arXiv subjects

Suryansh Kumar

Publications and source records attributed to Suryansh Kumar.

42 records · Page 3Linked to original sources

arXiv2019

Jumping Manifolds: Geometry Aware Dense Non-Rigid Structure from Motion

Given dense image feature correspondences of a non-rigidly moving object across multiple frames, this paper proposes an algorithm to estimate its 3D shape for each frame. To solve this problem accurately, the recent state-of-the-art algorithm reduces this task to set of local linear subspace reconstruction and clustering problem using Grassmann manifold representation \cite{kumar2018scalable}. Unfortunately, their method missed on some of the critical issues associated with the modeling of surface deformations, for e.g., the dependence of a local surface deformation on its neighbors. Furthermore, their representation to group high dimensional data points inevitably introduce the drawbacks of categorizing samples on the high-dimensional Grassmann manifold \cite{huang2015projection, harandi2014manifold}. Hence, to deal with such limitations with \cite{kumar2018scalable}, we propose an algorithm that jointly exploits the benefit of high-dimensional Grassmann manifold to perform reconstruction, and its equivalent lower-dimensional representation to infer suitable clusters. To accomplish this, we project each Grassmannians onto a lower-dimensional Grassmann manifold which preserves and respects the deformation of the structure w.r.t its neighbors. These Grassmann points in the lower-dimension then act as a representative for the selection of high-dimensional Grassmann samples to perform each local reconstruction. In practice, our algorithm provides a geometrically efficient way to solve dense NRSfM by switching between manifolds based on its benefit and usage. Experimental results show that the proposed algorithm is very effective in handling noise with reconstruction accuracy as good as or better than the competing methods.

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arXiv2019

Dense Depth Estimation of a Complex Dynamic Scene without Explicit 3D Motion Estimation

Recent geometric methods need reliable estimates of 3D motion parameters to procure accurate dense depth map of a complex dynamic scene from monocular images \cite{kumar2017monocular, ranftl2016dense}. Generally, to estimate \textbf{precise} measurements of relative 3D motion parameters and to validate its accuracy using image data is a challenging task. In this work, we propose an alternative approach that circumvents the 3D motion estimation requirement to obtain a dense depth map of a dynamic scene. Given per-pixel optical flow correspondences between two consecutive frames and, the sparse depth prior for the reference frame, we show that, we can effectively recover the dense depth map for the successive frames without solving for 3D motion parameters. Our method assumes a piece-wise planar model of a dynamic scene, which undergoes rigid transformation locally, and as-rigid-as-possible transformation globally between two successive frames. Under our assumption, we can avoid the explicit estimation of 3D rotation and translation to estimate scene depth. In essence, our formulation provides an unconventional way to think and recover the dense depth map of a complex dynamic scene which is incremental and motion free in nature. Our proposed method does not make object level or any other high-level prior assumption about the dynamic scene, as a result, it is applicable to a wide range of scenarios. Experimental results on the benchmarks dataset show the competence of our approach for multiple frames.

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arXiv2018

Scalable Dense Non-rigid Structure-from-Motion: A Grassmannian Perspective

This paper addresses the task of dense non-rigid structure-from-motion (NRSfM) using multiple images. State-of-the-art methods to this problem are often hurdled by scalability, expensive computations, and noisy measurements. Further, recent methods to NRSfM usually either assume a small number of sparse feature points or ignore local non-linearities of shape deformations, and thus cannot reliably model complex non-rigid deformations. To address these issues, in this paper, we propose a new approach for dense NRSfM by modeling the problem on a Grassmann manifold. Specifically, we assume the complex non-rigid deformations lie on a union of local linear subspaces both spatially and temporally. This naturally allows for a compact representation of the complex non-rigid deformation over frames. We provide experimental results on several synthetic and real benchmark datasets. The procured results clearly demonstrate that our method, apart from being scalable and more accurate than state-of-the-art methods, is also more robust to noise and generalizes to highly non-linear deformations.

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arXiv2017

Monocular Dense 3D Reconstruction of a Complex Dynamic Scene from Two Perspective Frames

This paper proposes a new approach for monocular dense 3D reconstruction of a complex dynamic scene from two perspective frames. By applying superpixel over-segmentation to the image, we model a generically dynamic (hence non-rigid) scene with a piecewise planar and rigid approximation. In this way, we reduce the dynamic reconstruction problem to a "3D jigsaw puzzle" problem which takes pieces from an unorganized "soup of superpixels". We show that our method provides an effective solution to the inherent relative scale ambiguity in structure-from-motion. Since our method does not assume a template prior, or per-object segmentation, or knowledge about the rigidity of the dynamic scene, it is applicable to a wide range of scenarios. Extensive experiments on both synthetic and real monocular sequences demonstrate the superiority of our method compared with the state-of-the-art methods.

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arXiv2017

Spatial-Temporal Union of Subspaces for Multi-body Non-rigid Structure-from-Motion

Non-rigid structure-from-motion (NRSfM) has so far been mostly studied for recovering 3D structure of a single non-rigid/deforming object. To handle the real world challenging multiple deforming objects scenarios, existing methods either pre-segment different objects in the scene or treat multiple non-rigid objects as a whole to obtain the 3D non-rigid reconstruction. However, these methods fail to exploit the inherent structure in the problem as the solution of segmentation and the solution of reconstruction could not benefit each other. In this paper, we propose a unified framework to jointly segment and reconstruct multiple non-rigid objects. To compactly represent complex multi-body non-rigid scenes, we propose to exploit the structure of the scenes along both temporal direction and spatial direction, thus achieving a spatio-temporal representation. Specifically, we represent the 3D non-rigid deformations as lying in a union of subspaces along the temporal direction and represent the 3D trajectories as lying in the union of subspaces along the spatial direction. This spatio-temporal representation not only provides competitive 3D reconstruction but also outputs robust segmentation of multiple non-rigid objects. The resultant optimization problem is solved efficiently using the Alternating Direction Method of Multipliers (ADMM). Extensive experimental results on both synthetic and real multi-body NRSfM datasets demonstrate the superior performance of our proposed framework compared with the state-of-the-art methods.

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arXiv2016

Multi-body Non-rigid Structure-from-Motion

Conventional structure-from-motion (SFM) research is primarily concerned with the 3D reconstruction of a single, rigidly moving object seen by a static camera, or a static and rigid scene observed by a moving camera --in both cases there are only one relative rigid motion involved. Recent progress have extended SFM to the areas of {multi-body SFM} (where there are {multiple rigid} relative motions in the scene), as well as {non-rigid SFM} (where there is a single non-rigid, deformable object or scene). Along this line of thinking, there is apparently a missing gap of "multi-body non-rigid SFM", in which the task would be to jointly reconstruct and segment multiple 3D structures of the multiple, non-rigid objects or deformable scenes from images. Such a multi-body non-rigid scenario is common in reality (e.g. two persons shaking hands, multi-person social event), and how to solve it represents a natural {next-step} in SFM research. By leveraging recent results of subspace clustering, this paper proposes, for the first time, an effective framework for multi-body NRSFM, which simultaneously reconstructs and segments each 3D trajectory into their respective low-dimensional subspace. Under our formulation, 3D trajectories for each non-rigid structure can be well approximated with a sparse affine combination of other 3D trajectories from the same structure (self-expressiveness). We solve the resultant optimization with the alternating direction method of multipliers (ADMM). We demonstrate the efficacy of the proposed framework through extensive experiments on both synthetic and real data sequences. Our method clearly outperforms other alternative methods, such as first clustering the 2D feature tracks to groups and then doing non-rigid reconstruction in each group or first conducting 3D reconstruction by using single subspace assumption and then clustering the 3D trajectories into groups.

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