204 research outputs found
Semantically Guided Depth Upsampling
We present a novel method for accurate and efficient up- sampling of sparse
depth data, guided by high-resolution imagery. Our approach goes beyond the use
of intensity cues only and additionally exploits object boundary cues through
structured edge detection and semantic scene labeling for guidance. Both cues
are combined within a geodesic distance measure that allows for
boundary-preserving depth in- terpolation while utilizing local context. We
model the observed scene structure by locally planar elements and formulate the
upsampling task as a global energy minimization problem. Our method determines
glob- ally consistent solutions and preserves fine details and sharp depth
bound- aries. In our experiments on several public datasets at different levels
of application, we demonstrate superior performance of our approach over the
state-of-the-art, even for very sparse measurements.Comment: German Conference on Pattern Recognition 2016 (Oral
SceneFlowFields: Dense Interpolation of Sparse Scene Flow Correspondences
While most scene flow methods use either variational optimization or a strong
rigid motion assumption, we show for the first time that scene flow can also be
estimated by dense interpolation of sparse matches. To this end, we find sparse
matches across two stereo image pairs that are detected without any prior
regularization and perform dense interpolation preserving geometric and motion
boundaries by using edge information. A few iterations of variational energy
minimization are performed to refine our results, which are thoroughly
evaluated on the KITTI benchmark and additionally compared to state-of-the-art
on MPI Sintel. For application in an automotive context, we further show that
an optional ego-motion model helps to boost performance and blends smoothly
into our approach to produce a segmentation of the scene into static and
dynamic parts.Comment: IEEE Winter Conference on Applications of Computer Vision (WACV),
201
Non-Convex and Geometric Methods for Tomography and Label Learning
Data labeling is a fundamental problem of mathematical data analysis in which each data point is assigned exactly one single label (prototype) from a finite predefined set. In this thesis we study two challenging extensions, where either the input data cannot be observed directly or prototypes are not available beforehand.
The main application of the first setting is discrete tomography. We propose several non-convex variational as well as smooth geometric approaches to joint image label assignment and reconstruction from indirect measurements with known prototypes. In particular, we consider spatial regularization of assignments, based on the KL-divergence, which takes into account the smooth geometry of discrete probability distributions endowed with the Fisher-Rao (information) metric, i.e. the assignment manifold. Finally, the geometric point of view leads to a smooth flow evolving on a Riemannian submanifold including the tomographic projection constraints directly into the geometry of assignments. Furthermore we investigate corresponding implicit numerical schemes which amount to solving a sequence of convex problems.
Likewise, for the second setting, when the prototypes are absent, we introduce and study a smooth dynamical system for unsupervised data labeling which evolves by geometric integration on the assignment manifold. Rigorously abstracting from ``data-label'' to ``data-data'' decisions leads to interpretable low-rank data representations, which themselves are parameterized by label assignments. The resulting self-assignment flow simultaneously performs learning of latent prototypes in the very same framework while they are used for inference. Moreover, a single parameter, the scale of regularization in terms of spatial context, drives the entire process. By smooth geodesic interpolation between different normalizations of self-assignment matrices on the positive definite matrix manifold, a one-parameter family of self-assignment flows is defined. Accordingly, the proposed approach can be characterized from different viewpoints such as discrete optimal transport, normalized spectral cuts and combinatorial optimization by completely positive factorizations, each with additional built-in spatial regularization
Surface Comparison with Mass Transportation
We use mass-transportation as a tool to compare surfaces (2-manifolds). In
particular, we determine the "similarity" of two given surfaces by solving a
mass-transportation problem between their conformal densities. This mass
transportation problem differs from the standard case in that we require the
solution to be invariant under global M\"obius transformations. Our approach
provides a constructive way of defining a metric in the abstract space of
simply-connected smooth surfaces with boundary (i.e. surfaces of disk-type);
this metric can also be used to define meaningful intrinsic distances between
pairs of "patches" in the two surfaces, which allows automatic alignment of the
surfaces. We provide numerical experiments on "real-life" surfaces to
demonstrate possible applications in natural sciences
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