2,285 research outputs found
Functional maps representation on product manifolds
We consider the tasks of representing, analysing and manipulating maps between shapes. We model maps as densities over the product manifold of the input shapes; these densities can be treated as scalar functions and therefore are manipulable using the language of signal processing on manifolds. Being a manifold itself, the product space endows the set of maps with a geometry of its own, which we exploit to define map operations in the spectral domain; we also derive relationships with other existing representations (soft maps and functional maps). To apply these ideas in practice, we discretize product manifolds and their LaplaceâBeltrami operators, and we introduce localized spectral analysis of the product manifold as a novel tool for map processing. Our framework applies to maps defined between and across 2D and 3D shapes without requiring special adjustment, and it can be implemented efficiently with simple operations on sparse matrices
Non-Rigid Puzzles
Shape correspondence is a fundamental problem in computer graphics and vision, with applications in various problems including animation, texture mapping, robotic vision, medical imaging, archaeology and many more. In settings where the shapes are allowed to undergo non-rigid deformations and only partial views are available, the problem becomes very challenging. To this end, we present a non-rigid multi-part shape matching algorithm. We assume to be given a reference shape and its multiple parts undergoing a non-rigid deformation. Each of these query parts can be additionally contaminated by clutter, may overlap with other parts, and there might be missing parts or redundant ones. Our method simultaneously solves for the segmentation of the reference model, and for a dense correspondence to (subsets of) the parts. Experimental results on synthetic as well as real scans demonstrate the effectiveness of our method in dealing with this challenging matching scenario
Force platform recordings in the diagnosis of primary orthostatic tremor
Primary orthostatic tremor (OT) consists of rhythmical muscle contractions at a frequency of around 16 Hz, causing discomfort and/or unsteadiness while standing. Diagnosis has hitherto relied on recording Electromyography (EMG) from affected muscles. The main aim of this study was to see if the characteristic postural tremor in OT can be identified with force platforms. We also quantified postural sway in OT patients to assess their degree of objective unsteadiness. Finally, we investigated the time relations between bursts of activity in the various affected muscle groups. Subjects stood on a force platform with concurrent multichannel surface EMG recordings from the lower limbs. Seven patients with clinical and EMG diagnosis of OT were examined and the force platform data compared with those of 21 other neurological patients with postural tremor and eight normal controls. All OT patients had high frequency peaks in power spectra of posturography and EMG recordings (12â16 Hz). No such high frequency activity was evident in patients with Parkinson's disease, cerebellar degenerations, essential tremor or in healthy controls. Additionally, OT patients showed increased sway at low frequencies relative to normal controls, suggesting that the unsteadiness reported by OT patients is at least partly due to increased postural sway. Examination of EMG timing showed fixed patterns of muscle activation when maintaining a quiet stance within but not across OT patients. These data show a high correlation between EMG and posturography and confirm that OT may be diagnosed using short epochs of force platform recordings
Making Laplacians commute
In this paper, we construct multimodal spectral geometry by finding a pair of
closest commuting operators (CCO) to a given pair of Laplacians. The CCOs are
jointly diagonalizable and hence have the same eigenbasis. Our construction
naturally extends classical data analysis tools based on spectral geometry,
such as diffusion maps and spectral clustering. We provide several synthetic
and real examples of applications in dimensionality reduction, shape analysis,
and clustering, demonstrating that our method better captures the inherent
structure of multi-modal data
SHREC'16: partial matching of deformable shapes
Matching deformable 3D shapes under partiality transformations is a challenging problem that has received limited focus in the computer vision and graphics communities. With this benchmark, we explore and thoroughly investigate the robustness of existing matching methods in this challenging task. Participants are asked to provide a point-to-point correspondence (either sparse or dense) between deformable shapes undergoing different kinds of partiality transformations, resulting in a total of 400 matching problems to be solved for each method - making this benchmark the biggest and most challenging of its kind. Five matching algorithms were evaluated in the contest; this paper presents the details of the dataset, the adopted evaluation measures, and shows thorough comparisons among all competing methods
Naturalness and stability of the generalized Chaplygin gas in the seesaw cosmon scenario
The seesaw mechanism is conceived on the basis that a mass scale, , and
a dimensionless scale, , can be fine-tuned in order to control the dynamics
of active and sterile neutrinos through cosmon-type equations of motion: the
seesaw cosmon equations. This allows for sterile neutrinos to be a dark matter
candidate. In this scenario, the dynamical masses and energy densities of
active and sterile neutrinos can be consistently embedded into the generalized
Chaplygin gas (GCG), the unified dark sector model. In addition, dark matter
adiabatically coupled to dark energy allows for a natural decoupling of the
(active) mass varying neutrino (MaVaN) component from the dark sector. Thus
MaVaN's turn into a secondary effect. Through the scale parameters, and
, the proposed scenario allows for a convergence among three distinct
frameworks: the cosmon scenario, the seesaw mechanism for mass generation and
the GCG model. It is found that the equation of state of the perturbations is
the very one of the GCG background cosmology so that all the results from this
approach are maintained, being smoothly modified by active neutrinos.
Constrained by the seesaw relations, it is shown that the mass varying
mechanism is responsible for the stability against linear perturbations and is
indirectly related to the late time cosmological acceleration.Comment: 24 pages, 6 figure
Interference between postural control and mental task performance in patients with vestibular disorder and healthy controls
OBJECTIVES - To determine whether interference between postural control and mental task performance in patients with balance system impairment and healthy subjects is due to general capacity limitations, motor control interference, competition for spatial processing resources, or a combination of these.METHOD - Postural stability was assessed in 48 patients with vestibular disorder and 24 healthy controls while they were standing with eyes closed on (a) a stable and (b) a moving platform. Mental task performance was measured by accuracy and reaction time on mental tasks, comprising high and low load, spatial and non-spatial tasks. Interference between balancing and performing mental tasks was assessed by comparing baseline (single task) levels of sway and mental task performance with levels while concurrently balancing and carrying out mental tasks.RESULTS - As the balancing task increased in difficulty, reaction times on both low load mental tasks grew progressively longer and accuracy on both high load tasks declined in patients and controls. Postural sway was essentially unaffected by mental activity in patients and controls.CONCLUSIONS - It is unlikely that dual task interference between balancing and mental activity is due to competition for spatial processing resources, as levels of interference were similar in patients with vestibular disorder and healthy controls, and were also similar for spatial and non-spatial tasks. Moreover, the finding that accuracy declined on the high load tasks when balancing cannot be attributed to motor control interference, as no motor control processing is involved in maintaining accuracy of responses. Therefore, interference between mental activity and postural control can be attributed principally to general capacity limitations, and is hence proportional to the attentional demands of both tasks
Interacting dark energy in gravity
The field equations in gravity derived from the Palatini variational
principle and formulated in the Einstein conformal frame yield a cosmological
term which varies with time. Moreover, they break the conservation of the
energy--momentum tensor for matter, generating the interaction between matter
and dark energy. Unlike phenomenological models of interacting dark energy,
gravity derives such an interaction from a covariant Lagrangian which is
a function of a relativistically invariant quantity (the curvature scalar ).
We derive the expressions for the quantities describing this interaction in
terms of an arbitrary function , and examine how the simplest
phenomenological models of a variable cosmological constant are related to
gravity. Particularly, we show that for a flat,
homogeneous and isotropic, pressureless universe. For the Lagrangian of form
, which is the simplest way of introducing current cosmic acceleration
in gravity, the predicted matter--dark energy interaction rate changes
significantly in time, and its current value is relatively weak (on the order
of 1% of ), in agreement with astronomical observations.Comment: 8 pages; published versio
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