1,130 research outputs found
Regularized pointwise map recovery from functional correspondence
The concept of using functional maps for representing dense correspondences between deformable shapes has proven to be extremely effective in many applications. However, despite the impact of this framework, the problem of recovering the point-to-point correspondence from a given functional map has received surprisingly little interest. In this paper, we analyse the aforementioned problem and propose a novel method for reconstructing pointwise correspondences from a given functional map. The proposed algorithm phrases the matching problem as a regularized alignment problem of the spectral embeddings of the two shapes. Opposed to established methods, our approach does not require the input shapes to be nearly-isometric, and easily extends to recovering the point-to-point correspondence in part-to-whole shape matching problems. Our numerical experiments demonstrate that the proposed approach leads to a significant improvement in accuracy in several challenging cases
Point-wise Map Recovery and Refinement from Functional Correspondence
Since their introduction in the shape analysis community, functional maps
have met with considerable success due to their ability to compactly represent
dense correspondences between deformable shapes, with applications ranging from
shape matching and image segmentation, to exploration of large shape
collections. Despite the numerous advantages of such representation, however,
the problem of converting a given functional map back to a point-to-point map
has received a surprisingly limited interest. In this paper we analyze the
general problem of point-wise map recovery from arbitrary functional maps. In
doing so, we rule out many of the assumptions required by the currently
established approach -- most notably, the limiting requirement of the input
shapes being nearly-isometric. We devise an efficient recovery process based on
a simple probabilistic model. Experiments confirm that this approach achieves
remarkable accuracy improvements in very challenging cases
Rigid and Articulated Point Registration with Expectation Conditional Maximization
This paper addresses the issue of matching rigid and articulated shapes through probabilistic point registration. The problem is recast into a missing data framework where unknown correspondences are handled via mixture models. Adopting a maximum likelihood principle, we introduce an innovative EM-like algorithm, namely the Expectation Conditional Maximization for Point Registration (ECMPR) algorithm. The algorithm allows the use of general covariance matrices for the mixture model components and improves over the isotropic covariance case. We analyse in detail the associated consequences in terms of estimation of the registration parameters, and we propose an optimal method for estimating the rotational and translational parameters based on semi-definite positive relaxation. We extend rigid registration to articulated registration. Robustness is ensured by detecting and rejecting outliers through the addition of a uniform component to the Gaussian mixture model at hand. We provide an in-depth analysis of our method and we compare it both theoretically and experimentally with other robust methods for point registration
GASP : Geometric Association with Surface Patches
A fundamental challenge to sensory processing tasks in perception and
robotics is the problem of obtaining data associations across views. We present
a robust solution for ascertaining potentially dense surface patch (superpixel)
associations, requiring just range information. Our approach involves
decomposition of a view into regularized surface patches. We represent them as
sequences expressing geometry invariantly over their superpixel neighborhoods,
as uniquely consistent partial orderings. We match these representations
through an optimal sequence comparison metric based on the Damerau-Levenshtein
distance - enabling robust association with quadratic complexity (in contrast
to hitherto employed joint matching formulations which are NP-complete). The
approach is able to perform under wide baselines, heavy rotations, partial
overlaps, significant occlusions and sensor noise.
The technique does not require any priors -- motion or otherwise, and does
not make restrictive assumptions on scene structure and sensor movement. It
does not require appearance -- is hence more widely applicable than appearance
reliant methods, and invulnerable to related ambiguities such as textureless or
aliased content. We present promising qualitative and quantitative results
under diverse settings, along with comparatives with popular approaches based
on range as well as RGB-D data.Comment: International Conference on 3D Vision, 201
Multiframe Scene Flow with Piecewise Rigid Motion
We introduce a novel multiframe scene flow approach that jointly optimizes
the consistency of the patch appearances and their local rigid motions from
RGB-D image sequences. In contrast to the competing methods, we take advantage
of an oversegmentation of the reference frame and robust optimization
techniques. We formulate scene flow recovery as a global non-linear least
squares problem which is iteratively solved by a damped Gauss-Newton approach.
As a result, we obtain a qualitatively new level of accuracy in RGB-D based
scene flow estimation which can potentially run in real-time. Our method can
handle challenging cases with rigid, piecewise rigid, articulated and moderate
non-rigid motion, and does not rely on prior knowledge about the types of
motions and deformations. Extensive experiments on synthetic and real data show
that our method outperforms state-of-the-art.Comment: International Conference on 3D Vision (3DV), Qingdao, China, October
201
Multiframe Scene Flow with Piecewise Rigid Motion
We introduce a novel multiframe scene flow approach that jointly optimizes
the consistency of the patch appearances and their local rigid motions from
RGB-D image sequences. In contrast to the competing methods, we take advantage
of an oversegmentation of the reference frame and robust optimization
techniques. We formulate scene flow recovery as a global non-linear least
squares problem which is iteratively solved by a damped Gauss-Newton approach.
As a result, we obtain a qualitatively new level of accuracy in RGB-D based
scene flow estimation which can potentially run in real-time. Our method can
handle challenging cases with rigid, piecewise rigid, articulated and moderate
non-rigid motion, and does not rely on prior knowledge about the types of
motions and deformations. Extensive experiments on synthetic and real data show
that our method outperforms state-of-the-art.Comment: International Conference on 3D Vision (3DV), Qingdao, China, October
201
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