can produce reconstructions with similar or higher quality than state-of-the-art methods while being more efficient.

3D deep learning performance depends on object representation and local feature extraction. In this work, we present MAT-Net, a neural network which captures local and global features from the Medial Axis Transform (MAT). Different from K-Nearest-Neighbor method which extracts local features by a fixed number of neighbors, our MAT-Net exploits effective modules Group-MAT and Edge-Net to process topological structure. Experimental results illustrate that MAT-Net demonstrates competitive or better performance on 3D shape recognition than state-of-the-art methods, and prove that MAT representation has excellent capacity in 3D deep learning, even in the case of low resolution.