Andrei Sharf

GlobFit: consistently fitting primitives by discovering global relations

Given a noisy and incomplete point set, we introduce a method that simultaneously recovers a set of locally fitted primitives along with their global mutual relations. We operate under the assumption that the data corresponds to a man-made engineering object consisting of basic primitives, possibly repeated and globally aligned under common relations. We introduce an algorithm to directly couple the local and global aspects of the problem. The local fit of the model is determined by how well the inferred model agrees to the observed data, while the global relations are iteratively learned and enforced through a constrained optimization. Starting with a set of initial RANSAC based locally fitted primitives, relations across the primitives such as orientation, placement, and equality are progressively learned and conformed to. In each stage, a set of feasible relations are extracted among the candidate relations, and then aligned to, while best fitting to the input data. The global coupling corrects the primitives obtained in the local RANSAC stage, and brings them to precise global alignment. We test the robustness of our algorithm on a range of synthesized and scanned data, with varying amounts of noise, outliers, and non-uniform sampling, and validate the results against ground truth, where available.

Build-to-last: strength to weight 3D printed objects

The emergence of low-cost 3D printers steers the investigation of new geometric problems that control the quality of the fabricated object. In this paper, we present a method to reduce the material cost and weight of a given object while providing a durable printed model that is resistant to impact and external forces. We introduce a hollowing optimization algorithm based on the concept of honeycomb-cells structure. Honeycombs structures are known to be of minimal material cost while providing strength in tension. We utilize the Voronoi diagram to compute irregular honeycomb-like volume tessellations which define the inner structure. We formulate our problem as a strength--to--weight optimization and cast it as mutually finding an optimal interior tessellation and its maximal hollowing subject to relieve the interior stress. Thus, our system allows to build-to-last 3D printed objects with large control over their strength-to-weight ratio and easily model various interior structures. We demonstrate our method on a collection of 3D objects from different categories. Furthermore, we evaluate our method by printing our hollowed models and measure their stress and weights.

Real-time parallel hashing on the GPU

We demonstrate an efficient data-parallel algorithm for building large hash tables of millions of elements in real-time. We consider two parallel algorithms for the construction: a classical sparse perfect hashing approach, and cuckoo hashing, which packs elements densely by allowing an element to be stored in one of multiple possible locations. Our construction is a hybrid approach that uses both algorithms. We measure the construction time, access time, and memory usage of our implementations and demonstrate real-time performance on large datasets: for 5 million key-value pairs, we construct a hash table in 35.7 ms using 1.42 times as much memory as the input data itself, and we can access all the elements in that hash table in 15.3 ms. For comparison, sorting the same data requires 36.6 ms, but accessing all the elements via binary search requires 79.5 ms. Furthermore, we show how our hashing methods can be applied to two graphics applications: 3D surface intersection for moving data and geometric hashing for image matching.

A search-classify approach for cluttered indoor scene understanding

We 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.

SmartBoxes for interactive urban reconstruction

We introduce an interactive tool which enables a user to quickly assemble an architectural model directly over a 3D point cloud acquired from large-scale scanning of an urban scene. The user loosely defines and manipulates simple building blocks, which we call SmartBoxes, over the point samples. These boxes quickly snap to their proper locations to conform to common architectural structures. The key idea is that the building blocks are smart in the sense that their locations and sizes are automatically adjusted on-the-fly to fit well to the point data, while at the same time respecting contextual relations with nearby similar blocks. SmartBoxes are assembled through a discrete optimization to balance between two snapping forces defined respectively by a data-fitting term and a contextual term, which together assist the user in reconstructing the architectural model from a sparse and noisy point cloud. We show that a combination of the users interactive guidance and high-level knowledge about the semantics of the underlying model, together with the snapping forces, allows the reconstruction of structures which are partially or even completely missing from the input.

State of the Art in Surface Reconstruction from Point Clouds

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 contains 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. This state-of-the-art report surveys the field of surface reconstruction, providing a categorization with respect to priors, data imperfections, and reconstruction output. By considering a holistic view of surface reconstruction, this report provides a detailed characterization of the field, highlights similarities between diverse reconstruction techniques, and provides directions for future work in surface reconstruction.

Non-local scan consolidation for 3D urban scenes

Recent advances in scanning technologies, in particular devices that extract depth through active sensing, allow fast scanning of urban scenes. Such rapid acquisition incurs imperfections: large regions remain missing, significant variation in sampling density is common, and the data is often corrupted with noise and outliers. However, buildings often exhibit large scale repetitions and self-similarities. Detecting, extracting, and utilizing such large scale repetitions provide powerful means to consolidate the imperfect data. Our key observation is that the same geometry, when scanned multiple times over reoccurrences of instances, allow application of a simple yet effective non-local filtering. The multiplicity of the geometry is fused together and projected to a base-geometry defined by clustering corresponding surfaces. Denoising is applied by separating the process into off-plane and in-plane phases. We show that the consolidation of the reoccurrences provides robust denoising and allow reliable completion of missing parts. We present evaluation results of the algorithm on several LiDAR scans of buildings of varying complexity and styles.

ℓ 1 -Sparse reconstruction of sharp point set surfaces

We introduce an ℓ1-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.

SnapPaste: an interactive technique for easy mesh composition

Editing and manipulation of existing 3D geometric objects are a means to extend their repertoire and promote their availability. Traditionally, tools to compose or manipulate objects defined by 3D meshes are in the realm of artists and experts. In this paper, we introduce a simple and effective user interface for easy composition of 3D mesh-parts for non-professionals. Our technique borrows from the cut-and-paste paradigm where a user can cut parts out of existing objects and paste them onto others to create new designs. To assist the user attach objects to each other in a quick and simple manner, many applications in computer graphics support the notion of “snapping”. Similarly, our tool allows the user to loosely drag one mesh part onto another with an overlap, and lets the system snap them together in a graceful manner. Snapping is accomplished using our Soft-ICP algorithm which replaces the global transformation in the ICP algorithm with a set of point-wise locally supported transformations. The technique enhances registration with a set of rigid to elastic transformations that account for simultaneous global positioning and local blending of the objects. For completeness of our framework, we present an additional simple mesh-cutting tool, adapting the graph-cut algorithm to meshes.

Interactive topology-aware surface reconstruction

The reconstruction of a complete watertight model from scan data is still a difficult process. In particular, since scanned data is often incomplete, the reconstruction of the expected shape is an ill-posed problem. Techniques that reconstruct poorly-sampled areas without any user intervention fail in many cases to faithfully reconstruct the topology of the model. The method that we introduce in this paper is topology-aware: it uses minimal user input to make correct decisions at regions where the topology of the model cannot be automatically induced with a reasonable degree of confidence. We first construct a continuous function over a three-dimensional domain. This function is constructed by minimizing a penalty function combining the data points, user constraints, and a regularization term. The optimization problem is formulated in a mesh-independent manner, and mapped onto a specific mesh using the finite-element method. The zero level-set of this function is a first approximation of the reconstructed surface. At complex under-sampled regions, the constraints might be insufficient. Hence, we analyze the local topological stability of the zero level-set to detect weak regions of the surface. These regions are suggested to the user for adding local inside/outside constraints by merely scribbling over a 2D tablet. Each new user constraint modifies the minimization problem, which is solved incrementally. The process is repeated, converging to a topology-stable reconstruction. Reconstructions of models acquired by a structured-light scanner with a small number of scribbles demonstrate the effectiveness of the method.