Recently proposed 3D object reconstruction methods represent a mesh with an atlas - a set of planar patches approximating the surface. However, their application in a real-world scenario is limited since the surfaces of reconstructed objects contain discontinuities, which degrades the quality of the final mesh. This is mainly caused by independent processing of individual patches, and in this work, we postulate to mitigate this limitation by preserving local consistency around patch vertices. To that end, we introduce a Locally Conditioned Atlas (LoCondA), a framework for representing a 3D object hierarchically in a generative model. Firstly, the model maps a point cloud of an object into a sphere. Secondly, by leveraging a spherical prior, we enforce the mapping to be locally consistent on the sphere and on the target object. This way, we can sample a mesh quad on that sphere and project it back onto the object's manifold. With LoCondA, we can produce topologically diverse objects while maintaining quads to be stitched together. We show that the proposed approach provides structurally coherent reconstructions while producing meshes of quality comparable to the competitors.

翻译：近期提出的三维物体重建方法采用图册（atlas）——即一组逼近曲面的平面补丁——来表示网格。然而，由于重建物体表面存在不连续性，导致最终网格质量下降，这类方法在实际场景中的应用受到限制。这主要源于各补丁的独立处理，为此本文提出通过保持补丁顶点周围的局部一致性来缓解该问题。我们引入局部条件图册（LoCondA），这是一种在生成模型中层次化表示三维物体的框架。首先，该模型将物体点云映射到球面上；其次，通过利用球面先验，我们强制映射在球面和目标物体上保持局部一致性。通过这种方式，我们可在球面上采样网格四边形，并将其投影回物体流形。借助LoCondA，我们能生成拓扑多样化的物体，同时保持四边形彼此拼接。实验表明，所提方法在产生结构连贯的重建结果的同时，能生成与竞争方法质量相当的网格。