Shape basis interpretation for monocular deformable 3D reconstruction

© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.In this paper, we propose a novel interpretable shape model to encode object non-rigidity. We first use the initial frames of a monocular video to recover a rest shape, used later to compute a dissimilarity measure based on a distance matrix measurement. Spectral analysis is then applied to this matrix to obtain a reduced shape basis, that in contrast to existing approaches, can be physically interpreted. In turn, these pre-computed shape bases are used to linearly span the deformation of a wide variety of objects. We introduce the low-rank basis into a sequential approach to recover both camera motion and non-rigid shape from the monocular video, by simply optimizing the weights of the linear combination using bundle adjustment. Since the number of parameters to optimize per frame is relatively small, specially when physical priors are considered, our approach is fast and can potentially run in real time. Validation is done in a wide variety of real-world objects, undergoing both inextensible and extensible deformations. Our approach achieves remarkable robustness to artifacts such as noisy and missing measurements and shows an improved performance to competing methods.Peer ReviewedPostprint (author's final draft

Image collection pop-up: 3D reconstruction and clustering of rigid and non-rigid categories

© 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.This paper introduces an approach to simultaneously estimate 3D shape, camera pose, and object and type of deformation clustering, from partial 2D annotations in a multi-instance collection of images. Furthermore, we can indistinctly process rigid and non-rigid categories. This advances existing work, which only addresses the problem for one single object or, if multiple objects are considered, they are assumed to be clustered a priori. To handle this broader version of the problem, we model object deformation using a formulation based on multiple unions of subspaces, able to span from small rigid motion to complex deformations. The parameters of this model are learned via Augmented Lagrange Multipliers, in a completely unsupervised manner that does not require any training data at all. Extensive validation is provided in a wide variety of synthetic and real scenarios, including rigid and non-rigid categories with small and large deformations. In all cases our approach outperforms state-of-the-art in terms of 3D reconstruction accuracy, while also providing clustering results that allow segmenting the images into object instances and their associated type of deformation (or action the object is performing).Postprint (author's final draft

Intrinsic Dynamic Shape Prior for Fast, Sequential and Dense Non-Rigid Structure from Motion with Detection of Temporally-Disjoint Rigidity

While dense non-rigid structure from motion (NRSfM) has been extensively studied from the perspective of the reconstructability problem over the recent years, almost no attempts have been undertaken to bring it into the practical realm. The reasons for the slow dissemination are the severe ill-posedness, high sensitivity to motion and deformation cues and the difficulty to obtain reliable point tracks in the vast majority of practical scenarios. To fill this gap, we propose a hybrid approach that extracts prior shape knowledge from an input sequence with NRSfM and uses it as a dynamic shape prior for sequential surface recovery in scenarios with recurrence. Our Dynamic Shape Prior Reconstruction (DSPR) method can be combined with existing dense NRSfM techniques while its energy functional is optimised with stochastic gradient descent at real-time rates for new incoming point tracks. The proposed versatile framework with a new core NRSfM approach outperforms several other methods in the ability to handle inaccurate and noisy point tracks, provided we have access to a representative (in terms of the deformation variety) image sequence. Comprehensive experiments highlight convergence properties and the accuracy of DSPR under different disturbing effects. We also perform a joint study of tracking and reconstruction and show applications to shape compression and heart reconstruction under occlusions. We achieve state-of-the-art metrics (accuracy and compression ratios) in different scenarios

Quantum rotors and their symmetries

A connection between nuclear symmetries other than those of an ellipsoidal nucleus and the properties of the implied rotational spectra are discussed. The discussion is focussed on a few examples of exotic shapes predicted recently by microscopic calculations. Some possible interpretation difficulties related to experiment are shortly mentioned.Comment: Invited talk at "High Spin Physics 2001", see http://www.fuw.edu.pl/~hs2001/ , to be published in Acta Physica Polonica

Deformable and articulated 3D reconstruction from monocular video sequences

PhDThis thesis addresses the problem of deformable and articulated structure from motion from monocular uncalibrated video sequences. Structure from motion is defined as the problem of recovering information about the 3D structure of scenes imaged by a camera in a video sequence. Our study aims at the challenging problem of non-rigid shapes (e.g. a beating heart or a smiling face). Non-rigid structures appear constantly in our everyday life, think of a bicep curling, a torso twisting or a smiling face. Our research seeks a general method to perform 3D shape recovery purely from data, without having to rely on a pre-computed model or training data. Open problems in the field are the difficulty of the non-linear estimation, the lack of a real-time system, large amounts of missing data in real-world video sequences, measurement noise and strong deformations. Solving these problems would take us far beyond the current state of the art in non-rigid structure from motion. This dissertation presents our contributions in the field of non-rigid structure from motion, detailing a novel algorithm that enforces the exact metric structure of the problem at each step of the minimisation by projecting the motion matrices onto the correct deformable or articulated metric motion manifolds respectively. An important advantage of this new algorithm is its ability to handle missing data which becomes crucial when dealing with real video sequences. We present a generic bilinear estimation framework, which improves convergence and makes use of the manifold constraints. Finally, we demonstrate a sequential, frame-by-frame estimation algorithm, which provides a 3D model and camera parameters for each video frame, while simultaneously building a model of object deformation

Modal space: a physics-based model for sequential estimation of time-varying shape from monocular video

The final publication is available at link.springer.comThis paper describes two sequential methods for recovering the camera pose together with the 3D shape of highly deformable surfaces from a monocular video. The nonrigid 3D shape is modeled as a linear combination of mode shapes with time-varying weights that define the shape at each frame and are estimated on-the-fly. The low-rank constraint is combined with standard smoothness priors to optimize the model parameters over a sliding window of image frames. We propose to obtain a physics-based shape basis using the initial frames on the video to code the time-varying shape along the sequence, reducing the problem from trilinear to bilinear. To this end, the 3D shape is discretized by means of a soup of elastic triangular finite elements where we apply a force balance equation. This equation is solved using modal analysis via a simple eigenvalue problem to obtain a shape basis that encodes the modes of deformation. Even though this strategy can be applied in a wide variety of scenarios, when the observations are denser, the solution can become prohibitive in terms of computational load. We avoid this limitation by proposing two efficient coarse-to-fine approaches that allow us to easily deal with dense 3D surfaces. This results in a scalable solution that estimates a small number of parameters per frame and could potentially run in real time. We show results on both synthetic and real videos with ground truth 3D data, while robustly dealing with artifacts such as noise and missing data.Peer ReviewedPostprint (author's final draft