The area of surface reconstruction has seen substantial progress in the past two decades. The traditional problem addressed by surface reconstruction is to recover the digital representation of a physical shape that has been scanned, where the scanned data contain a wide variety of defects. While much of the earlier work has been focused on reconstructing a piece‐wise smooth representation of the original shape, recent work has taken on more specialized priors to address significantly challenging data imperfections, where the reconstruction can take on different representations—not necessarily the explicit geometry. We survey the field of surface reconstruction, and provide a categorization with respect to priors, data imperfections and reconstruction output. By considering a holistic view of surface reconstruction, we show a detailed characterization of the field, highlight similarities between diverse reconstruction techniques and provide directions for future work in surface reconstruction.

Figure 1: A raw scan of a highly cluttered indoor scene is given (left). Applying our search-classify method, we segment the scene into meaningful objects (middle: chairs (blue) and tables (purple)), followed by a template deform-to-fit reconstruction (right). AbstractWe present an algorithm for recognition and reconstruction of scanned 3D indoor scenes. 3D indoor reconstruction is particularly challenging due to object interferences, occlusions and overlapping which yield incomplete yet very complex scene arrangements. Since it is hard to assemble scanned segments into complete models, traditional methods for object recognition and reconstruction would be inefficient. We present a search-classify approach which interleaves segmentation and classification in an iterative manner. Using a robust classifier we traverse the scene and gradually propagate classification information. We reinforce classification by a template fitting step which yields a scene reconstruction. We deform-to-fit templates to classified objects to resolve classification ambiguities. The resulting reconstruction is an approximation which captures the general scene arrangement. Our results demonstrate successful classification and reconstruction of cluttered indoor scenes, captured in just few minutes.

Figure 1: Completing a hole in a point-based model. In the darker colored region we removed sample points to demonstrate the surface completion technique. In the middle right the region is filled with a smooth patch conforming with the densely sampled areas, and the result of our context-based surface completion is on the right. AbstractSampling complex, real-world geometry with range scanning devices almost always yields imperfect surface samplings. These "holes" in the surface are commonly filled with a smooth patch that conforms with the boundary. We introduce a context-based method: the characteristics of the given surface are analyzed, and the hole is iteratively filled by copying patches from valid regions of the given surface. In particular, the method needs to determine best matching patches, and then, fit imported patches by aligning them with the surrounding surface. The completion process works top down, where details refine intermediate coarser approximations. To align an imported patch with the existing surface, we apply a rigid transformation followed by an iterative closest point procedure with nonrigid transformations. The surface is essentially treated as a point set, and local implicit approximations aid in measuring the similarity between two point set patches. We demonstrate the method at several point-sampled surfaces, where the holes either result from imperfect sampling during range scanning or manual removal.

We introduce an 1 -sparse method for the reconstruction of a piecewise smooth point set surface. The technique is motivated by recent advancements in sparse signal reconstruction. The assumption underlying our work is that common objects, even geometrically complex ones, can typically be characterized by a rather small number of features. This, in turn, naturally lends itself to incorporating the powerful notion of sparsity into the model. The sparse reconstruction principle gives rise to a reconstructed point set surface that consists mainly of smooth modes, with the residual of the objective function strongly concentrated near sharp features. Our technique is capable of recovering orientation and positions of highly noisy point sets. The global nature of the optimization yields a sparse solution and avoids local minima. Using an interior-point log-barrier solver with a customized preconditioning scheme, the solver for the corresponding convex optimization problem is competitive and the results are of high quality.

Figure 1: Overview of our construction for a voxelized Lucy model, colored by mapping x, y, and z coordinates to red, green, and blue respectively (far left). The 3.5 million voxels (left) are input as 32-bit keys and placed into buckets of ≤ 512 items, averaging 409 each (center). Each bucket then builds a cuckoo hash with three sub-tables and stores them in a larger structure with 5 million entries (right). Close-ups follow the progress of a single bucket, showing the keys allocated to it (center; the bucket is linear and wraps around left to right) and each of its completed cuckoo sub-tables (right). Finding any key requires checking only three possible locations.