Lan Hu

Wanting Xu, Lan Hu, Manolis C. Tsakiris et al.

Over the past decade, the Gröbner basis theory and automatic solver generation have lead to a large number of solutions to geometric vision problems. In practically all cases, the derived solvers apply a fixed elimination template to calculate the Gröbner basis and thereby identify the zero-dimensional variety of the original polynomial constraints. However, it is clear that different variable or monomial orderings lead to different elimination templates, and we show that they may present a large variability in accuracy for a certain instance of a problem. The present paper has two contributions. We first show that for a common class of problems in geometric vision, variable reordering simply translates into a permutation of the columns of the initial coefficient matrix, and that -- as a result -- one and the same elimination template can be reused in different ways, each one leading to potentially different accuracy. We then prove that the original set of coefficients may contain sufficient information to train a classifier for online selection of a good solver, most notably at the cost of only a small computational overhead. We demonstrate wide applicability at the hand of generic dense polynomial problem solvers, as well as a concrete solver from geometric vision.

Lan Hu, Haomin Shi, Laurent Kneip

The present work proposes a solution to the challenging problem of registering two partial point sets of the same object with very limited overlap. We leverage the fact that most objects found in man-made environments contain a plane of symmetry. By reflecting the points of each set with respect to the plane of symmetry, we can largely increase the overlap between the sets and therefore boost the registration process. However, prior knowledge about the plane of symmetry is generally unavailable or at least very hard to find, especially with limited partial views, and finding this plane could strongly benefit from a prior alignment of the partial point sets. We solve this chicken-and-egg problem by jointly optimizing the relative pose and symmetry plane parameters, and notably do so under global optimality by employing the branch-and-bound (BnB) paradigm. Our results demonstrate a great improvement over the current state-of-the-art in globally optimal point set registration for common objects. We furthermore show an interesting application of our method to dense 3D reconstruction of scenes with repetitive objects.

Lan Hu, Wanting Xu, Kun Huang et al.

In an effort to increase the capabilities of SLAM systems and produce object-level representations, the community increasingly investigates the imposition of higher-level priors into the estimation process. One such example is given by employing object detectors to load and register full CAD models. Our work extends this idea to environments with unknown objects and imposes object priors by employing modern class-specific neural networks to generate complete model geometry proposals. The difficulty of using such predictions in a real SLAM scenario is that the prediction performance depends on the view-point and measurement quality, with even small changes of the input data sometimes leading to a large variability in the network output. We propose a discrete selection strategy that finds the best among multiple proposals from different registered views by re-enforcing the agreement with the online depth measurements. The result is an effective object-level RGBD SLAM system that produces compact, high-fidelity, and dense 3D maps with semantic annotations. It outperforms traditional fusion strategies in terms of map completeness and resilience against degrading measurement quality.