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Illustrations of some of the challenges in the dataset. (a) Partial scans (green indicates the boundary). (b) Complex deformations. (c) Missing geometry caused by self-occlusion.
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... with different material fillings is sufficient and makes data capture and analysis more manageable. The poses and materials used were carefully selected to incrementally vary the deformation challenge so that algorithm deficiencies-with respect to these varying properties-may be identified. Some examples of challenging problems are shown in Fig. ...
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... Shape registration is a special case of correspondence, where our goal is to find an optimal deformation between the scan and a fixed template. For this, we consider the recent SHREC'20 benchmark [81], consisting of 11 partial scans of stuffed toy rabbits to be registered to a single scan. This benchmark is particularly challenging due to granulated surface deformation, scanning artefacts, and limited data and supervision. ...
In this work we present a novel approach for computing correspondences between non-rigid objects, by exploiting a reduced representation of deformation fields. Different from existing works that represent deformation fields by training a general-purpose neural network, we advocate for an approximation based on mesh-free methods. By letting the network learn deformation parameters at a sparse set of positions in space (nodes), we reconstruct the continuous deformation field in a closed-form with guaranteed smoothness. With this reduction in degrees of freedom, we show significant improvement in terms of data-efficiency thus enabling limited supervision. Furthermore, our approximation provides direct access to first-order derivatives of deformation fields, which facilitates enforcing desirable regularization effectively. Our resulting model has high expressive power and is able to capture complex deformations. We illustrate its effectiveness through state-of-the-art results across multiple deformable shape matching benchmarks. Our code and data are publicly available at: https://github.com/Sentient07/DeformationBasis.
... This choice to treat point correspondences between objects as functions leads to simpler convex leastsquare optimisation problems and provide greater flexibility to incorporate linear constraints to the problem. FM with several applications in different areas of computer graphics such as partial matching, deformation and symmetry analysis, exploration of shape collections etc. [21]- [23], has been shown to perform well in challenging settings [24]. ...
... We have also conducted experiments on the SHREC'2020 dataset (Task.1 [59]). Here, the dataset contains 11 partial scans and one full scan of a rabbit toy. ...
... From left to right : test-set0 (articulated deformations), test-set1 (near-isometric deformations), test-set2 (non-isometric deformations), test-set3 (topological and geometric changes), all test-sets. Quantitative evaluation (Geodesic Error Curves) on SHREC'2020 and comparison with existing approaches including variants of the Functional Maps framework, as reported in[59]. Considered poses/deformations, from left to right: twist, indent, inflate, stretch, and overall. ...
In deformable registration, the geometric framework -- large deformation diffeomorphic metric mapping (or LDDMM, in short) -- has inspired numerous techniques for comparing, deforming, averaging and analyzing shapes or images. In this work, we make use of deep residual neural networks to solve the non-stationary ODE (flow equation) based on a Eulers discretization scheme. The central idea is to represent time-dependent velocity fields as fully connected ReLU neural networks (building blocks) and derive optimal weights by minimizing a regularized loss function. Computing minimizing paths between deformations, thus between shapes, turns to find optimal network parameters by back-propagating over the intermediate building blocks. Geometrically, at each time step, ResNet-LDDMM searches for an optimal partition of the space into multiple polytopes, and then computes optimal velocity vectors as affine transformations on each of these polytopes. As a result, different parts of the shape, even if they are close, can be made to belong to different polytopes, and therefore be moved in different directions without costing too much energy. Importantly, we show how diffeomorphic transformations, or more precisely bilipshitz transformations, are predicted by our algorithm. We illustrate these ideas on diverse registration problems of 3D shapes under complex topology-preserving transformations.
... This choice to treat point correspondences between objects as functions leads to simpler convex leastsquare optimisation problems and provide greater flexibility to incorporate linear constraints to the problem. FM with several applications in different areas of computer graphics such as partial matching, deformation and symmetry analysis, exploration of shape collections etc. [21]- [23], has been shown to perform well in challenging settings [24]. ...
Handling object deformations for robotic grasping is still a major problem to solve. In this paper, we propose an efficient learning-free solution for this problem where generated grasp hypotheses of a region of an object are adapted to its deformed configurations. To this end, we investigate the applicability of functional map (FM) correspondence, where the shape matching problem is treated as searching for correspondences between geometric functions in a reduced basis. For a user selected region of an object, a ranked list of grasp candidates is generated with local contact moment (LoCoMo) based grasp planner. The proposed FM-based methodology maps these candidates to an instance of the object that has suffered arbitrary level of deformation. The best grasp, by analysing its kinematic feasibility while respecting the original finger configuration as much as possible, is then executed on the object. We have compared the performance of our method with two different state-of-the-art correspondence mapping techniques in terms of grasp stability and region grasping accuracy for 4 different objects with 5 different deformations.
... In this study, the so-called non-rigid template registration method [43] is used using Wrap 3.4 software (Russian3dscanner, Moscow, Russia). First, a high-quality individual scan was selected to serve as the template mesh. ...
The use of 3D anthropometric data of children’s heads and faces has great potential in the development of protective gear and medical products that need to provide a close fit in order to function well. Given the lack of detailed data of this kind, the aim of this study is to map the size and shape variation of Dutch children’s heads and faces and investigate possible implications for the design of a ventilation mask. In this study, a dataset of heads and faces of 303 Dutch children aged six months to seven years consisting of traditional measurements and 3D scans were analysed. A principal component analysis (PCA) of facial measurements was performed to map the variation of the children’s face shapes. The first principal component describes the overall size, whilst the second principal component captures the more width related variation of the face. After establishing a homology between the 3D scanned face shapes, a second principal component analysis was done on the point coordinates, revealing the most prominent variations in 3D shape within the sample.
... In this section, we conduct comprehensive experiments to evaluate the performance of our method on various data sets including TOSCA [9], SCAPE [3], SHREC'16 [14] and SHREC'20 [16] as well as patches extracted from TOSCA. TOSCA and SCAPE are data sets of approximately isometric shapes; SHREC'16 is also a data set of approximately isometric shapes but includes cuts and holes. ...
In this work, a simple and efficient dual iterative refinement (DIR) method is proposed for dense correspondence between two nearly isometric shapes. The key idea is to use dual information, such as spatial and spectral, or local and global features, in a complementary and effective way, and extract more accurate information from current iteration to use for the next iteration. In each DIR iteration, starting from current correspondence, a zoom-in process at each point is used to select well matched anchor pairs by a local mapping distortion criterion. These selected anchor pairs are then used to align spectral features (or other appropriate global features) whose dimension adaptively matches the capacity of the selected anchor pairs. Thanks to the effective combination of complementary information in a data-adaptive way, DIR is not only efficient but also robust to render accurate results within a few iterations. By choosing appropriate dual features, DIR has the flexibility to handle patch and partial matching as well. Extensive experiments on various data sets demonstrate the superiority of DIR over other state-of-the-art methods in terms of both accuracy and efficiency.
Non-rigid registration computes an alignment between a source surface with a target surface in a non-rigid manner. In the past decade, with the advances in 3D sensing technologies that can measure time-varying surfaces, non-rigid registration has been applied for the acquisition of deformable shapes and has a wide range of applications. This survey presents a comprehensive review of non-rigid registration methods for 3D shapes, focusing on techniques related to dynamic shape acquisition and reconstruction. In particular, we review different approaches for representing the deformation field, and the methods for computing the desired deformation. Both optimization-based and learning-based methods are covered. We also review benchmarks and datasets for evaluating non-rigid registration methods, and discuss potential future research directions.
