70 research outputs found
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
Analysis of surface parametrizations for modern photometric stereo modeling
Tridimensional shape recovery based on Photometric Stereo (PS) recently received a strong improvement due to new mathematical models based on partial differential irradiance equation ratios. This modern approach to PS faces more realistic physical effects among which light attenuation and radial light propagation from a point light source. Since the approximation of the surface is performed with single step method, accurate reconstruction is prevented by sensitiveness to noise. In this paper we analyse a well-known parametrization of the tridimensional surface extending it on any auxiliary convex projection functions. Experiments on synthetic data show preliminary results where more accurate reconstruction can be achieved using more suitable parametrization specially in case of noisy input images
Learning shape correspondence with anisotropic convolutional neural networks
Establishing correspondence between shapes is a fundamental problem in
geometry processing, arising in a wide variety of applications. The problem is
especially difficult in the setting of non-isometric deformations, as well as
in the presence of topological noise and missing parts, mainly due to the
limited capability to model such deformations axiomatically. Several recent
works showed that invariance to complex shape transformations can be learned
from examples. In this paper, we introduce an intrinsic convolutional neural
network architecture based on anisotropic diffusion kernels, which we term
Anisotropic Convolutional Neural Network (ACNN). In our construction, we
generalize convolutions to non-Euclidean domains by constructing a set of
oriented anisotropic diffusion kernels, creating in this way a local intrinsic
polar representation of the data (`patch'), which is then correlated with a
filter. Several cascades of such filters, linear, and non-linear operators are
stacked to form a deep neural network whose parameters are learned by
minimizing a task-specific cost. We use ACNNs to effectively learn intrinsic
dense correspondences between deformable shapes in very challenging settings,
achieving state-of-the-art results on some of the most difficult recent
correspondence benchmarks
Nonlinear Spectral Geometry Processing via the TV Transform
We introduce a novel computational framework for digital geometry processing,
based upon the derivation of a nonlinear operator associated to the total
variation functional. Such operator admits a generalized notion of spectral
decomposition, yielding a sparse multiscale representation akin to
Laplacian-based methods, while at the same time avoiding undesirable
over-smoothing effects typical of such techniques. Our approach entails
accurate, detail-preserving decomposition and manipulation of 3D shape geometry
while taking an especially intuitive form: non-local semantic details are well
separated into different bands, which can then be filtered and re-synthesized
with a straightforward linear step. Our computational framework is flexible,
can be applied to a variety of signals, and is easily adapted to different
geometry representations, including triangle meshes and point clouds. We
showcase our method throughout multiple applications in graphics, ranging from
surface and signal denoising to detail transfer and cubic stylization.Comment: 16 pages, 20 figure
Optimal intrinsic descriptors for non-rigid shape analysis
We propose novel point descriptors for 3D shapes with the potential to match two shapes representing the same object undergoing natural deformations. These deformations are more general than the often assumed isometries, and we use labeled training data to learn optimal descriptors for such cases. Furthermore, instead of explicitly defining the descriptor, we introduce new Mercer kernels, for which we formally show that their corresponding feature space mapping is a generalization of either the Heat Kernel Signature or the Wave Kernel Signature. I.e. the proposed descriptors are guaranteed to be at least as precise as any Heat Kernel Signature or Wave Kernel Signature of any parameterisation. In experiments, we show that our implicitly defined, infinite-dimensional descriptors can better deal with non-isometric deformations than state-of-the-art methods
Deep Functional Maps: Structured Prediction for Dense Shape Correspondence
We introduce a new framework for learning dense correspondence between
deformable 3D shapes. Existing learning based approaches model shape
correspondence as a labelling problem, where each point of a query shape
receives a label identifying a point on some reference domain; the
correspondence is then constructed a posteriori by composing the label
predictions of two input shapes. We propose a paradigm shift and design a
structured prediction model in the space of functional maps, linear operators
that provide a compact representation of the correspondence. We model the
learning process via a deep residual network which takes dense descriptor
fields defined on two shapes as input, and outputs a soft map between the two
given objects. The resulting correspondence is shown to be accurate on several
challenging benchmarks comprising multiple categories, synthetic models, real
scans with acquisition artifacts, topological noise, and partiality.Comment: Accepted for publication at ICCV 201
- …