Piecewise Quadratic Reconstruction of Non-Rigid Surfaces from Monocular Sequences

Abstract

Abstract. In this paper we present a new method for the 3D reconstruction of highly deforming surfaces (for instance a flag waving in the wind) viewed by a single orthographic camera. We assume that the surface is described by a set of feature points which are tracked along an image sequence. Most non-rigid structure from motion algorithms assume a global deformation model where a rigid mean shape component accounts for most of the motion and the deformation modes are small deviations from it. However, in the case of strongly deforming objects, the deformations become more complex and a global model will often fail to explain the intricate deformations which are no longer small linear deviations from a strong mean component. Our proposed algorithm divides the surface into overlapping patches, reconstructs each of these patches individually using a quadratic deformation model and finally registers them imposing the constraint that points shared by patches must correspond to the same 3D points in space. We show good results on challenging motion capture and real video sequences with strong deformations where global methods fail to achieve good reconstructions.

Combining Local-Physical and Global-Statistical Models for Sequential Deformable Shape from Motion

“…Recently, results from this field have significantly advanced. Stronger deformations have been tackled using piecewise models (Chhatkuli et al 2014;Fayad et al 2010;Russell et al 2011;Taylor et al 2010), even combining segmentation and reconstruction under local rigidity (Russell et al 2014), or eliminating the rank dependency by means of Procustean normal distributions (Lee et al 2013). In (Garg et al 2013), a variational approach integrating a low-rank shape model with spatial smoothness allowed per-pixel dense reconstructions.…”

“…(8) to zero, to allow the model to be split in two, Table 6 Quantitative comparison on Back sequence. Reconstruction error 3D [%] for batch methods PQ (Fayad et al 2010), CSF2 (Gotardo and Martínez 2011b), KSTA (Gotardo and Martínez 2011a), NOM (Russell et al 2011) and EM-PND (Lee et al 2013). ‡ Numbers for PQ and NOM baselines are from (Russell et al 2011).…”

“…In this case, we compare against the following batch methods: piecewise quadratic model (PQ) of Fayad et al (2010), the network of overlapping models using also quadratic GLSMM CSF2 Fig. 8 Tear sequence.…”

Soft Inextensibility Constraints for Template-Free Non-rigid Reconstruction

“…Also related to our approach are the recently introduced piecewise models [7,8,11,6]. In general, these methods can cope with sequences with stronger deformations than previous global approaches.…”

“…Points i and j are neighbours if their image distance is small in all frames. considered (piecewise planarity [7], local rigidity [8] and quadratic deformations [11,6]) and in the way the surface is divided into patches. For example in [8] each patch is a triangle formed by neighbouring points, while in [7] the surface is divided into regular rectangular patches.…”