Procrustean Normal Distribution for Non-rigid Structure from Motion

Lee, Minsik; Cho, Jungchan; Choi, Chong‐Ho; Oh, Songhwai

doi:10.1109/cvpr.2013.169

Cited by 74 publications

(19 citation statements)

References 13 publications

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“…In order to be consistent with the comparisons, we changed the Frobenius norm in Eq. (13) to the L2-norm, as is used in [21]. It can be seen that our errors decrease steadily as the per-camera separation and the camera speed increase, which leads to more robust triangulation of trajectories.…”

Section: Results and Experimentsmentioning

confidence: 83%

“…We varied the per-frame camera separation for our algorithm between 3 o and 8 o , simulating different camera speeds. In Table 2 we compare our error to three state-of-the-art techniques for NRSfM: CSF [16], SPM [12] and EM-PND [21]. In order to be consistent with the comparisons, we changed the Frobenius norm in Eq.…”

Section: Results and Experimentsmentioning

confidence: 88%

“…There is less distortion on the arms in our result. [21]. Green cells are marked as the ones with the lowest error, and blue cells with the second lowest error.…”

Section: Resultsmentioning

confidence: 99%

See 2 more Smart Citations

Reconstruction of Articulated Objects from a Moving Camera

Yücer

Wang

Sorkine-Hornung

et al. 2015

2015 IEEE International Conference on Computer Vision Workshop (ICCVW)

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Many scenes that we would like to reconstruct contain articulated objects, and are often captured by only a single, non-fixed camera. Existing techniques for reconstructing articulated objects either require templates, which can be challenging to acquire, or have difficulties with perspective effects and missing data. In this paper, we present a novel reconstruction pipeline that first treats each feature point tracked on the object independently and incrementally imposes constraints. We make use of the idea that the unknown 3D trajectory of a point tracked in 2D should lie on a manifold that is described by the camera rays going through the tracked 2D positions. We compute an initial reconstruction by solving for latent 3D trajectories that maximize temporal smoothness on these manifolds. We then leverage these 3D estimates to automatically segment an object into piecewise rigid parts, and compute a refined shape and motion using sparse bundle adjustment. Finally, we apply kinematic constraints on automatically computed joint positions to enforce connectivity between different rigid parts, which further reduces ambiguous motion and increases reconstruction accuracy. Each step of our pipeline enforces temporal smoothness, and together results in a high quality articulated object reconstruction. We show the usefulness of our approach in both synthetic and real datasets and compare against other non-rigid reconstruction techniques.

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Section: Results and Experimentsmentioning

confidence: 83%

Section: Results and Experimentsmentioning

confidence: 88%

See 1 more Smart Citation

Reconstruction of Articulated Objects from a Moving Camera

Yücer

Wang

Sorkine-Hornung

et al. 2015

2015 IEEE International Conference on Computer Vision Workshop (ICCVW)

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show abstract

“…improved the shape basis approach through a new op timization framework [3]. Recently Lee et al [6] proposed Procrustean normal distribution to model nonrigid deforma tions. The practical limitations common to all these meth ods include the inability to handle small camera motions, short input sequences and realistic occlusions.…”

Section: Related Workmentioning

confidence: 99%

NRSfM using local rigidity

Rehan

Zaheer

Akhter

et al. 2014

IEEE Winter Conference on Applications of Computer Vision

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In this paper we show that typical nonrigid structure can often be approximated well as locally rigid sub-structures in time and space. Specifically, we assume that: I) the structure can be approximated as rigid in a short local time window and 2) some point-pairs stay relatively rigid in space, maintaining a fixed distance between them during the sequence. First, we use the triangulation constraints in rigid SjM over a sliding time window to get an initial estimate of the nonrigid 3D structure. Then we automat ically identify relatively rigid point-pairs in this structure, and use their length-constancy simultaneously with trian gulation constraints to refine the structure estimate. Lo cal factorization inherently handles small camera motion, short sequences and significant natural occlusions grace fully, performing better than nonrigid factorization meth ods. We show more stable and accurate results as compared to the state-of-the art on even short sequences starting from 15 frames only, containing camera rotations as small as 2° and up to 50% contiguous missing data.

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“…The application of the above model converts the NRSFM into a three-wire problem, which can be solved using the decomposition technology 11 or optimization strategy, implementing smooth spatial, 10 temporal, 19,20 or tight 3-D shapes. 21 The advantage of this method is that it can reduce excessive and fuzzy changes between the frames of a camera and structure.…”

Section: Related Workmentioning

confidence: 99%

Three-dimensional nonrigid reconstruction based on probability model

Wang

Shen

Huang

et al. 2020

International Journal of Advanced Robotic Systems

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Most nonrigid motions use shape-based methods to solve the problem; however, the use of discrete cosine transform trajectory-based methods to solve the nonrigid motion problem is also very prominent. The signal undergoes discrete transformation due to the transform characteristics of the discrete cosine transform. The correlation of the data is well extracted such that a better compression of data is achieved. However, it is important to select the number and sequence of discrete cosine transform trajectory basis appropriately. The error of reconstruction and operational costs will increase for a high value of K (number of trajectory basis). On the other hand, a lower value of K would lead to the exclusion of information components. This will lead to poor accuracy as the structure of the object cannot be fully represented. When the number of trajectory basis is determined, the combination form has a considerable influence on the reconstruction algorithm. This article selects an appropriate number and combination of trajectory basis by analyzing the spectrum of re-projection errors and realizes the automatic selection of trajectory basis. Then, combining with the probability framework of normal distribution of a low-order model matrix, the energy information of the high-frequency part is retained, which not only helps maintain accuracy but also improves reconstruction efficiency. The proposed method can be used to reconstruct the three-dimensional structure of sparse data under more precise prior conditions and lower computational costs.

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Procrustean Normal Distribution for Non-rigid Structure from Motion

Abstract: Non-rigid structure from motion is a fundamental problem in computer vision, which

Cited by 74 publications

References 13 publications

Reconstruction of Articulated Objects from a Moving Camera

Reconstruction of Articulated Objects from a Moving Camera

NRSfM using local rigidity

Three-dimensional nonrigid reconstruction based on probability model

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