522 research outputs found
A Low-Dimensional Representation for Robust Partial Isometric Correspondences Computation
Intrinsic isometric shape matching has become the standard approach for pose
invariant correspondence estimation among deformable shapes. Most existing
approaches assume global consistency, i.e., the metric structure of the whole
manifold must not change significantly. While global isometric matching is well
understood, only a few heuristic solutions are known for partial matching.
Partial matching is particularly important for robustness to topological noise
(incomplete data and contacts), which is a common problem in real-world 3D
scanner data. In this paper, we introduce a new approach to partial, intrinsic
isometric matching. Our method is based on the observation that isometries are
fully determined by purely local information: a map of a single point and its
tangent space fixes an isometry for both global and the partial maps. From this
idea, we develop a new representation for partial isometric maps based on
equivalence classes of correspondences between pairs of points and their
tangent spaces. From this, we derive a local propagation algorithm that find
such mappings efficiently. In contrast to previous heuristics based on RANSAC
or expectation maximization, our method is based on a simple and sound
theoretical model and fully deterministic. We apply our approach to register
partial point clouds and compare it to the state-of-the-art methods, where we
obtain significant improvements over global methods for real-world data and
stronger guarantees than previous heuristic partial matching algorithms.Comment: 17 pages, 12 figure
Geometric modeling of non-rigid 3D shapes : theory and application to object recognition.
One of the major goals of computer vision is the development of flexible and efficient methods for shape representation. This is true, especially for non-rigid 3D shapes where a great variety of shapes are produced as a result of deformations of a non-rigid object. Modeling these non-rigid shapes is a very challenging problem. Being able to analyze the properties of such shapes and describe their behavior is the key issue in research. Also, considering photometric features can play an important role in many shape analysis applications, such as shape matching and correspondence because it contains rich information about the visual appearance of real objects. This new information (contained in photometric features) and its important applications add another, new dimension to the problem\u27s difficulty. Two main approaches have been adopted in the literature for shape modeling for the matching and retrieval problem, local and global approaches. Local matching is performed between sparse points or regions of the shape, while the global shape approaches similarity is measured among entire models. These methods have an underlying assumption that shapes are rigidly transformed. And Most descriptors proposed so far are confined to shape, that is, they analyze only geometric and/or topological properties of 3D models. A shape descriptor or model should be isometry invariant, scale invariant, be able to capture the fine details of the shape, computationally efficient, and have many other good properties. A shape descriptor or model is needed. This shape descriptor should be: able to deal with the non-rigid shape deformation, able to handle the scale variation problem with less sensitivity to noise, able to match shapes related to the same class even if these shapes have missing parts, and able to encode both the photometric, and geometric information in one descriptor. This dissertation will address the problem of 3D non-rigid shape representation and textured 3D non-rigid shapes based on local features. Two approaches will be proposed for non-rigid shape matching and retrieval based on Heat Kernel (HK), and Scale-Invariant Heat Kernel (SI-HK) and one approach for modeling textured 3D non-rigid shapes based on scale-invariant Weighted Heat Kernel Signature (WHKS). For the first approach, the Laplace-Beltrami eigenfunctions is used to detect a small number of critical points on the shape surface. Then a shape descriptor is formed based on the heat kernels at the detected critical points for different scales. Sparse representation is used to reduce the dimensionality of the calculated descriptor. The proposed descriptor is used for classification via the Collaborative Representation-based Classification with a Regularized Least Square (CRC-RLS) algorithm. The experimental results have shown that the proposed descriptor can achieve state-of-the-art results on two benchmark data sets. For the second approach, an improved method to introduce scale-invariance has been also proposed to avoid noise-sensitive operations in the original transformation method. Then a new 3D shape descriptor is formed based on the histograms of the scale-invariant HK for a number of critical points on the shape at different time scales. A Collaborative Classification (CC) scheme is then employed for object classification. The experimental results have shown that the proposed descriptor can achieve high performance on the two benchmark data sets. An important observation from the experiments is that the proposed approach is more able to handle data under several distortion scenarios (noise, shot-noise, scale, and under missing parts) than the well-known approaches. For modeling textured 3D non-rigid shapes, this dissertation introduces, for the first time, a mathematical framework for the diffusion geometry on textured shapes. This dissertation presents an approach for shape matching and retrieval based on a weighted heat kernel signature. It shows how to include photometric information as a weight over the shape manifold, and it also propose a novel formulation for heat diffusion over weighted manifolds. Then this dissertation presents a new discretization method for the weighted heat kernel induced by the linear FEM weights. Finally, the weighted heat kernel signature is used as a shape descriptor. The proposed descriptor encodes both the photometric, and geometric information based on the solution of one equation. Finally, this dissertation proposes an approach for 3D face recognition based on the front contours of heat propagation over the face surface. The front contours are extracted automatically as heat is propagating starting from a detected set of landmarks. The propagation contours are used to successfully discriminate the various faces. The proposed approach is evaluated on the largest publicly available database of 3D facial images and successfully compared to the state-of-the-art approaches in the literature. This work can be extended to the problem of dense correspondence between non-rigid shapes. The proposed approaches with the properties of the Laplace-Beltrami eigenfunction can be utilized for 3D mesh segmentation. Another possible application of the proposed approach is the view point selection for 3D objects by selecting the most informative views that collectively provide the most descriptive presentation of the surface
Globally minimal surfaces by continuous maximal flows
In this paper we address the computation of globally minimal curves and surfaces for image segmentation and stereo reconstruction. We present a solution, simulating a continuous maximal flow by a novel system of partial differential equations. Existing methods are either grid-biased (graph-based methods) or sub-optimal (active contours and surfaces). The solution simulates the flow of an ideal fluid with isotropic velocity constraints. Velocity constraints are defined by a metric derived from image data. An auxiliary potential function is introduced to create a system of partial differential equations. It is proven that the algorithm produces a globally maximal continuous flow at convergence, and that the globally minimal surface may be obtained trivially from the auxiliary potential. The bias of minimal surface methods toward small objects is also addressed. An efficient implementation is given for the flow simulation. The globally minimal surface algorithm is applied to segmentation in 2D and 3D as well as to stereo matching. Results in 2D agree with an existing minimal contour algorithm for planar images. Results in 3D segmentation and stereo matching demonstrate that the new algorithm is robust and free from grid bias
Proposal Flow
Finding image correspondences remains a challenging problem in the presence
of intra-class variations and large changes in scene layout.~Semantic flow
methods are designed to handle images depicting different instances of the same
object or scene category. We introduce a novel approach to semantic flow,
dubbed proposal flow, that establishes reliable correspondences using object
proposals. Unlike prevailing semantic flow approaches that operate on pixels or
regularly sampled local regions, proposal flow benefits from the
characteristics of modern object proposals, that exhibit high repeatability at
multiple scales, and can take advantage of both local and geometric consistency
constraints among proposals. We also show that proposal flow can effectively be
transformed into a conventional dense flow field. We introduce a new dataset
that can be used to evaluate both general semantic flow techniques and
region-based approaches such as proposal flow. We use this benchmark to compare
different matching algorithms, object proposals, and region features within
proposal flow, to the state of the art in semantic flow. This comparison, along
with experiments on standard datasets, demonstrates that proposal flow
significantly outperforms existing semantic flow methods in various settings
Proposal Flow: Semantic Correspondences from Object Proposals
Finding image correspondences remains a challenging problem in the presence
of intra-class variations and large changes in scene layout. Semantic flow
methods are designed to handle images depicting different instances of the same
object or scene category. We introduce a novel approach to semantic flow,
dubbed proposal flow, that establishes reliable correspondences using object
proposals. Unlike prevailing semantic flow approaches that operate on pixels or
regularly sampled local regions, proposal flow benefits from the
characteristics of modern object proposals, that exhibit high repeatability at
multiple scales, and can take advantage of both local and geometric consistency
constraints among proposals. We also show that the corresponding sparse
proposal flow can effectively be transformed into a conventional dense flow
field. We introduce two new challenging datasets that can be used to evaluate
both general semantic flow techniques and region-based approaches such as
proposal flow. We use these benchmarks to compare different matching
algorithms, object proposals, and region features within proposal flow, to the
state of the art in semantic flow. This comparison, along with experiments on
standard datasets, demonstrates that proposal flow significantly outperforms
existing semantic flow methods in various settings.Comment: arXiv admin note: text overlap with arXiv:1511.0506
Defining the Pose of any 3D Rigid Object and an Associated Distance
The pose of a rigid object is usually regarded as a rigid transformation,
described by a translation and a rotation. However, equating the pose space
with the space of rigid transformations is in general abusive, as it does not
account for objects with proper symmetries -- which are common among man-made
objects.In this article, we define pose as a distinguishable static state of an
object, and equate a pose with a set of rigid transformations. Based solely on
geometric considerations, we propose a frame-invariant metric on the space of
possible poses, valid for any physical rigid object, and requiring no arbitrary
tuning. This distance can be evaluated efficiently using a representation of
poses within an Euclidean space of at most 12 dimensions depending on the
object's symmetries. This makes it possible to efficiently perform neighborhood
queries such as radius searches or k-nearest neighbor searches within a large
set of poses using off-the-shelf methods. Pose averaging considering this
metric can similarly be performed easily, using a projection function from the
Euclidean space onto the pose space. The practical value of those theoretical
developments is illustrated with an application of pose estimation of instances
of a 3D rigid object given an input depth map, via a Mean Shift procedure
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