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We present a general and modular algorithmic framework for path planning of robots. Our framework combines geometric methods for exact and complete analysis of low-dimensional configuration spaces, together with practical, considerably…
In this paper, we are concerned with the problem of creating flattening maps of simply-connected open surfaces in $\mathbb{R}^3$. Using a natural principle of density diffusion in physics, we propose an effective algorithm for computing…
In this paper, we revisit the long-standing problem of automatic reconstruction of 3D objects from single line drawings. Previous optimization-based methods can generate compact and accurate 3D models, but their success rates depend heavily…
This paper provides a normalized field product approach for topology optimization to achieve close-to-binary optimal designs. The method employs a parameter-free density measure that implicitly enforces a minimum length scale on the solid…
In addition to color and textural information, geometry provides important cues for 3D scene reconstruction. However, current reconstruction methods only include geometry at the feature level thus not fully exploiting the geometric…
Object-level SLAM introduces semantic meaningful and compact object landmarks that help both indoor robot applications and outdoor autonomous driving tasks. However, the back end of object-level SLAM suffers from singularity problems…
Seamless global parametrization of surfaces is a key operation in geometry processing, e.g. for high-quality quad mesh generation. A common approach is to prescribe the parametric domain structure, in particular the locations of…
3D shape analysis has been largely focused on traditional 3D representations of point clouds and meshes, but the discrete nature of these data makes the analysis susceptible to variations in input resolutions. Recent development of neural…
The advent of high resolution imaging has made data on surface shape widespread. Methods for the analysis of shape based on landmarks are well established but high resolution data require a functional approach. The starting point is a…
In this review we identify a new category of structural optimization methods that has emerged over the last 20 years, which we propose to call feature-mapping methods. The two defining aspects of these methods are that the design is…
Three-dimensional (3D) reconstruction from two-dimensional images is an active research field in computer vision, with applications ranging from navigation and object tracking to segmentation and three-dimensional modeling. Traditionally,…
The main objective of this work is to describe a general and original approach for computing an off-line solution for a set of parameters describing the geometry of the domain. That is, a solution able to include information for different…
Nearly all 3D displays need calibration for correct rendering. More often than not, the optical elements in a 3D display are misaligned from the designed parameter setting. As a result, 3D magic does not perform well as intended. The…
This paper presents a novel approach to reconstruct complete 3D deformable models over time by a single depth camera. These are the steps employed for deforming objects from single depth camera. The partial surfaces reconstructed from…
3D single object tracking remains a challenging problem due to the sparsity and incompleteness of the point clouds. Existing algorithms attempt to address the challenges in two strategies. The first strategy is to learn dense geometric…
We survey the role of symmetry in diffeomorphic registration of landmarks, curves, surfaces, images and higher-order data. The infinite dimensional problem of finding correspondences between objects can for a range of concrete data types be…
Generic 3D reconstruction from a single image is a difficult problem. A lot of data loss occurs in the projection. A domain based approach to reconstruction where we solve a smaller set of problems for a particular use case lead to greater…
Despite the success of deep functional maps in non-rigid 3D shape matching, there exists no learning framework that models both self-symmetry and shape matching simultaneously. This is despite the fact that errors due to symmetry mismatch…
In the industrial practice, additive manufacturing processes are often followed by post-processing operations such as subtractive machining, milling, etc. to achieve the desired surface quality and dimensional accuracy. Hence, a given part…
Although 3D shape matching and interpolation are highly interrelated, they are often studied separately and applied sequentially to relate different 3D shapes, thus resulting in sub-optimal performance. In this work we present a unified…