44,066 research outputs found
Data complexity measured by principal graphs
How to measure the complexity of a finite set of vectors embedded in a
multidimensional space? This is a non-trivial question which can be approached
in many different ways. Here we suggest a set of data complexity measures using
universal approximators, principal cubic complexes. Principal cubic complexes
generalise the notion of principal manifolds for datasets with non-trivial
topologies. The type of the principal cubic complex is determined by its
dimension and a grammar of elementary graph transformations. The simplest
grammar produces principal trees.
We introduce three natural types of data complexity: 1) geometric (deviation
of the data's approximator from some "idealized" configuration, such as
deviation from harmonicity); 2) structural (how many elements of a principal
graph are needed to approximate the data), and 3) construction complexity (how
many applications of elementary graph transformations are needed to construct
the principal object starting from the simplest one).
We compute these measures for several simulated and real-life data
distributions and show them in the "accuracy-complexity" plots, helping to
optimize the accuracy/complexity ratio. We discuss various issues connected
with measuring data complexity. Software for computing data complexity measures
from principal cubic complexes is provided as well.Comment: Computers and Mathematics with Applications, in pres
3-D Hand Pose Estimation from Kinect's Point Cloud Using Appearance Matching
We present a novel appearance-based approach for pose estimation of a human
hand using the point clouds provided by the low-cost Microsoft Kinect sensor.
Both the free-hand case, in which the hand is isolated from the surrounding
environment, and the hand-object case, in which the different types of
interactions are classified, have been considered. The hand-object case is
clearly the most challenging task having to deal with multiple tracks. The
approach proposed here belongs to the class of partial pose estimation where
the estimated pose in a frame is used for the initialization of the next one.
The pose estimation is obtained by applying a modified version of the Iterative
Closest Point (ICP) algorithm to synthetic models to obtain the rigid
transformation that aligns each model with respect to the input data. The
proposed framework uses a "pure" point cloud as provided by the Kinect sensor
without any other information such as RGB values or normal vector components.
For this reason, the proposed method can also be applied to data obtained from
other types of depth sensor, or RGB-D camera
Segmentation of Fault Networks Determined from Spatial Clustering of Earthquakes
We present a new method of data clustering applied to earthquake catalogs,
with the goal of reconstructing the seismically active part of fault networks.
We first use an original method to separate clustered events from uncorrelated
seismicity using the distribution of volumes of tetrahedra defined by closest
neighbor events in the original and randomized seismic catalogs. The spatial
disorder of the complex geometry of fault networks is then taken into account
by defining faults as probabilistic anisotropic kernels, whose structures are
motivated by properties of discontinuous tectonic deformation and previous
empirical observations of the geometry of faults and of earthquake clusters at
many spatial and temporal scales. Combining this a priori knowledge with
information theoretical arguments, we propose the Gaussian mixture approach
implemented in an Expectation-Maximization (EM) procedure. A cross-validation
scheme is then used and allows the determination of the number of kernels that
should be used to provide an optimal data clustering of the catalog. This
three-steps approach is applied to a high quality relocated catalog of the
seismicity following the 1986 Mount Lewis () event in California and
reveals that events cluster along planar patches of about 2 km, i.e.
comparable to the size of the main event. The finite thickness of those
clusters (about 290 m) suggests that events do not occur on well-defined
euclidean fault core surfaces, but rather that the damage zone surrounding
faults may be seismically active at depth. Finally, we propose a connection
between our methodology and multi-scale spatial analysis, based on the
derivation of spatial fractal dimension of about 1.8 for the set of hypocenters
in the Mnt Lewis area, consistent with recent observations on relocated
catalogs
A Few Photons Among Many: Unmixing Signal and Noise for Photon-Efficient Active Imaging
Conventional LIDAR systems require hundreds or thousands of photon detections
to form accurate depth and reflectivity images. Recent photon-efficient
computational imaging methods are remarkably effective with only 1.0 to 3.0
detected photons per pixel, but they are not demonstrated at
signal-to-background ratio (SBR) below 1.0 because their imaging accuracies
degrade significantly in the presence of high background noise. We introduce a
new approach to depth and reflectivity estimation that focuses on unmixing
contributions from signal and noise sources. At each pixel in an image,
short-duration range gates are adaptively determined and applied to remove
detections likely to be due to noise. For pixels with too few detections to
perform this censoring accurately, we borrow data from neighboring pixels to
improve depth estimates, where the neighborhood formation is also adaptive to
scene content. Algorithm performance is demonstrated on experimental data at
varying levels of noise. Results show improved performance of both reflectivity
and depth estimates over state-of-the-art methods, especially at low
signal-to-background ratios. In particular, accurate imaging is demonstrated
with SBR as low as 0.04. This validation of a photon-efficient, noise-tolerant
method demonstrates the viability of rapid, long-range, and low-power LIDAR
imaging
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